{"id":31581,"date":"2025-07-11T14:00:04","date_gmt":"2025-07-11T14:00:04","guid":{"rendered":"https:\/\/medexperts.pro\/?p=31581"},"modified":"2025-07-11T14:23:22","modified_gmt":"2025-07-11T14:23:22","slug":"how-much-of-our-math-revealed-series-did-you-retain-try-this-quiz","status":"publish","type":"post","link":"https:\/\/medexperts.pro\/?p=31581","title":{"rendered":"How Much of Our \u2018Math, Revealed\u2019 Series Did You Retain? Try This Quiz."},"content":{"rendered":"
\n
\n

\u201cMath, Revealed<\/a>,\u201d our four-part series exploring the mathematics behind everyday objects and experiences, recently came to a smashing conclusion. One installment took a spin through \u201ctaxicab geometry<\/a>,\u201d a wacky but vital corner of mathematics in which circles aren\u2019t round and pi equals 4. Another journey began with apples and pentagrams<\/a> and led to Leonardo da Vinci, the golden ratio and ideal positioning of belly buttons. <\/p>\n

We had great fun on this adventure and hope to resume it before too long. In the meantime, here\u2019s a quiz to test what you learned and your general math knowledge. Enjoy!<\/p>\n<\/div>\n<\/div>\n

\n
\n
\n
\n html{–answer-background:#eaf2f9;–answer-text:#053e69;–answer-answered:#f7f7f7;–answer-answered-text:#656565;–unanswered-question-selected-answer-background:#053e69;–unanswered-question-selected-answer-text:#fff;–answered-question-incorrect-answer-background:#e27676;–answered-question-correct-answer-background:#95c198;–breadcrumb-button-background:#eee;–breadcrumb-active-background:#c6cfdf;–breadcrumb-complete-background:#053e69;–response-text:#777;–caption-text:#666;–default-button-background:#fff;–default-button-foreground:#053e69;–scorecard-text:#323232}@media(prefers-color-scheme:dark){html.Hybrid.NYTApp{–answer-background:var(–color-content-secondary);–answer-text:var(–color-content-inversePrimary);–answer-answered:var(–color-background-quaternary);–answer-answered-text:var(–color-content-secondary);–unanswered-question-selected-answer-background:var(–color-signal-accent);–unanswered-question-selected-answer-text:var(–color-content-primary);–answered-question-incorrect-answer-background:var(–color-signal-negative);–answered-question-correct-answer-background:var(–color-signal-positive);–breadcrumb-button-background:var(–color-background-tertiary);–breadcrumb-active-background:var(–color-background-inverseSecondary);–breadcrumb-complete-background:var(–color-content-quaternary);–response-text:var(–color-content-primary);–caption-text:var(–color-content-secondary);–default-button-background:var(–color-background-quaternary);–default-button-foreground:var(–color-stroke-primary);–scorecard-text:var(–color-content-primary)}}#interactive .interactive-leadin{font-family:nyt-franklin,Arial,helvetica,sans-serif}#interactive .interactive-leadin a{color:#326891;text-decoration:none}#interactive .interactive-leadin a:hover{outline:0;text-decoration:underline}.quiz p{margin:0 0 1rem}.quiz a{color:#326891;text-decoration:none}.quiz a:hover{outline:0;text-decoration:underline}.quiz em{font-style:italic}.quiz strong{font-weight:700}.quiz .caption,.quiz figcaption{color:#666;font-family:nyt-cheltenham-sh,georgia,times new roman,times,serif;font-style:normal;font-weight:400}.quiz .credit{color:var(–credit-text);display:inline-block;font-size:.75rem}.sortable-list-item{align-items:center;background-color:#2f84f3;border-radius:3px;box-sizing:border-box;color:#fff;cursor:grab;display:flex;gap:10px;justify-content:left;list-style:none;padding:15px 20px;touch-action:none;transition:background-color .5s;width:100%}.sortable-list-item.active-item{cursor:grabbing;touch-action:none}.sortable-list-item.active-item-hidden{opacity:0}.sortable-list-wrapper{margin-bottom:1.8rem;position:relative}.question .reveal-toggle{background-color:unset;color:#326891}.question.answered .sortable-list-item{cursor:default}.sortable-list-item .text-block p{font-family:nyt-franklin,Arial,helvetica,sans-serif;font-size:20px}.sortable-list-item.sortable-list-item–correct{background-color:rgba(38,124,48,.5)}.sortable-list-item.sortable-list-item–incorrect{background-color:hsla(0,0%,46%,.6)}@media only screen and (max-width:480px){.sortable-list-item{margin:auto;min-width:18rem;width:100%}}.draggable-grouping-question .done-button>.text-block,.list-order-question .done-button>.text-block{background-color:inherit;border:unset;color:inherit;margin-top:0}.done-button{background-color:#fff;border:1px solid #053e69;border-radius:5px;margin-top:10px}.done-button:hover{background-color:#053e69;color:#fff}.done-button .text-block:hover{background-color:unset}.draggable-grouping-question.answered .done-button,.list-order-question.answered .done-button{display:none}.done-button:hover .text-block,.draggable-grouping-question.answered .done-button .text-block,.list-order-question.answered .done-button .text-block{background-color:#053e69;color:#fff!important}.done-button:hover .text-block p,.draggable-grouping-question.answered .done-button .text-block p,.list-order-question.answered .done-button .text-block p{color:#fff}.done-button .text-block p{margin:0}.question.answered .done-button .text-block{cursor:default}.sortable-list-item .text-block p{margin:0}.summary.response{margin:10px 0 0}.draggable-grouping-question .summary.response .text-block p,.list-order-question .summary.response .text-block p{font-family:nyt-franklin,Arial,helvetica,sans-serif;font-size:1rem}.buckets-wrapper{display:grid;gap:10px;margin-top:1.6rem;transition:1s}.buckets-wrapper.even-group{gap:1.6rem;grid-template-columns:1fr 1fr}.buckets-wrapper.odd-group{gap:10px;grid-template-columns:1fr 1fr 1fr}.droppable-bucket{align-items:center;background-color:#f0f0f0;border-radius:5px;box-sizing:border-box;color:#000;display:flex;flex-direction:column;font-family:nyt-franklin,Arial,helvetica,sans-serif;font-size:1rem;gap:3px;height:12rem;justify-content:center;padding:8px;position:relative;text-align:center;width:100%}.droppable-bucket.hovered-over{border:2px solid #333;font-weight:700}.droppable-bucket.faded{opacity:.6}.droppable-bucket-label–top{font-size:.95rem;left:50%;position:absolute;top:calc(-.95rem – 1px);transform:translate(-50%);white-space:nowrap}.draggable-item-shelf{align-items:flex-start;box-sizing:border-box;display:flex;flex-direction:row;flex-wrap:wrap;gap:4px;margin-bottom:1.8rem;min-height:3.5rem;width:100%}.draggable-bucket-item{background-color:#2f84f3;border:1px solid #fff;border-radius:4px;cursor:grab;touch-action:none;transition:background-color .5s}.draggable-bucket-item.grabbing{cursor:grabbing}.draggable-bucket-item.disabled{cursor:default}.draggable-bucket-item.correct{background-color:rgba(38,124,48,.7)}.draggable-bucket-item.incorrect{background-color:rgba(169,1,17,.7)}.draggable-bucket-item .text-block p{color:#fff;font-family:nyt-franklin,Arial,helvetica,sans-serif;font-size:.9rem;margin:0;padding:.8rem .9rem}@media only screen and (max-width:650px){.draggable-item-shelf{box-sizing:border-box;gap:3px;margin:auto;min-height:6rem;width:95%}.buckets-wrapper{display:flex;flex-direction:column;gap:1.5rem!important;margin-top:1.5rem}.droppable-bucket{flex-wrap:wrap;height:7rem;width:100%}.draggable-bucket-item .text-block p{padding:.6rem .9rem}}.question-score .score-text{font-weight:700}.interactive-model canvas{height:300px!important}.interactive-model.hidden{display:none}.text-block.explanation p{font-size:.9rem;font-style:italic}.question.draggable-grouping-question,.question.list-order-question{border-bottom:1px solid #ccc;box-sizing:border-box;max-width:100%;padding-bottom:39px;padding-top:47px;position:relative}.sortable-list-item svg.drag-handle{min-width:24px}.question.draggable-grouping-question .response,.question.list-order-question .response{border-left:1px solid rgba(0,0,0,.05);padding-left:19px}@media only screen and (min-width:480px){.question.draggable-grouping-question,.question.list-order-question{box-sizing:border-box;margin-left:auto;margin-right:auto;max-width:600px}}.draggable-grouping-question .counter,.list-order-question .counter{color:#656565;font-family:nyt-imperial,georgia,times new roman,times,serif;font-size:18px;font-size:20px;font-style:normal;font-weight:400;line-height:1.625rem;line-height:1.5;margin-bottom:12px;margin-top:47px}@media only screen and (min-width:480px){.draggable-grouping-question .counter,.list-order-question .counter{display:inline-block;font-size:20px;left:-210px;line-height:1.5;padding-bottom:0;position:absolute;text-align:right;top:0;width:180px}}.fade{opacity:0;transition:opacity .8s}.fade.faded{opacity:1}.fill-in-blank{border-bottom:1px solid #000;display:inline-block;width:100px}.cascade,.one-at-a-time,.quiz{margin-top:30px}.cascade .media img,.one-at-a-time .media img,.quiz .media img{display:block;width:100%}.cascade .media .caption,.cascade .media figcaption,.one-at-a-time .media .caption,.one-at-a-time .media figcaption,.quiz .media .caption,.quiz .media figcaption{font-size:.85rem;line-height:1.15rem;margin-top:.5em}.cascade h2,.one-at-a-time h2,.quiz h2{font-size:24px;margin-bottom:1em;margin-top:2em}.cascade p,.one-at-a-time p,.quiz p{font-family:nyt-imperial,georgia,times new roman,times,serif;font-size:18px;font-style:normal;font-weight:400;line-height:1.625rem}@media only screen and (min-width:480px){.cascade p,.one-at-a-time p,.quiz p{font-size:20px;line-height:1.5}}.cascade>.media,.cascade>.video,.one-at-a-time>.media,.one-at-a-time>.video,.quiz>.media,.quiz>.video{margin-bottom:45px;margin-left:auto;margin-right:auto;max-width:1020px;width:100%}@media only screen and (min-width:480px){.cascade .conclusion,.cascade .response,.cascade>.text-block,.one-at-a-time .conclusion,.one-at-a-time .response,.one-at-a-time>.text-block,.quiz .conclusion,.quiz .response,.quiz>.text-block{box-sizing:border-box;margin-left:auto;margin-right:auto;max-width:600px}}.cascade .response,.one-at-a-time .response,.quiz .response{margin-top:2em}.cascade .conclusion>.text-block p:first-of-type,.one-at-a-time .conclusion>.text-block p:first-of-type,.quiz .conclusion>.text-block p:first-of-type{margin-top:1em}.done-button{box-sizing:border-box;display:inline-block;display:block;text-align:center}.done-button>.text-block{background-color:var(–default-button-background);border:1px solid var(–default-button-foreground);border-radius:3px;cursor:pointer;display:inline-block;margin-top:10px;padding:10px 15px;transition:all .35s ease-out;transition-property:background-color}@media only screen and (min-width:480px){.done-button>.text-block{padding:10px 15px}}.done-button>.text-block p,.response .done-button>.text-block p{color:var(–default-button-foreground);margin-bottom:0;margin-top:0}.question.unanswered .done-button>.text-block:hover{background-color:#053e69}.question.unanswered .done-button>.text-block:hover p{color:#fff}.advance-button{background-color:inherit;border:none;box-sizing:border-box;display:inline-block;display:block;margin-left:auto;margin-right:auto;text-align:center}.advance-button>.text-block:hover{background-color:#053e69}.advance-button>.text-block:hover p{color:#fff}.advance-button>.text-block{background-color:var(–default-button-background);border:1px solid var(–default-button-foreground);border-radius:3px;cursor:pointer;display:inline-block;margin-top:10px;padding:10px 15px;transition:all .35s ease-out;transition-property:background-color}@media only screen and (min-width:480px){.advance-button>.text-block{padding:10px 15px}}.advance-button>.text-block p,.response .advance-button>.text-block p{color:var(–default-button-foreground);margin-bottom:0;margin-top:0}.breadcrumb-wrapper{display:flex;flex-direction:row;gap:8px;justify-content:center;margin-top:1rem}.breadcrumb-button{background-color:var(–breadcrumb-button-background);border-radius:50%;box-sizing:border-box;cursor:pointer;font-family:nyt-franklin;font-size:14px;height:26px;position:relative;text-align:center;width:26px}.breadcrumb-button–active{background-color:var(–breadcrumb-active-background)}.breadcrumb-button–correct.breadcrumb-button–complete{background-color:#267c30}.breadcrumb-button–partial-correct.breadcrumb-button–complete{background-color:#d4ca8f}.breadcrumb-button–incorrect.breadcrumb-button–complete{background-color:#a90111}.breadcrumb-button–complete{background-color:var(–breadcrumb-complete-background);color:#fff}.breadcrumbs-button–no-index{height:12px;width:12px}.breadcrumb-button__inner-text{left:50%;position:absolute;top:50%;transform:translate(-50%,-50%)}.breadcrumb-button–disabled{cursor:default}.breadcrumb-wrapper.narrow{display:flex;flex-direction:row;gap:4px;justify-content:space-between;margin:auto;max-width:600px}.breadcrumb-wrapper.narrow .breadcrumb-button{background-position:100%;background-size:200% 100%!important;border-radius:unset;box-sizing:border-box;cursor:pointer;font-family:nyt-franklin,Arial,helvetica,sans-serif;font-size:14px;height:4px;position:relative;text-align:center;width:100%}.breadcrumb-wrapper.narrow .breadcrumb-button:first-of-type{border-radius:3px 0 0 3px!important}.breadcrumb-wrapper.narrow .breadcrumb-button:last-of-type{border-radius:0 3px 3px 0!important}.breadcrumb-wrapper.narrow .breadcrumb-button–correct.breadcrumb-button–complete{background:linear-gradient(270deg,#000 50%,#267c30 0) 0;color:hsla(0,0%,100%,.99);transition:3.2s linear}.breadcrumb-wrapper.narrow .breadcrumb-button–incorrect.breadcrumb-button–complete{background:linear-gradient(270deg,#000 50%,#a90111 0) 0;color:hsla(0,0%,100%,.99);transition:3.2s linear}.breadcrumb-wrapper.narrow .breadcrumb-button–correct.breadcrumb-button–inactive{background:#267c30!important;color:#fff!important;transition:0s linear!important}.breadcrumb-wrapper.narrow .breadcrumb-button–incorrect.breadcrumb-button–inactive{background:#a90111!important;color:#fff!important;transition:0s linear!important}.breadcrumb-wrapper.narrow .breadcrumb-button–active,.breadcrumb-wrapper.narrow .breadcrumbs-button–no-index.breadcrumb-button–active{background-color:#000!important}.breadcrumb-wrapper.narrow .breadcrumb-button–complete{background-color:#444}.clear-saved{background:var(–default-button-foreground);border-radius:4px;color:var(–default-button-background);cursor:pointer;display:inline-block;font-family:nyt-franklin,Arial,helvetica,sans-serif;font-size:15px;line-height:1.5;padding:8px 20px}.clear-saved,.clear-saved:hover{text-decoration:none}.clear-saved p{margin-bottom:0}.video{margin-bottom:.5em}.video .credit{font-size:14px}.audio{float:left;margin-right:20px}@media only screen and (min-width:480px){.audio{margin-right:25px}}.audio .track-progress{color:#656565;font-family:nyt-franklin,Arial,helvetica,sans-serif;font-size:12px;margin-top:3px}.audio .track-progress .elapsed:after{content:”\/”;padding:0 3px}.audio-control-button{background:none;border:none;box-sizing:border-box;cursor:pointer;height:35px;outline:none;padding:0;position:relative;width:35px;-webkit-tap-highlight-color:rgba(0,0,0,0);margin:0 0 0 calc(50% – 17.5px)}.audio-button-spinner{border:1px solid #6288a5;border-radius:50%;opacity:1;z-index:1}.audio-button-spinner,.audio-button-spinner span{bottom:0;box-sizing:border-box;display:block;height:35px;left:0;position:absolute;right:0;top:0;width:35px}.audio-button-spinner span{clip:rect(20px,40px,40px,0);animation:none;opacity:0}.audio-button-spinner span:after,.audio-button-spinner span:before{animation:none;border:1px solid transparent;border-radius:50%;border-top-color:#6288a5;bottom:0;box-sizing:border-box;content:””;display:block;height:35px;left:0;position:absolute;right:0;top:0;width:35px}.audio-icon{align-items:center;display:flex;height:100%;justify-content:center;width:100%}.audio-icon svg{height:35px;width:35px;fill:#6288a5;opacity:1;transform:scale(.33) translateX(5px);transform-origin:center;transition:opacity .3s ease-in;z-index:2}@media only screen and (min-width:480px){.step{box-sizing:border-box;margin-left:auto;margin-right:auto;max-width:600px}}.multiple-choice-question,.multiple-select-question{border-bottom:1px solid #ccc;padding-bottom:34px;padding-top:23px;position:relative}@media only screen and (min-width:480px){.multiple-choice-question,.multiple-select-question{padding-bottom:39px;padding-top:47px}}.multiple-choice-question p,.multiple-select-question p{font-family:nyt-imperial,georgia,times new roman,times,serif;font-size:18px;font-style:normal;font-weight:400;line-height:1.625rem;-webkit-font-smoothing:antialiased}@media only screen and (min-width:480px){.multiple-choice-question p,.multiple-select-question p{font-size:20px;line-height:1.5}}.multiple-choice-question .counter,.multiple-select-question .counter{color:#656565;font-family:nyt-imperial,georgia,times new roman,times,serif;font-size:18px;font-size:20px;font-style:normal;font-weight:400;line-height:1.625rem;line-height:1.5;margin-bottom:12px;margin-top:47px}@media only screen and (min-width:480px){.multiple-choice-question .counter,.multiple-select-question .counter{font-size:20px;line-height:1.5}}.multiple-choice-question .media,.multiple-select-question .media{margin-bottom:14px}.multiple-choice-question .media img,.multiple-select-question .media img{width:100%}.multiple-choice-question .response,.multiple-select-question .response{border-left:1px solid rgba(0,0,0,.05);padding-left:19px}.multiple-choice-question .response p,.multiple-select-question .response p{color:var(–response-text);font-family:nyt-imperial,georgia,times new roman,times,serif;font-size:18px;font-style:normal;font-weight:400;line-height:1.625rem}@media only screen and (min-width:480px){.multiple-choice-question .response p,.multiple-select-question .response p{font-size:20px;line-height:1.5}}.multiple-choice-question .done-button,.multiple-select-question .done-button{background-color:inherit;border:none;margin-left:auto;margin-right:auto;text-align:center}.multiple-choice-question .done-button.is-complete,.multiple-select-question .done-button.is-complete{display:none}.multiple-choice-question.answering .done-button,.multiple-select-question.answering .done-button{display:block}.multiple-choice-question .answer,.multiple-select-question .answer{background:var(–answer-background);border-radius:3px;color:var(–answer-text);cursor:pointer;display:block;line-height:1.25;margin-top:10px;padding:15px 20px;position:relative;text-align:left;transition:all .35s ease-out;transition-property:padding,background-color;width:100%}.multiple-choice-question .answer p,.multiple-select-question .answer p{margin-bottom:0;margin-top:0}.multiple-choice-question.answered .answer,.multiple-select-question.answered .answer{background-color:var(–answer-answered);border:none;color:var(–answer-answered-text);cursor:default}.multiple-choice-question.answered .answer.selected,.multiple-select-question.answered .answer.selected{background-color:transparent;color:var(–answer-answered-text)}.multiple-choice-question.unanswered .answer.selected,.multiple-select-question.unanswered .answer.selected{background-color:var(–unanswered-question-selected-answer-background);color:var(–unanswered-question-selected-answer-text)}.multiple-choice-question.has-correct-answers .answer,.multiple-select-question.has-correct-answers .answer{background-position:calc(100% – 20px) 20px;background-repeat:no-repeat;background-size:19px 19px}.multiple-choice-question.answered.has-correct-answers .answer.selected,.multiple-select-question.answered.has-correct-answers .answer.selected{background-color:var(–answered-question-incorrect-answer-background);background-image:url(https:\/\/static01.nyt.com\/inc\/quiz-x_light.svg);color:var(–unanswered-question-selected-answer-text)}.multiple-choice-question.answered.has-correct-answers .answer.correct,.multiple-select-question.answered.has-correct-answers .answer.correct{background-image:url(https:\/\/int.nyt.com\/assets\/adventure\/images\/quiz-check_green.svg);color:var(–answered-question-correct-answer-background)}.multiple-choice-question.answered.has-correct-answers .answer.selected.correct,.multiple-select-question.answered.has-correct-answers .answer.selected.correct{background-color:var(–answered-question-correct-answer-background);background-image:url(https:\/\/static01.nyt.com\/inc\/quiz-check_light.svg);color:var(–unanswered-question-selected-answer-text)}.multiple-choice-question.unanswered .poll-answer-graph,.multiple-select-question.unanswered .poll-answer-graph{width:0!important}.multiple-choice-question.unanswered .poll-answer-percentage,.multiple-select-question.unanswered .poll-answer-percentage{display:none}.multiple-choice-question.answered .poll-answer,.multiple-select-question.answered .poll-answer{background-color:transparent}.multiple-choice-question.answered .poll-answer.answer.selected,.multiple-select-question.answered .poll-answer.answer.selected{color:#656565}.multiple-choice-question.answered.has-correct-answers .poll-answer,.multiple-select-question.answered.has-correct-answers .poll-answer{color:#656565;padding-right:50px}.multiple-choice-question.answered.has-correct-answers .poll-answer.selected,.multiple-select-question.answered.has-correct-answers .poll-answer.selected{background-color:transparent;background-image:url(https:\/\/static01.nyt.com\/inc\/quiz-x_red.svg);color:#656565}.multiple-choice-question.answered.has-correct-answers .poll-answer.selected.correct,.multiple-select-question.answered.has-correct-answers .poll-answer.selected.correct{background-color:transparent;background-image:url(https:\/\/int.nyt.com\/assets\/adventure\/images\/quiz-check_green.svg);color:#656565}.multiple-choice-question .stats p,.multiple-select-question .stats p{color:#666;font-family:nyt-franklin,Arial,helvetica,sans-serif;font-size:14px;font-weight:500;text-align:right}@media only screen and (min-width:480px){.multiple-choice-question .counter,.multiple-select-question .counter{font-size:20px}}@media only screen and (min-width:480px)and (min-width:480px){.multiple-choice-question .counter,.multiple-select-question .counter{display:inline-block;left:-210px;padding-bottom:0;position:absolute;text-align:right;top:0;width:180px}}@media only screen and (min-width:480px){.multiple-choice-question .answer.question-unanswered:hover,.multiple-select-question .answer.question-unanswered:hover{background-color:#053e69;color:#fff}}.multiple-choice-question .freeform-answer,.multiple-select-question .freeform-answer{position:relative}.multiple-choice-question .freeform-answer .freeform-answer-input,.multiple-choice-question .freeform-answer input[type=text].freeform-answer-input,.multiple-select-question .freeform-answer .freeform-answer-input,.multiple-select-question .freeform-answer input[type=text].freeform-answer-input{font-size:18px;line-height:1.625rem;-webkit-font-smoothing:antialiased;background-color:#fff;border:1px solid #e2e2e2;border-radius:3px;box-shadow:inset 2px 3px 3px rgba(0,0,0,.07);box-sizing:border-box;display:block;font-family:nyt-franklin,Arial,helvetica,sans-serif;height:auto;margin-right:5%;padding:10px;width:100%}@media only screen and (min-width:480px){.multiple-choice-question .freeform-answer .freeform-answer-input,.multiple-choice-question .freeform-answer input[type=text].freeform-answer-input,.multiple-select-question .freeform-answer .freeform-answer-input,.multiple-select-question .freeform-answer input[type=text].freeform-answer-input{font-size:17px;line-height:1.5}}.multiple-choice-question .freeform-answer .freeform-answer-input .correct-part,.multiple-choice-question .freeform-answer input[type=text].freeform-answer-input .correct-part,.multiple-select-question .freeform-answer .freeform-answer-input .correct-part,.multiple-select-question .freeform-answer input[type=text].freeform-answer-input .correct-part{color:#95c198}.multiple-choice-question .freeform-answer.question-answered.incorrect .freeform-answer-input,.multiple-choice-question .freeform-answer.question-answered.incorrect input[type=text].freeform-answer-input,.multiple-select-question .freeform-answer.question-answered.incorrect .freeform-answer-input,.multiple-select-question .freeform-answer.question-answered.incorrect input[type=text].freeform-answer-input{border-color:#e27676;box-shadow:inset 2px 3px 3px hsla(0,65%,67%,.3)}.multiple-choice-question .freeform-answer.question-answered.correct .freeform-answer-input,.multiple-choice-question .freeform-answer.question-answered.correct input[type=text].freeform-answer-input,.multiple-select-question .freeform-answer.question-answered.correct .freeform-answer-input,.multiple-select-question .freeform-answer.question-answered.correct input[type=text].freeform-answer-input{border-color:#95c198;box-shadow:inset 2px 3px 3px rgba(149,193,152,.3)}.multiple-choice-question .freeform-answer .reset-freeform-answer,.multiple-select-question .freeform-answer .reset-freeform-answer{background-clip:padding-box;background-color:#ccc;border:none;border-radius:50%;cursor:pointer;font-family:nyt-franklin,Arial,helvetica,sans-serif;height:26px;padding:0;position:absolute;right:9px;top:12px;transition:background-color .2s ease-in;width:26px;z-index:100}.multiple-choice-question .freeform-answer .reset-freeform-answer.inactive,.multiple-select-question .freeform-answer .reset-freeform-answer.inactive{display:none}.multiple-choice-question .freeform-answer .reset-freeform-answer:hover,.multiple-select-question .freeform-answer .reset-freeform-answer:hover{background-color:#666}.multiple-choice-question .freeform-answer .reset-freeform-answer .icon,.multiple-select-question .freeform-answer .reset-freeform-answer .icon{display:block;font-style:normal;height:26px;left:0;line-height:0;position:absolute;top:0;width:26px;z-index:100}.multiple-choice-question .freeform-answer .reset-freeform-answer .icon:after,.multiple-choice-question .freeform-answer .reset-freeform-answer .icon:before,.multiple-select-question .freeform-answer .reset-freeform-answer .icon:after,.multiple-select-question .freeform-answer .reset-freeform-answer .icon:before{background-color:#fff;content:””;display:block;height:2px;left:6px;position:absolute;top:12px;width:14px}.multiple-choice-question .freeform-answer .reset-freeform-answer .icon:before,.multiple-select-question .freeform-answer .reset-freeform-answer .icon:before{transform:rotate(45deg)}.multiple-choice-question .freeform-answer .reset-freeform-answer .icon:after,.multiple-select-question .freeform-answer .reset-freeform-answer .icon:after{transform:rotate(135deg)}.multiple-choice-question .freeform-answer .complete-freeform-answer,.multiple-select-question .freeform-answer .complete-freeform-answer{box-sizing:border-box;display:inline-block}.multiple-choice-question .freeform-answer .complete-freeform-answer>.text-block,.multiple-select-question .freeform-answer .complete-freeform-answer>.text-block{background-color:var(–default-button-background);border:1px solid var(–default-button-foreground);border-radius:3px;cursor:pointer;display:inline-block;margin-top:10px;padding:10px 15px;transition:all .35s ease-out;transition-property:background-color}@media only screen and (min-width:480px){.multiple-choice-question .freeform-answer .complete-freeform-answer>.text-block,.multiple-select-question .freeform-answer .complete-freeform-answer>.text-block{padding:10px 15px}}.multiple-choice-question .freeform-answer .complete-freeform-answer>.text-block p,.multiple-select-question .freeform-answer .complete-freeform-answer>.text-block p,.response .multiple-choice-question .freeform-answer .complete-freeform-answer>.text-block p,.response .multiple-select-question .freeform-answer .complete-freeform-answer>.text-block p{color:var(–default-button-foreground);margin-bottom:0;margin-top:0}.multiple-choice-question .freeform-answer .complete-freeform-answer.active>.text-block:hover,.multiple-select-question .freeform-answer .complete-freeform-answer.active>.text-block:hover{background-color:#053e69}.multiple-choice-question .freeform-answer .complete-freeform-answer.active>.text-block:hover p,.multiple-select-question .freeform-answer .complete-freeform-answer.active>.text-block:hover p{color:#fff}@media only screen and (min-width:480px){.multiple-choice-question,.multiple-select-question{box-sizing:border-box;margin-left:auto;margin-right:auto;max-width:600px}}.scorecard{font-family:nyt-cheltenham,georgia,times new roman,times,serif;margin-top:2em}@media only screen and (min-width:480px){.scorecard{box-sizing:border-box;margin-left:auto;margin-right:auto;max-width:600px}}.scorecard .scorecard-kicker{color:#656565;display:block;font-size:20px;font-weight:400;line-height:1.5}.scorecard .scorecard-inner{color:var(–scorecard-text);font-size:18px;font-weight:700;line-height:1.66;text-align:left}.stats{margin-top:2em}@media only screen and (min-width:480px){.stats{box-sizing:border-box;margin-left:auto;margin-right:auto;max-width:600px}}.stats p{color:#666;font-family:nyt-franklin,Arial,helvetica,sans-serif;font-size:14px;font-weight:500;text-align:right}@media only screen and (min-width:480px){.scorecard .scorecard-kicker{float:left;font-size:30px;margin:7px 0 0 -210px;text-align:right;width:180px}.scorecard .scorecard-inner{font-size:36px;margin-bottom:12px}}.accordion{margin-bottom:1rem}.accordion-trigger{background-color:unset;color:#326891;display:flex;font-family:nyt-franklin,Arial,Helvetica,sans-serif;font-size:inherit;font-style:italic;font-weight:700;gap:7px;margin:10px 0;text-align:left}.accordion-content{box-sizing:border-box;max-height:0;overflow:hidden;padding-top:1rem}.accordion-content .text-block{border:1px solid #333;border-radius:3px;padding:20px}.accordion-content p{font-size:16px;line-height:1.2}.accordion-content.accordion-open{max-height:3000px}.accordion-content.accordion-closed{max-height:0}.accordion-trigger .rotate-arrow.rotated{transform:rotate(-90deg)}.question-scorecard .score-text{font-weight:700}.question-scorecard p.question-scorecard-inner{font-family:nyt-franklin,Arial,helvetica,sans-serif;font-size:1rem}.quiz-ad{text-align:center}#interactive-header #interactive-heading,.quiz .caption,.quiz .counter,.quiz .credit,.quiz blockquote,.quiz p{-webkit-font-smoothing:antialiased}#interactive-header #interactive-heading{color:var(–color-primary);font-family:nyt-cheltenham,georgia,times new roman,times,serif;font-size:2.25rem;line-height:2.5rem;max-width:600px;text-align:left}#interactive-header #interactive-heading p{text-align:left}@media screen and (min-width:1024px){#interactive-header #interactive-heading{margin-top:75px}}h1#interactive-heading{font-style:normal;font-weight:200}@media screen and (min-width:740px){#interactive-header #interactive-heading{font-size:2.75rem;line-height:3.125rem}}@media screen and (min-width:1150px){#interactive-header #interactive-heading{font-size:2.9375rem;line-height:3.4375rem}}.quiz-ad-container{background-color:#f7f7f7;border-bottom:1px solid #f3f3f3;border-top:1px solid #f3f3f3;margin:37px auto;padding-bottom:30px;padding-top:12px;text-align:center}.quiz-ad-container:before{color:#727272;content:”Advertisement”;display:block;font-family:nyt-franklin;font-size:10px;font-weight:500;letter-spacing:.05rem;line-height:.5625rem;margin-bottom:9px;text-align:center;text-transform:uppercase}#interactive .interactive-leadin{font-family:nyt-cheltenham,georgia,times new roman,times,serif!important;font-size:20px;font-weight:300;line-height:25px;margin:auto;max-width:calc(100% – 40px)}.interactive-byline{color:var(–color-secondary);font-size:14px;font-weight:700;line-height:18px;margin-left:0;max-width:600px}.interactive-byline .last-byline{color:var(–color-secondary)!important;margin-right:10px}.interactive-byline .interactive-timestamp{font-size:14px;font-weight:500;line-height:18px}.interactive-byline-container{font-family:nyt-franklin,Arial,helvetica,sans-serif;margin:auto auto 1.375rem;max-width:calc(100% – 40px)}.interactive-sharetools{justify-content:start}@media(min-width:340px)and (max-width:630px){html .interactive section{width:calc(100% – 40px)}}@media only screen and (min-width:600px){#interactive-header #interactive-heading{font-size:2.9375rem;line-height:3.4375rem}#interactive .interactive-leadin{font-size:23px;line-height:30px;max-width:600px}.interactive-byline-container{margin-bottom:1.5rem;max-width:600px}}.quiz{margin-top:30px}.quiz .email-signup-summary{color:var(–color-primary);font-family:nyt-franklin,Arial,helvetica,sans-serif;font-size:16px;line-height:20px}.quiz .email-signup-button{margin-top:20px}.quiz .intro-wrapper{margin:0 auto}.quiz .intro-wrapper .text-block p{color:var(–color-secondary);font-size:18px;font-weight:400;line-height:25px}.quiz .intro-wrapper .text-block p,.quiz .media .caption{font-family:nyt-imperial,georgia,times new roman,times,serif}.quiz .media .caption{color:var(–color-quaternary);font-size:14px;line-height:18px;margin:10px 20px 20px 0}.quiz .media .caption .credit{font-family:nyt-franklin,Arial,helvetica,sans-serif;font-size:12px}.quiz .poll-answer{border:transparent;box-sizing:border-box;overflow:hidden}.quiz .poll-answer-graph{background-color:var(–color-bg-tertiary);height:calc(100% + 8px);left:0;position:absolute;top:-5px;transition:width .5s ease-in-out;z-index:-1}.quiz .poll-answer-percentage{align-items:center;box-sizing:border-box;display:flex;height:100%}.quiz .poll-answer.question-answered.not-selected{background-color:transparent!important;border:1px solid var(–stroke-tertiary)}.quiz .poll-answer.question-answered.selected{border:1px solid var(–color-quintary)}.quiz .poll-answer.question-answered.selected .poll-answer-graph{background-color:var(–color-bg-quaternary)}.quiz .poll-answer.question-answered.selected.incorrect{background-image:none!important;border:none!important;box-shadow:inset 0 0 0 1px var(–color-negative);-webkit-box-shadow:inset 0 0 0 1px var(–color-negative);-moz-box-shadow:inset 0 0 0 1px var(–color-negative)}.quiz .poll-answer.question-answered.selected.incorrect .poll-answer-graph{background-color:var(–color-negative);opacity:30%}.quiz .poll-answer.question-answered.selected.incorrect .poll-answer-percentage:before{content:url(https:\/\/static01.nytimes.com\/newsgraphics\/2024-metropolitan-diary-voting\/_images\/incorrect.svg);margin-right:5px;margin-top:5px}.quiz .poll-answer.question-answered.correct{background-image:none!important;border:none!important;box-shadow:inset 0 0 0 1px var(–color-positive);-webkit-box-shadow:inset 0 0 0 1px var(–color-positive);-moz-box-shadow:inset 0 0 0 1px var(–color-positive)}.quiz .poll-answer.question-answered.correct .poll-answer-graph{background-color:var(–color-positive);opacity:40%}.quiz .poll-answer.question-answered.correct .poll-answer-percentage:before{content:url(https:\/\/static01.nytimes.com\/newsgraphics\/2024-metropolitan-diary-voting\/_images\/correct.svg);margin-right:5px;margin-top:5px}.quiz .poll-answer-content{width:95%}.quiz .poll-answer-content .text-block p{color:var(–color-primary)!important;font-family:nyt-franklin,Arial,helvetica,sans-serif!important}.quiz .poll-answer,.quiz .poll-answer p{font-family:nyt-franklin,Arial,Helvetica,sans-serif}.quiz .poll-answer-percentage{bottom:0;color:#bfbfbf;color:var(–color-primary);float:right;font-family:nyt-franklin,Arial,helvetica,sans-serif!important;font-size:16px;font-weight:400;line-height:1.5;margin-right:10px;position:absolute;right:0}.quiz #dialogButton{font-family:nyt-cheltenham!important}.quiz .multiple-choice-question,.quiz .multiple-select-question{background-color:initial;border:none!important;margin-top:0;padding:30px 0}.quiz .multiple-choice-question p,.quiz .multiple-select-question p{color:var(–color-primary);font-family:nyt-cheltenham,georgia,times new roman,times,serif;font-size:26px;line-height:30px;margin:0 0 20px}.quiz .multiple-choice-question .counter,.quiz .multiple-select-question .counter{color:var(–color-primary);font-family:nyt-franklin,Arial,helvetica,sans-serif;font-size:16px;font-weight:700;line-height:18px;margin-top:0}.quiz .multiple-choice-question .answer,.quiz .multiple-select-question .answer{background-color:var(–color-bg-tertiary);margin-top:12px;padding:12px 50px 12px 16px}.quiz .multiple-choice-question .answer.question-unanswered:hover,.quiz .multiple-select-question .answer.question-unanswered:hover{background-color:var(–color-bg-quaternary)}.quiz .multiple-choice-question .answer.question-answered p,.quiz .multiple-select-question .answer.question-answered p{color:var(–color-quaternary)}.quiz .multiple-choice-question .answer p,.quiz .multiple-select-question .answer p{font-family:nyt-franklin,Arial,helvetica,sans-serif!important;font-size:16px;line-height:20px;margin:0}.quiz .multiple-choice-question .response,.quiz .multiple-select-question .response{border-left:initial;padding-left:0}.quiz .multiple-choice-question .response .text-block p,.quiz .multiple-select-question .response .text-block p{color:var(–color-primary);font-family:nyt-imperial,georgia,times new roman,times,serif;font-feature-settings:”liga” off,”clig” off;font-size:18px;font-weight:400;line-height:25px;margin:0 0 6px}.quiz .multiple-choice-question .response .text-block p [class$=-label],.quiz .multiple-select-question .response .text-block p [class$=-label]{font-family:nyt-franklin,Arial,helvetica,sans-serif;font-weight:700;line-height:130%}.quiz .multiple-choice-question .response .text-block p .correct-label,.quiz .multiple-select-question .response .text-block p .correct-label{color:var(–color-positive)}.quiz .multiple-choice-question .response .text-block p .incorrect-label,.quiz .multiple-select-question .response .text-block p .incorrect-label{color:var(–color-negative)}.quiz .multiple-choice-question .response .text-block blockquote,.quiz .multiple-select-question .response .text-block blockquote{color:var(–color-secondary);line-height:24px;margin:10px 0}.quiz .multiple-choice-question .response .text-block blockquote:first-of-type,.quiz .multiple-select-question .response .text-block blockquote:first-of-type{margin:20px 0 10px}.quiz .multiple-choice-question .response .text-block blockquote:last-of-type,.quiz .multiple-select-question .response .text-block blockquote:last-of-type{margin:10px 0 20px}.quiz .multiple-choice-question .response .stats,.quiz .multiple-select-question .response .stats{margin:0}.quiz .multiple-choice-question .response .stats p,.quiz .multiple-select-question .response .stats p{color:var(–color-quaternary);font-family:nyt-franklin,Arial,helvetica,sans-serif!important;font-size:12px;font-weight:500;text-align:initial}.quiz .multiple-choice-question .response:last-of-type,.quiz .multiple-select-question .response:last-of-type{margin:16px 0 0}.quiz .multiple-choice-question .done-button .text-block,.quiz .multiple-choice-question .email-signup-button .text-block,.quiz .multiple-select-question .done-button .text-block,.quiz .multiple-select-question .email-signup-button .text-block{border:1px solid var(–stroke-quaternary);padding:6px 12px}.quiz .multiple-choice-question .done-button .text-block p,.quiz .multiple-choice-question .email-signup-button .text-block p,.quiz .multiple-select-question .done-button .text-block p,.quiz .multiple-select-question .email-signup-button .text-block p{color:var(–color-primary);font-family:nyt-franklin,Arial,helvetica,sans-serif!important;font-size:14px;font-weight:600;margin:0}.quiz .multiple-choice-question .freeform-answer,.quiz .multiple-select-question .freeform-answer{text-align:center}.quiz .multiple-choice-question .freeform-answer .complete-freeform-answer,.quiz .multiple-select-question .freeform-answer .complete-freeform-answer{margin:10px 0 0}.quiz .multiple-choice-question .freeform-answer .complete-freeform-answer .text-block,.quiz .multiple-select-question .freeform-answer .complete-freeform-answer .text-block{border:1px solid var(–stroke-quaternary);margin-top:0;padding:6px 12px}.quiz .multiple-choice-question .freeform-answer .complete-freeform-answer .text-block p,.quiz .multiple-select-question .freeform-answer .complete-freeform-answer .text-block p{color:var(–color-primary);font-family:nyt-franklin,Arial,helvetica,sans-serif;font-size:14px;font-weight:600}.quiz .multiple-choice-question .freeform-answer .complete-freeform-answer .text-block:hover,.quiz .multiple-select-question .freeform-answer .complete-freeform-answer .text-block:hover{border:3px solid var(–light-stroke-hover)}.quiz .multiple-choice-question.answered.has-correct-answers .answer.selected.correct,.quiz .multiple-select-question.answered.has-correct-answers .answer.selected.correct{background:var(–light-color-positive);background-image:url(https:\/\/static01.nytimes.com\/newsgraphics\/2024-metropolitan-diary-voting\/_images\/correct.svg);background-position:calc(100% – 20px);background-repeat:no-repeat;background-size:19px 19px;border:none!important;box-shadow:inset 0 0 0 1px var(–color-positive);-webkit-box-shadow:inset 0 0 0 1px var(–color-positive);-moz-box-shadow:inset 0 0 0 1px var(–color-positive)}.quiz .multiple-choice-question.answered.has-correct-answers .answer.selected.correct p,.quiz .multiple-select-question.answered.has-correct-answers .answer.selected.correct p{color:var(–color-positive)}.quiz .multiple-choice-question.answered.has-correct-answers .answer.selected.incorrect,.quiz .multiple-select-question.answered.has-correct-answers .answer.selected.incorrect{background:var(–light-color-negative);background-image:url(https:\/\/static01.nytimes.com\/newsgraphics\/2024-metropolitan-diary-voting\/_images\/incorrect.svg);background-position:calc(100% – 20px);background-repeat:no-repeat;background-size:19px 19px;border:none!important;box-shadow:inset 0 0 0 1px var(–color-negative);-webkit-box-shadow:inset 0 0 0 1px var(–color-negative);-moz-box-shadow:inset 0 0 0 1px var(–color-negative)}.quiz .multiple-choice-question.answered.has-correct-answers .answer.selected.incorrect p,.quiz .multiple-select-question.answered.has-correct-answers .answer.selected.incorrect p{color:var(–color-negative)}.quiz .multiple-choice-question.answered.has-correct-answers .answer.not-selected.correct,.quiz .multiple-select-question.answered.has-correct-answers .answer.not-selected.correct{background-image:url(https:\/\/static01.nytimes.com\/newsgraphics\/2024-metropolitan-diary-voting\/_images\/correct.svg);background-position:calc(100% – 20px);background-repeat:no-repeat;background-size:19px 19px}.quiz .multiple-choice-question.answered.has-correct-answers .answer.not-selected.correct p,.quiz .multiple-select-question.answered.has-correct-answers .answer.not-selected.correct p{color:var(–color-positive)}.quiz .multiple-choice-question.answered .done-button .text-block,.quiz .multiple-choice-question.answered .email-signup-button .text-block,.quiz .multiple-select-question.answered .done-button .text-block,.quiz .multiple-select-question.answered .email-signup-button .text-block{background:initial}.quiz .multiple-choice-question.unanswered .answer.selected,.quiz .multiple-select-question.unanswered .answer.selected{background-color:var(–color-bg-quaternary)}.quiz .multiple-choice-question.unanswered .done-button .text-block:hover,.quiz .multiple-choice-question.unanswered .email-signup-button .text-block:hover,.quiz .multiple-select-question.unanswered .done-button .text-block:hover,.quiz .multiple-select-question.unanswered .email-signup-button .text-block:hover{background-color:var(–default-button-background);box-shadow:inset 0 0 0 1px var(–light-stroke-hover);-webkit-box-shadow:inset 0 0 0 1px var(–light-stroke-hover);-moz-box-shadow:inset 0 0 0 1px var(–light-stroke-hover)}.quiz .multiple-choice-question.unanswered .done-button .text-block:hover p,.quiz .multiple-choice-question.unanswered .email-signup-button .text-block:hover p,.quiz .multiple-select-question.unanswered .done-button .text-block:hover p,.quiz .multiple-select-question.unanswered .email-signup-button .text-block:hover p{color:var(–color-primary);font-family:nyt-franklin,Arial,helvetica,sans-serif!important;margin:0}.quiz .scorecard{margin:20px auto}.quiz .scorecard .scorecard-kicker{color:var(–color-primary)}.quiz .scorecard .scorecard-inner{color:var(–color-primary);font-family:NYTCheltenham;font-feature-settings:”liga” off,”clig” off;font-size:26px;font-style:normal;font-weight:500;line-height:30px}.quiz .summary.conclusion{text-align:center}.quiz .summary.conclusion .text-block{text-align:left}.quiz .summary.conclusion .text-block p{color:var(–color-primary);font-family:nyt-imperial,georgia,times new roman,times,serif;font-feature-settings:”liga” off,”clig” off;font-size:18px;font-weight:400;line-height:25px;margin:0 auto 16px}.quiz .summary.conclusion .clear-saved{background-color:initial;margin:0}.quiz .summary.conclusion .clear-saved .text-block{background-color:initial;border:1px solid var(–stroke-quaternary);margin:2px;padding:6px 12px}.quiz .summary.conclusion .clear-saved .text-block p{color:var(–color-primary);font-family:nyt-franklin,Arial,helvetica,sans-serif;font-size:14px;font-weight:600;margin:0}.quiz .summary.conclusion .clear-saved .text-block:hover{border:3px solid var(–light-stroke-hover);margin:0}@media only screen and (min-width:480px){.quiz .intro-wrapper .text-block p{font-size:20px;line-height:30px}.quiz .email-signup-summary{font-family:nyt-franklin,Arial,helvetica,sans-serif;font-size:20px;line-height:24px}.quiz .multiple-choice-question,.quiz .multiple-select-question{padding:40px 0}.quiz .multiple-choice-question p,.quiz .multiple-select-question p{font-size:28px;line-height:34px}.quiz .multiple-choice-question .counter,.quiz .multiple-select-question .counter{font-size:20px;line-height:24px;position:static;text-align:initial}.quiz .multiple-choice-question .answer p,.quiz .multiple-select-question .answer p{font-size:20px;line-height:24px}.quiz .multiple-choice-question .response .text-block blockquote,.quiz .multiple-choice-question .response .text-block p,.quiz .multiple-select-question .response .text-block blockquote,.quiz .multiple-select-question .response .text-block p{font-size:20px;line-height:30px}.quiz .multiple-choice-question .response .stats,.quiz .multiple-select-question .response .stats{margin:0}.quiz .multiple-choice-question .response .stats p,.quiz .multiple-select-question .response .stats p{font-size:16px}.quiz .multiple-choice-question .response:last-of-type,.quiz .multiple-select-question .response:last-of-type{margin:20px 0 0}.quiz .multiple-choice-question .done-button .text-block,.quiz .multiple-choice-question .email-signup-button .text-block,.quiz .multiple-select-question .done-button .text-block,.quiz .multiple-select-question .email-signup-button .text-block{padding:6px 16px}.quiz .multiple-choice-question .done-button .text-block p,.quiz .multiple-choice-question .email-signup-button .text-block p,.quiz .multiple-select-question .done-button .text-block p,.quiz .multiple-select-question .email-signup-button .text-block p{font-family:nyt-franklin,Arial,helvetica,sans-serif!important;font-size:16px}.quiz .multiple-choice-question .done-button .text-block:hover p,.quiz .multiple-choice-question .email-signup-button .text-block:hover p,.quiz .multiple-select-question .done-button .text-block:hover p,.quiz .multiple-select-question .email-signup-button .text-block:hover p{font-size:16px}.quiz .multiple-choice-question .freeform-answer .complete-freeform-answer .text-block,.quiz .multiple-select-question .freeform-answer .complete-freeform-answer .text-block{padding:6px 16px}.quiz .multiple-choice-question .freeform-answer .complete-freeform-answer .text-block p,.quiz .multiple-choice-question .freeform-answer .complete-freeform-answer .text-block:hover p,.quiz .multiple-select-question .freeform-answer .complete-freeform-answer .text-block p,.quiz .multiple-select-question .freeform-answer .complete-freeform-answer .text-block:hover p{font-size:16px}.quiz .summary.conclusion .clear-saved .text-block{padding:6px 16px}.quiz .summary.conclusion .clear-saved .text-block p{font-size:16px}}@media screen and (min-width:600px){.quiz .full-width .caption{margin-left:20px}}@media screen and (min-width:1024px){.quiz .media .caption{margin:10px 20px 20px 0}}:root{–color-bg-elevated:#fff;–color-bg-primary:#fff;–color-bg-quaternary:#c7c7c7;–color-bg-secondary:#f8f8f8;–color-bg-tertiary:#ebebeb;–color-bg-inversePrimary:#121212;–color-bg-inverseSecondary:#363636;–color-overlay:#121212;–color-primary:#121212;–color-quaternary:#727272;–color-quintary:#8b8b8b;–color-secondary:#363636;–color-tertiary:#5a5a5a;–color-inversePrimary:#fff;–color-black:#000;–color-accent:#2671dc;–color-breaking:#d0021b;–color-developing:#e6540a;–color-editorial:#326891;–color-highlight:#fefad1;–color-negative:#a90111;–light-color-negative:rgba(169,1,17,.2);–color-positive:#267c30;–light-color-positive:rgba(38,124,48,.2);–stroke-primary:#121212;–stroke-quaternary:#dfdfdf;–stroke-secondary:#8b8b8b;–stroke-tertiary:#c7c7c7;–stroke-inversePrimary:#fff;–stroke-white:#fff;–stroke-gray100:#000;–light-stroke-hover:hsla(0,0%,7%,.12);–color-gold:#fccf0e;–color-silver:#b7b7b7;–color-bronze:#b78c79;–color-success:#40b29c;–color-failure:#dd5858;–viewport-xl:1366px;–viewport-lg:1245px;–viewport-md:975px;–viewport-sm:764px;–viewport-xs:374px;–viewport-xxs:340px;–viewport-switch-layout:$viewport-md;–viewport-hp-lg:1150px;–viewport-hp-md:740px}@media(prefers-color-scheme:dark){:root.NYTApp{–color-bg-elevated:var(–color-background-elevated,#fff);–color-bg-primary:var(–color-background-primary,#fff);–color-bg-quaternary:var(–color-background-quaternary,#c7c7c7);–color-bg-secondary:var(–color-background-secondary,#f8f8f8);–color-bg-tertiary:var(–color-background-tertiary,#ebebeb);–color-bg-inversePrimary:var(–color-background-inversePrimary,#121212);–color-bg-inverseSecondary:var( –color-background-inverseSecondary,#363636 );–color-overlay:var(–color-background-overlay,#121212);–color-primary:var(–color-content-primary,#121212);–color-quaternary:var(–color-content-quaternary,#727272);–color-quintary:var(–color-content-quintary,#8b8b8b);–color-secondary:var(–color-content-secondary,#363636);–color-tertiary:var(–color-content-tertiary,#5a5a5a);–color-inversePrimary:var(–color-content-inversePrimary,#fff);–color-black:var(–color-overlay-black,#000);–color-accent:var(–color-signal-accent,#2671dc);–color-breaking:var(–color-signal-breaking,#d0021b);–color-developing:var(–color-signal-developing,#e6540a);–color-editorial:var(–color-signal-editorial,#326891);–color-highlight:var(–color-signal-highlight,#fefad1);–color-negative:var(–color-signal-negative,#a90111);–color-positive:var(–color-signal-positive,#267c30);–stroke-primary:var(–color-stroke-primary,#121212);–stroke-quaternary:var(–color-stroke-quaternary,#dfdfdf);–stroke-secondary:var(–color-stroke-secondary,#8b8b8b);–stroke-tertiary:var(–color-stroke-tertiary,#c7c7c7);–stroke-inversePrimary:var(–color-stroke-inversePrimary,#fff);–stroke-white:var(–color-static-white,#fff);–stroke-gray100:var(–color-static-gray100,#000)}}.question>.text-block p{font-size:1.5rem;font-weight:500;letter-spacing:-.5px;line-height:1.2;text-wrap:pretty}.question>.text-block p a{text-decoration:1px underline;text-underline-offset:2px}.question>.text-block p a:hover{text-decoration:none}.question{margin-bottom:30px}.quiz figcaption .credit{display:none}.summary.response p a{text-decoration:1px underline;text-underline-offset:2px}.summary.response p a:hover{text-decoration:none}@media only screen and (min-width:480px){.scorecard .scorecard-kicker{float:none;font-size:24px;margin:0;position:relative;text-align:left}}span.equation{display:block;font-family:nyt-franklin;font-size:20px;font-weight:400;margin-top:18px;text-align:center}@media screen and (min-width:895px){.scorecard{position:relative}.scorecard .scorecard-kicker{font-size:28px;left:calc(50% – 390px);line-height:1;margin:0;position:absolute;top:-2px}span.equation{font-size:22px}}<\/p>\n
\n
<\/span><\/p>\n
\n
\n
Jens Mortensen for The New York Times<\/span><\/figcaption><\/figure>\n
\n

1.<\/span> In taxicab geometry<\/a>, circles don\u2019t look round \u2014 they form sharp, angular shapes. What shape do they resemble?<\/p>\n<\/div>\n<\/div>\n

\n
\"Wooden<\/figure>\n
\n

2.<\/span> In taxicab geometry<\/a>, even the value of pi is a surprise. What is it?<\/p>\n<\/div>\n<\/div>\n

\n
\"A
Jens Mortensen for The New York Times<\/span><\/figcaption><\/figure>\n
\n

3.<\/span> Mathematicians have long been fascinated by a special number that describes self-similar proportions. What is the approximate value of this \u201cgolden ratio\u201d<\/a>?<\/p>\n<\/div>\n<\/div>\n

\n
Jens Mortensen for The New York Times<\/span><\/figcaption><\/figure>\n
\n

4.<\/span> Leonardo da Vinci\u2019s \u201cVitruvian Man\u201d has been analyzed endlessly for hidden patterns. According to a 2015 study, does the navel divide the figure according to the golden ratio<\/a>?<\/p>\n<\/div>\n<\/div>\n

\n
\"A<\/figure>\n
\n

5.<\/span> In the densest possible arrangement<\/a> of soda cans standing on a flat surface, each can in the middle touches the same number of neighbors. How many is it?<\/p>\n<\/div>\n<\/div>\n

\n
\"Animation
Jens Mortensen for The New York Times<\/span><\/figcaption><\/figure>\n
\n

6.<\/span> In 2022, a mathematician won a Fields Medal for solving a problem about how to pack spheres<\/a> tightly in eight dimensions. Who did it?<\/p>\n<\/div>\n<\/div>\n

\n
\"A
Jens Mortensen for The New York Times<\/span><\/figcaption><\/figure>\n
\n

7.<\/span> The first four triangular numbers<\/a> are 1, 3, 6 and 10. Why is 10 considered a triangular number?<\/p>\n<\/div>\n<\/div>\n

\n
\"A
Jens Mortensen for The New York Times<\/span><\/figcaption><\/figure>\n
\n

8.<\/span> In 1672, Gottfried Wilhelm Leibniz found a clever way to add the reciprocals of all the triangular numbers<\/a>. What sum did he get? 1 + 1\/3 + 1\/6 + 1\/10 + …<\/span><\/p>\n<\/div>\n<\/div>\n

\n
\"Eight
The New York Times, photo via Alamy<\/span><\/figcaption><\/figure>\n
\n

9.<\/span> At a wedding reception, the bride seats eight of her ex-boyfriends together at a table. (This actually happened to me once.) If each ex-boyfriend shakes hands with each of the others, how many handshakes occur in total?<\/p>\n<\/div>\n<\/div>\n

\n
\"Four
Photo illustration by The New York Times, source photos by Balarama Heller for The New York Times<\/span><\/figcaption><\/figure>\n
\n

10.<\/span> Four bugs start in the corners of a square that measures 1 foot by 1 foot. Each bug chases its clockwise neighbor, always crawling directly toward the neighbor\u2019s current position. If they all crawl at the same speed, how far does each bug travel before they all meet at the center?<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<\/div>\n

\n
\n

Questions and answers 1 through 8: photo illustrations by Jens Mortensen for The New York Times; answer 6: photo by Brendan Hoffman for The New York Times; question 9: photo illustration by The New York Times, source photo via Alamy; question 10: photo illustration by The New York Times, source photos by Balarama Heller for The New York Times.<\/p>\n

Produced by Alan Burdick, Alice Fang, Marcelle Hopkins and Matt McCann. <\/p>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

\u201cMath, Revealed,\u201d our four-part series exploring the mathematics behind everyday objects and experiences, recently came to a smashing conclusion. One installment took a spin through \u201ctaxicab geometry,\u201d a wacky but vital corner of mathematics in which circles aren\u2019t round and pi equals 4. Another journey began with apples and pentagrams and led to Leonardo da Vinci, the golden ratio and ideal positioning of belly buttons. We had great fun on this adventure and hope to resume it before too long. In the meantime, here\u2019s a quiz to test what you learned and your general math knowledge. Enjoy!<\/p>\n

html{–answer-background:#eaf2f9;–answer-text:#053e69;–answer-answered:#f7f7f7;–answer-answered-text:#656565;–unanswered-question-selected-answer-background:#053e69;–unanswered-question-selected-answer-text:#fff;–answered-question-incorrect-answer-background:#e27676;–answered-question-correct-answer-background:#95c198;–breadcrumb-button-background:#eee;–breadcrumb-active-background:#c6cfdf;–breadcrumb-complete-background:#053e69;–response-text:#777;–caption-text:#666;–default-button-background:#fff;–default-button-foreground:#053e69;–scorecard-text:#323232}@media(prefers-color-scheme:dark){html.Hybrid.NYTApp{–answer-background:var(–color-content-secondary);–answer-text:var(–color-content-inversePrimary);–answer-answered:var(–color-background-quaternary);–answer-answered-text:var(–color-content-secondary);–unanswered-question-selected-answer-background:var(–color-signal-accent);–unanswered-question-selected-answer-text:var(–color-content-primary);–answered-question-incorrect-answer-background:var(–color-signal-negative);–answered-question-correct-answer-background:var(–color-signal-positive);–breadcrumb-button-background:var(–color-background-tertiary);–breadcrumb-active-background:var(–color-background-inverseSecondary);–breadcrumb-complete-background:var(–color-content-quaternary);–response-text:var(–color-content-primary);–caption-text:var(–color-content-secondary);–default-button-background:var(–color-background-quaternary);–default-button-foreground:var(–color-stroke-primary);–scorecard-text:var(–color-content-primary)}}#interactive .interactive-leadin{font-family:nyt-franklin,Arial,helvetica,sans-serif}#interactive .interactive-leadin a{color:#326891;text-decoration:none}#interactive .interactive-leadin a:hover{outline:0;text-decoration:underline}.quiz p{margin:0 0 1rem}.quiz a{color:#326891;text-decoration:none}.quiz a:hover{outline:0;text-decoration:underline}.quiz em{font-style:italic}.quiz strong{font-weight:700}.quiz .caption,.quiz figcaption{color:#666;font-family:nyt-cheltenham-sh,georgia,times new roman,times,serif;font-style:normal;font-weight:400}.quiz .credit{color:var(–credit-text);display:inline-block;font-size:.75rem}.sortable-list-item{align-items:center;background-color:#2f84f3;border-radius:3px;box-sizing:border-box;color:#fff;cursor:grab;display:flex;gap:10px;justify-content:left;list-style:none;padding:15px 20px;touch-action:none;transition:background-color .5s;width:100%}.sortable-list-item.active-item{cursor:grabbing;touch-action:none}.sortable-list-item.active-item-hidden{opacity:0}.sortable-list-wrapper{margin-bottom:1.8rem;position:relative}.question .reveal-toggle{background-color:unset;color:#326891}.question.answered .sortable-list-item{cursor:default}.sortable-list-item .text-block p{font-family:nyt-franklin,Arial,helvetica,sans-serif;font-size:20px}.sortable-list-item.sortable-list-item–correct{background-color:rgba(38,124,48,.5)}.sortable-list-item.sortable-list-item–incorrect{background-color:hsla(0,0%,46%,.6)}@media only screen and (max-width:480px){.sortable-list-item{margin:auto;min-width:18rem;width:100%}}.draggable-grouping-question .done-button >.text-block,.list-order-question .done-button >.text-block{background-color:inherit;border:unset;color:inherit;margin-top:0}.done-button{background-color:#fff;border:1px solid #053e69;border-radius:5px;margin-top:10px}.done-button:hover{background-color:#053e69;color:#fff}.done-button .text-block:hover{background-color:unset}.draggable-grouping-question.answered .done-button,.list-order-question.answered .done-button{display:none}.done-button:hover .text-block,.draggable-grouping-question.answered .done-button .text-block,.list-order-question.answered .done-button .text-block{background-color:#053e69;color:#fff!important}.done-button:hover .text-block p,.draggable-grouping-question.answered .done-button .text-block p,.list-order-question.answered .done-button .text-block p{color:#fff}.done-button .text-block p{margin:0}.question.answered .done-button .text-block{cursor:default}.sortable-list-item .text-block p{margin:0}.summary.response{margin:10px 0 0}.draggable-grouping-question .summary.response .text-block p,.list-order-question .summary.response .text-block p{font-family:nyt-franklin,Arial,helvetica,sans-serif;font-size:1rem}.buckets-wrapper{display:grid;gap:10px;margin-top:1.6rem;transition:1s}.buckets-wrapper.even-group{gap:1.6rem;grid-template-columns:1fr 1fr}.buckets-wrapper.odd-group{gap:10px;grid-template-columns:1fr 1fr 1fr}.droppable-bucket{align-items:center;background-color:#f0f0f0;border-radius:5px;box-sizing:border-box;color:#000;display:flex;flex-direction:column;font-family:nyt-franklin,Arial,helvetica,sans-serif;font-size:1rem;gap:3px;height:12rem;justify-content:center;padding:8px;position:relative;text-align:center;width:100%}.droppable-bucket.hovered-over{border:2px solid #333;font-weight:700}.droppable-bucket.faded{opacity:.6}.droppable-bucket-label–top{font-size:.95rem;left:50%;position:absolute;top:calc(-.95rem – 1px);transform:translate(-50%);white-space:nowrap}.draggable-item-shelf{align-items:flex-start;box-sizing:border-box;display:flex;flex-direction:row;flex-wrap:wrap;gap:4px;margin-bottom:1.8rem;min-height:3.5rem;width:100%}.draggable-bucket-item{background-color:#2f84f3;border:1px solid #fff;border-radius:4px;cursor:grab;touch-action:none;transition:background-color .5s}.draggable-bucket-item.grabbing{cursor:grabbing}.draggable-bucket-item.disabled{cursor:default}.draggable-bucket-item.correct{background-color:rgba(38,124,48,.7)}.draggable-bucket-item.incorrect{background-color:rgba(169,1,17,.7)}.draggable-bucket-item .text-block p{color:#fff;font-family:nyt-franklin,Arial,helvetica,sans-serif;font-size:.9rem;margin:0;padding:.8rem .9rem}@media only screen and (max-width:650px){.draggable-item-shelf{box-sizing:border-box;gap:3px;margin:auto;min-height:6rem;width:95%}.buckets-wrapper{display:flex;flex-direction:column;gap:1.5rem!important;margin-top:1.5rem}.droppable-bucket{flex-wrap:wrap;height:7rem;width:100%}.draggable-bucket-item .text-block p{padding:.6rem .9rem}}.question-score .score-text{font-weight:700}.interactive-model canvas{height:300px!important}.interactive-model.hidden{display:none}.text-block.explanation p{font-size:.9rem;font-style:italic}.question.draggable-grouping-question,.question.list-order-question{border-bottom:1px solid #ccc;box-sizing:border-box;max-width:100%;padding-bottom:39px;padding-top:47px;position:relative}.sortable-list-item svg.drag-handle{min-width:24px}.question.draggable-grouping-question .response,.question.list-order-question .response{border-left:1px solid rgba(0,0,0,.05);padding-left:19px}@media only screen and (min-width:480px){.question.draggable-grouping-question,.question.list-order-question{box-sizing:border-box;margin-left:auto;margin-right:auto;max-width:600px}}.draggable-grouping-question .counter,.list-order-question .counter{color:#656565;font-family:nyt-imperial,georgia,times new roman,times,serif;font-size:18px;font-size:20px;font-style:normal;font-weight:400;line-height:1.625rem;line-height:1.5;margin-bottom:12px;margin-top:47px}@media only screen and (min-width:480px){.draggable-grouping-question .counter,.list-order-question .counter{display:inline-block;font-size:20px;left:-210px;line-height:1.5;padding-bottom:0;position:absolute;text-align:right;top:0;width:180px}}.fade{opacity:0;transition:opacity .8s}.fade.faded{opacity:1}.fill-in-blank{border-bottom:1px solid #000;display:inline-block;width:100px}.cascade,.one-at-a-time,.quiz{margin-top:30px}.cascade .media img,.one-at-a-time .media img,.quiz .media img{display:block;width:100%}.cascade .media .caption,.cascade .media figcaption,.one-at-a-time .media .caption,.one-at-a-time .media figcaption,.quiz .media .caption,.quiz .media figcaption{font-size:.85rem;line-height:1.15rem;margin-top:.5em}.cascade h2,.one-at-a-time h2,.quiz h2{font-size:24px;margin-bottom:1em;margin-top:2em}.cascade p,.one-at-a-time p,.quiz p{font-family:nyt-imperial,georgia,times new roman,times,serif;font-size:18px;font-style:normal;font-weight:400;line-height:1.625rem}@media only screen and (min-width:480px){.cascade p,.one-at-a-time p,.quiz p{font-size:20px;line-height:1.5}}.cascade >.media,.cascade >.video,.one-at-a-time >.media,.one-at-a-time >.video,.quiz >.media,.quiz >.video{margin-bottom:45px;margin-left:auto;margin-right:auto;max-width:1020px;width:100%}@media only screen and (min-width:480px){.cascade .conclusion,.cascade .response,.cascade >.text-block,.one-at-a-time .conclusion,.one-at-a-time .response,.one-at-a-time >.text-block,.quiz .conclusion,.quiz .response,.quiz >.text-block{box-sizing:border-box;margin-left:auto;margin-right:auto;max-width:600px}}.cascade .response,.one-at-a-time .response,.quiz .response{margin-top:2em}.cascade .conclusion >.text-block p:first-of-type,.one-at-a-time .conclusion >.text-block p:first-of-type,.quiz .conclusion >.text-block p:first-of-type{margin-top:1em}.done-button{box-sizing:border-box;display:inline-block;display:block;text-align:center}.done-button >.text-block{background-color:var(–default-button-background);border:1px solid var(–default-button-foreground);border-radius:3px;cursor:pointer;display:inline-block;margin-top:10px;padding:10px 15px;transition:all .35s ease-out;transition-property:background-color}@media only screen and (min-width:480px){.done-button >.text-block{padding:10px 15px}}.done-button >.text-block p,.response .done-button >.text-block p{color:var(–default-button-foreground);margin-bottom:0;margin-top:0}.question.unanswered .done-button >.text-block:hover{background-color:#053e69}.question.unanswered .done-button >.text-block:hover p{color:#fff}.advance-button{background-color:inherit;border:none;box-sizing:border-box;display:inline-block;display:block;margin-left:auto;margin-right:auto;text-align:center}.advance-button >.text-block:hover{background-color:#053e69}.advance-button >.text-block:hover p{color:#fff}.advance-button >.text-block{background-color:var(–default-button-background);border:1px solid var(–default-button-foreground);border-radius:3px;cursor:pointer;display:inline-block;margin-top:10px;padding:10px 15px;transition:all .35s ease-out;transition-property:background-color}@media only screen and (min-width:480px){.advance-button >.text-block{padding:10px 15px}}.advance-button >.text-block p,.response .advance-button >.text-block p{color:var(–default-button-foreground);margin-bottom:0;margin-top:0}.breadcrumb-wrapper{display:flex;flex-direction:row;gap:8px;justify-content:center;margin-top:1rem}.breadcrumb-button{background-color:var(–breadcrumb-button-background);border-radius:50%;box-sizing:border-box;cursor:pointer;font-family:nyt-franklin;font-size:14px;height:26px;position:relative;text-align:center;width:26px}.breadcrumb-button–active{background-color:var(–breadcrumb-active-background)}.breadcrumb-button–correct.breadcrumb-button–complete{background-color:#267c30}.breadcrumb-button–partial-correct.breadcrumb-button–complete{background-color:#d4ca8f}.breadcrumb-button–incorrect.breadcrumb-button–complete{background-color:#a90111}.breadcrumb-button–complete{background-color:var(–breadcrumb-complete-background);color:#fff}.breadcrumbs-button–no-index{height:12px;width:12px}.breadcrumb-button__inner-text{left:50%;position:absolute;top:50%;transform:translate(-50%,-50%)}.breadcrumb-button–disabled{cursor:default}.breadcrumb-wrapper.narrow{display:flex;flex-direction:row;gap:4px;justify-content:space-between;margin:auto;max-width:600px}.breadcrumb-wrapper.narrow .breadcrumb-button{background-position:100%;background-size:200% 100%!important;border-radius:unset;box-sizing:border-box;cursor:pointer;font-family:nyt-franklin,Arial,helvetica,sans-serif;font-size:14px;height:4px;position:relative;text-align:center;width:100%}.breadcrumb-wrapper.narrow .breadcrumb-button:first-of-type{border-radius:3px 0 0 3px!important}.breadcrumb-wrapper.narrow .breadcrumb-button:last-of-type{border-radius:0 3px 3px 0!important}.breadcrumb-wrapper.narrow .breadcrumb-button–correct.breadcrumb-button–complete{background:linear-gradient(270deg,#000 50%,#267c30 0) 0;color:hsla(0,0%,100%,.99);transition:3.2s linear}.breadcrumb-wrapper.narrow .breadcrumb-button–incorrect.breadcrumb-button–complete{background:linear-gradient(270deg,#000 50%,#a90111 0) 0;color:hsla(0,0%,100%,.99);transition:3.2s linear}.breadcrumb-wrapper.narrow .breadcrumb-button–correct.breadcrumb-button–inactive{background:#267c30!important;color:#fff!important;transition:0s linear!important}.breadcrumb-wrapper.narrow .breadcrumb-button–incorrect.breadcrumb-button–inactive{background:#a90111!important;color:#fff!important;transition:0s linear!important}.breadcrumb-wrapper.narrow .breadcrumb-button–active,.breadcrumb-wrapper.narrow .breadcrumbs-button–no-index.breadcrumb-button–active{background-color:#000!important}.breadcrumb-wrapper.narrow .breadcrumb-button–complete{background-color:#444}.clear-saved{background:var(–default-button-foreground);border-radius:4px;color:var(–default-button-background);cursor:pointer;display:inline-block;font-family:nyt-franklin,Arial,helvetica,sans-serif;font-size:15px;line-height:1.5;padding:8px 20px}.clear-saved,.clear-saved:hover{text-decoration:none}.clear-saved p{margin-bottom:0}.video{margin-bottom:.5em}.video .credit{font-size:14px}.audio{float:left;margin-right:20px}@media only screen and (min-width:480px){.audio{margin-right:25px}}.audio .track-progress{color:#656565;font-family:nyt-franklin,Arial,helvetica,sans-serif;font-size:12px;margin-top:3px}.audio .track-progress .elapsed:after{content:”\/”;padding:0 3px}.audio-control-button{background:none;border:none;box-sizing:border-box;cursor:pointer;height:35px;outline:none;padding:0;position:relative;width:35px;-webkit-tap-highlight-color:rgba(0,0,0,0);margin:0 0 0 calc(50% – 17.5px)}.audio-button-spinner{border:1px solid #6288a5;border-radius:50%;opacity:1;z-index:1}.audio-button-spinner,.audio-button-spinner span{bottom:0;box-sizing:border-box;display:block;height:35px;left:0;position:absolute;right:0;top:0;width:35px}.audio-button-spinner span{clip:rect(20px,40px,40px,0);animation:none;opacity:0}.audio-button-spinner span:after,.audio-button-spinner span:before{animation:none;border:1px solid transparent;border-radius:50%;border-top-color:#6288a5;bottom:0;box-sizing:border-box;content:””;display:block;height:35px;left:0;position:absolute;right:0;top:0;width:35px}.audio-icon{align-items:center;display:flex;height:100%;justify-content:center;width:100%}.audio-icon svg{height:35px;width:35px;fill:#6288a5;opacity:1;transform:scale(.33) translateX(5px);transform-origin:center;transition:opacity .3s ease-in;z-index:2}@media only screen and (min-width:480px){.step{box-sizing:border-box;margin-left:auto;margin-right:auto;max-width:600px}}.multiple-choice-question,.multiple-select-question{border-bottom:1px solid #ccc;padding-bottom:34px;padding-top:23px;position:relative}@media only screen and (min-width:480px){.multiple-choice-question,.multiple-select-question{padding-bottom:39px;padding-top:47px}}.multiple-choice-question p,.multiple-select-question p{font-family:nyt-imperial,georgia,times new roman,times,serif;font-size:18px;font-style:normal;font-weight:400;line-height:1.625rem;-webkit-font-smoothing:antialiased}@media only screen and (min-width:480px){.multiple-choice-question p,.multiple-select-question p{font-size:20px;line-height:1.5}}.multiple-choice-question .counter,.multiple-select-question .counter{color:#656565;font-family:nyt-imperial,georgia,times new roman,times,serif;font-size:18px;font-size:20px;font-style:normal;font-weight:400;line-height:1.625rem;line-height:1.5;margin-bottom:12px;margin-top:47px}@media only screen and (min-width:480px){.multiple-choice-question .counter,.multiple-select-question .counter{font-size:20px;line-height:1.5}}.multiple-choice-question .media,.multiple-select-question .media{margin-bottom:14px}.multiple-choice-question .media img,.multiple-select-question .media img{width:100%}.multiple-choice-question .response,.multiple-select-question .response{border-left:1px solid rgba(0,0,0,.05);padding-left:19px}.multiple-choice-question .response p,.multiple-select-question .response p{color:var(–response-text);font-family:nyt-imperial,georgia,times new roman,times,serif;font-size:18px;font-style:normal;font-weight:400;line-height:1.625rem}@media only screen and (min-width:480px){.multiple-choice-question .response p,.multiple-select-question .response p{font-size:20px;line-height:1.5}}.multiple-choice-question .done-button,.multiple-select-question .done-button{background-color:inherit;border:none;margin-left:auto;margin-right:auto;text-align:center}.multiple-choice-question .done-button.is-complete,.multiple-select-question .done-button.is-complete{display:none}.multiple-choice-question.answering .done-button,.multiple-select-question.answering .done-button{display:block}.multiple-choice-question .answer,.multiple-select-question .answer{background:var(–answer-background);border-radius:3px;color:var(–answer-text);cursor:pointer;display:block;line-height:1.25;margin-top:10px;padding:15px 20px;position:relative;text-align:left;transition:all .35s ease-out;transition-property:padding,background-color;width:100%}.multiple-choice-question .answer p,.multiple-select-question .answer p{margin-bottom:0;margin-top:0}.multiple-choice-question.answered .answer,.multiple-select-question.answered .answer{background-color:var(–answer-answered);border:none;color:var(–answer-answered-text);cursor:default}.multiple-choice-question.answered .answer.selected,.multiple-select-question.answered .answer.selected{background-color:transparent;color:var(–answer-answered-text)}.multiple-choice-question.unanswered .answer.selected,.multiple-select-question.unanswered .answer.selected{background-color:var(–unanswered-question-selected-answer-background);color:var(–unanswered-question-selected-answer-text)}.multiple-choice-question.has-correct-answers .answer,.multiple-select-question.has-correct-answers .answer{background-position:calc(100% – 20px) 20px;background-repeat:no-repeat;background-size:19px 19px}.multiple-choice-question.answered.has-correct-answers .answer.selected,.multiple-select-question.answered.has-correct-answers .answer.selected{background-color:var(–answered-question-incorrect-answer-background);background-image:url(https:\/\/static01.nyt.com\/inc\/quiz-x_light.svg);color:var(–unanswered-question-selected-answer-text)}.multiple-choice-question.answered.has-correct-answers .answer.correct,.multiple-select-question.answered.has-correct-answers .answer.correct{background-image:url(https:\/\/int.nyt.com\/assets\/adventure\/images\/quiz-check_green.svg);color:var(–answered-question-correct-answer-background)}.multiple-choice-question.answered.has-correct-answers .answer.selected.correct,.multiple-select-question.answered.has-correct-answers .answer.selected.correct{background-color:var(–answered-question-correct-answer-background);background-image:url(https:\/\/static01.nyt.com\/inc\/quiz-check_light.svg);color:var(–unanswered-question-selected-answer-text)}.multiple-choice-question.unanswered .poll-answer-graph,.multiple-select-question.unanswered .poll-answer-graph{width:0!important}.multiple-choice-question.unanswered .poll-answer-percentage,.multiple-select-question.unanswered .poll-answer-percentage{display:none}.multiple-choice-question.answered .poll-answer,.multiple-select-question.answered .poll-answer{background-color:transparent}.multiple-choice-question.answered .poll-answer.answer.selected,.multiple-select-question.answered .poll-answer.answer.selected{color:#656565}.multiple-choice-question.answered.has-correct-answers .poll-answer,.multiple-select-question.answered.has-correct-answers .poll-answer{color:#656565;padding-right:50px}.multiple-choice-question.answered.has-correct-answers .poll-answer.selected,.multiple-select-question.answered.has-correct-answers .poll-answer.selected{background-color:transparent;background-image:url(https:\/\/static01.nyt.com\/inc\/quiz-x_red.svg);color:#656565}.multiple-choice-question.answered.has-correct-answers .poll-answer.selected.correct,.multiple-select-question.answered.has-correct-answers .poll-answer.selected.correct{background-color:transparent;background-image:url(https:\/\/int.nyt.com\/assets\/adventure\/images\/quiz-check_green.svg);color:#656565}.multiple-choice-question .stats p,.multiple-select-question .stats p{color:#666;font-family:nyt-franklin,Arial,helvetica,sans-serif;font-size:14px;font-weight:500;text-align:right}@media only screen and (min-width:480px){.multiple-choice-question .counter,.multiple-select-question .counter{font-size:20px}}@media only screen and (min-width:480px)and (min-width:480px){.multiple-choice-question .counter,.multiple-select-question .counter{display:inline-block;left:-210px;padding-bottom:0;position:absolute;text-align:right;top:0;width:180px}}@media only screen and (min-width:480px){.multiple-choice-question .answer.question-unanswered:hover,.multiple-select-question .answer.question-unanswered:hover{background-color:#053e69;color:#fff}}.multiple-choice-question .freeform-answer,.multiple-select-question .freeform-answer{position:relative}.multiple-choice-question .freeform-answer .freeform-answer-input,.multiple-choice-question .freeform-answer input[type=text].freeform-answer-input,.multiple-select-question .freeform-answer .freeform-answer-input,.multiple-select-question .freeform-answer input[type=text].freeform-answer-input{font-size:18px;line-height:1.625rem;-webkit-font-smoothing:antialiased;background-color:#fff;border:1px solid #e2e2e2;border-radius:3px;box-shadow:inset 2px 3px 3px rgba(0,0,0,.07);box-sizing:border-box;display:block;font-family:nyt-franklin,Arial,helvetica,sans-serif;height:auto;margin-right:5%;padding:10px;width:100%}@media only screen and (min-width:480px){.multiple-choice-question .freeform-answer .freeform-answer-input,.multiple-choice-question .freeform-answer input[type=text].freeform-answer-input,.multiple-select-question .freeform-answer .freeform-answer-input,.multiple-select-question .freeform-answer input[type=text].freeform-answer-input{font-size:17px;line-height:1.5}}.multiple-choice-question .freeform-answer .freeform-answer-input .correct-part,.multiple-choice-question .freeform-answer input[type=text].freeform-answer-input .correct-part,.multiple-select-question .freeform-answer .freeform-answer-input .correct-part,.multiple-select-question .freeform-answer input[type=text].freeform-answer-input .correct-part{color:#95c198}.multiple-choice-question .freeform-answer.question-answered.incorrect .freeform-answer-input,.multiple-choice-question .freeform-answer.question-answered.incorrect input[type=text].freeform-answer-input,.multiple-select-question .freeform-answer.question-answered.incorrect .freeform-answer-input,.multiple-select-question .freeform-answer.question-answered.incorrect input[type=text].freeform-answer-input{border-color:#e27676;box-shadow:inset 2px 3px 3px hsla(0,65%,67%,.3)}.multiple-choice-question .freeform-answer.question-answered.correct .freeform-answer-input,.multiple-choice-question .freeform-answer.question-answered.correct input[type=text].freeform-answer-input,.multiple-select-question .freeform-answer.question-answered.correct .freeform-answer-input,.multiple-select-question .freeform-answer.question-answered.correct input[type=text].freeform-answer-input{border-color:#95c198;box-shadow:inset 2px 3px 3px rgba(149,193,152,.3)}.multiple-choice-question .freeform-answer .reset-freeform-answer,.multiple-select-question .freeform-answer .reset-freeform-answer{background-clip:padding-box;background-color:#ccc;border:none;border-radius:50%;cursor:pointer;font-family:nyt-franklin,Arial,helvetica,sans-serif;height:26px;padding:0;position:absolute;right:9px;top:12px;transition:background-color .2s ease-in;width:26px;z-index:100}.multiple-choice-question .freeform-answer .reset-freeform-answer.inactive,.multiple-select-question .freeform-answer .reset-freeform-answer.inactive{display:none}.multiple-choice-question .freeform-answer .reset-freeform-answer:hover,.multiple-select-question .freeform-answer .reset-freeform-answer:hover{background-color:#666}.multiple-choice-question .freeform-answer .reset-freeform-answer .icon,.multiple-select-question .freeform-answer .reset-freeform-answer .icon{display:block;font-style:normal;height:26px;left:0;line-height:0;position:absolute;top:0;width:26px;z-index:100}.multiple-choice-question .freeform-answer .reset-freeform-answer .icon:after,.multiple-choice-question .freeform-answer .reset-freeform-answer .icon:before,.multiple-select-question .freeform-answer .reset-freeform-answer .icon:after,.multiple-select-question .freeform-answer .reset-freeform-answer .icon:before{background-color:#fff;content:””;display:block;height:2px;left:6px;position:absolute;top:12px;width:14px}.multiple-choice-question .freeform-answer .reset-freeform-answer .icon:before,.multiple-select-question .freeform-answer .reset-freeform-answer .icon:before{transform:rotate(45deg)}.multiple-choice-question .freeform-answer .reset-freeform-answer .icon:after,.multiple-select-question .freeform-answer .reset-freeform-answer .icon:after{transform:rotate(135deg)}.multiple-choice-question .freeform-answer .complete-freeform-answer,.multiple-select-question .freeform-answer .complete-freeform-answer{box-sizing:border-box;display:inline-block}.multiple-choice-question .freeform-answer .complete-freeform-answer >.text-block,.multiple-select-question .freeform-answer .complete-freeform-answer >.text-block{background-color:var(–default-button-background);border:1px solid var(–default-button-foreground);border-radius:3px;cursor:pointer;display:inline-block;margin-top:10px;padding:10px 15px;transition:all .35s ease-out;transition-property:background-color}@media only screen and (min-width:480px){.multiple-choice-question .freeform-answer .complete-freeform-answer >.text-block,.multiple-select-question .freeform-answer .complete-freeform-answer >.text-block{padding:10px 15px}}.multiple-choice-question .freeform-answer .complete-freeform-answer >.text-block p,.multiple-select-question .freeform-answer .complete-freeform-answer >.text-block p,.response .multiple-choice-question .freeform-answer .complete-freeform-answer >.text-block p,.response .multiple-select-question .freeform-answer .complete-freeform-answer >.text-block p{color:var(–default-button-foreground);margin-bottom:0;margin-top:0}.multiple-choice-question .freeform-answer .complete-freeform-answer.active >.text-block:hover,.multiple-select-question .freeform-answer .complete-freeform-answer.active >.text-block:hover{background-color:#053e69}.multiple-choice-question .freeform-answer .complete-freeform-answer.active >.text-block:hover p,.multiple-select-question .freeform-answer .complete-freeform-answer.active >.text-block:hover p{color:#fff}@media only screen and (min-width:480px){.multiple-choice-question,.multiple-select-question{box-sizing:border-box;margin-left:auto;margin-right:auto;max-width:600px}}.scorecard{font-family:nyt-cheltenham,georgia,times new roman,times,serif;margin-top:2em}@media only screen and (min-width:480px){.scorecard{box-sizing:border-box;margin-left:auto;margin-right:auto;max-width:600px}}.scorecard .scorecard-kicker{color:#656565;display:block;font-size:20px;font-weight:400;line-height:1.5}.scorecard .scorecard-inner{color:var(–scorecard-text);font-size:18px;font-weight:700;line-height:1.66;text-align:left}.stats{margin-top:2em}@media only screen and (min-width:480px){.stats{box-sizing:border-box;margin-left:auto;margin-right:auto;max-width:600px}}.stats p{color:#666;font-family:nyt-franklin,Arial,helvetica,sans-serif;font-size:14px;font-weight:500;text-align:right}@media only screen and (min-width:480px){.scorecard .scorecard-kicker{float:left;font-size:30px;margin:7px 0 0 -210px;text-align:right;width:180px}.scorecard .scorecard-inner{font-size:36px;margin-bottom:12px}}.accordion{margin-bottom:1rem}.accordion-trigger{background-color:unset;color:#326891;display:flex;font-family:nyt-franklin,Arial,Helvetica,sans-serif;font-size:inherit;font-style:italic;font-weight:700;gap:7px;margin:10px 0;text-align:left}.accordion-content{box-sizing:border-box;max-height:0;overflow:hidden;padding-top:1rem}.accordion-content .text-block{border:1px solid #333;border-radius:3px;padding:20px}.accordion-content p{font-size:16px;line-height:1.2}.accordion-content.accordion-open{max-height:3000px}.accordion-content.accordion-closed{max-height:0}.accordion-trigger .rotate-arrow.rotated{transform:rotate(-90deg)}.question-scorecard .score-text{font-weight:700}.question-scorecard p.question-scorecard-inner{font-family:nyt-franklin,Arial,helvetica,sans-serif;font-size:1rem}.quiz-ad{text-align:center}#interactive-header #interactive-heading,.quiz .caption,.quiz .counter,.quiz .credit,.quiz blockquote,.quiz p{-webkit-font-smoothing:antialiased}#interactive-header #interactive-heading{color:var(–color-primary);font-family:nyt-cheltenham,georgia,times new roman,times,serif;font-size:2.25rem;line-height:2.5rem;max-width:600px;text-align:left}#interactive-header #interactive-heading p{text-align:left}@media screen and (min-width:1024px){#interactive-header #interactive-heading{margin-top:75px}}h1#interactive-heading{font-style:normal;font-weight:200}@media screen and (min-width:740px){#interactive-header #interactive-heading{font-size:2.75rem;line-height:3.125rem}}@media screen and (min-width:1150px){#interactive-header #interactive-heading{font-size:2.9375rem;line-height:3.4375rem}}.quiz-ad-container{background-color:#f7f7f7;border-bottom:1px solid #f3f3f3;border-top:1px solid #f3f3f3;margin:37px auto;padding-bottom:30px;padding-top:12px;text-align:center}.quiz-ad-container:before{color:#727272;content:”Advertisement”;display:block;font-family:nyt-franklin;font-size:10px;font-weight:500;letter-spacing:.05rem;line-height:.5625rem;margin-bottom:9px;text-align:center;text-transform:uppercase}#interactive .interactive-leadin{font-family:nyt-cheltenham,georgia,times new roman,times,serif!important;font-size:20px;font-weight:300;line-height:25px;margin:auto;max-width:calc(100% – 40px)}.interactive-byline{color:var(–color-secondary);font-size:14px;font-weight:700;line-height:18px;margin-left:0;max-width:600px}.interactive-byline .last-byline{color:var(–color-secondary)!important;margin-right:10px}.interactive-byline .interactive-timestamp{font-size:14px;font-weight:500;line-height:18px}.interactive-byline-container{font-family:nyt-franklin,Arial,helvetica,sans-serif;margin:auto auto 1.375rem;max-width:calc(100% – 40px)}.interactive-sharetools{justify-content:start}@media(min-width:340px)and (max-width:630px){html .interactive section{width:calc(100% – 40px)}}@media only screen and (min-width:600px){#interactive-header #interactive-heading{font-size:2.9375rem;line-height:3.4375rem}#interactive .interactive-leadin{font-size:23px;line-height:30px;max-width:600px}.interactive-byline-container{margin-bottom:1.5rem;max-width:600px}}.quiz{margin-top:30px}.quiz .email-signup-summary{color:var(–color-primary);font-family:nyt-franklin,Arial,helvetica,sans-serif;font-size:16px;line-height:20px}.quiz .email-signup-button{margin-top:20px}.quiz .intro-wrapper{margin:0 auto}.quiz .intro-wrapper .text-block p{color:var(–color-secondary);font-size:18px;font-weight:400;line-height:25px}.quiz .intro-wrapper .text-block p,.quiz .media .caption{font-family:nyt-imperial,georgia,times new roman,times,serif}.quiz .media .caption{color:var(–color-quaternary);font-size:14px;line-height:18px;margin:10px 20px 20px 0}.quiz .media .caption .credit{font-family:nyt-franklin,Arial,helvetica,sans-serif;font-size:12px}.quiz .poll-answer{border:transparent;box-sizing:border-box;overflow:hidden}.quiz .poll-answer-graph{background-color:var(–color-bg-tertiary);height:calc(100% + 8px);left:0;position:absolute;top:-5px;transition:width .5s ease-in-out;z-index:-1}.quiz .poll-answer-percentage{align-items:center;box-sizing:border-box;display:flex;height:100%}.quiz .poll-answer.question-answered.not-selected{background-color:transparent!important;border:1px solid var(–stroke-tertiary)}.quiz .poll-answer.question-answered.selected{border:1px solid var(–color-quintary)}.quiz .poll-answer.question-answered.selected .poll-answer-graph{background-color:var(–color-bg-quaternary)}.quiz .poll-answer.question-answered.selected.incorrect{background-image:none!important;border:none!important;box-shadow:inset 0 0 0 1px var(–color-negative);-webkit-box-shadow:inset 0 0 0 1px var(–color-negative);-moz-box-shadow:inset 0 0 0 1px var(–color-negative)}.quiz .poll-answer.question-answered.selected.incorrect .poll-answer-graph{background-color:var(–color-negative);opacity:30%}.quiz .poll-answer.question-answered.selected.incorrect .poll-answer-percentage:before{content:url(https:\/\/static01.nytimes.com\/newsgraphics\/2024-metropolitan-diary-voting\/_images\/incorrect.svg);margin-right:5px;margin-top:5px}.quiz .poll-answer.question-answered.correct{background-image:none!important;border:none!important;box-shadow:inset 0 0 0 1px var(–color-positive);-webkit-box-shadow:inset 0 0 0 1px var(–color-positive);-moz-box-shadow:inset 0 0 0 1px var(–color-positive)}.quiz .poll-answer.question-answered.correct .poll-answer-graph{background-color:var(–color-positive);opacity:40%}.quiz .poll-answer.question-answered.correct .poll-answer-percentage:before{content:url(https:\/\/static01.nytimes.com\/newsgraphics\/2024-metropolitan-diary-voting\/_images\/correct.svg);margin-right:5px;margin-top:5px}.quiz .poll-answer-content{width:95%}.quiz .poll-answer-content .text-block p{color:var(–color-primary)!important;font-family:nyt-franklin,Arial,helvetica,sans-serif!important}.quiz .poll-answer,.quiz .poll-answer p{font-family:nyt-franklin,Arial,Helvetica,sans-serif}.quiz .poll-answer-percentage{bottom:0;color:#bfbfbf;color:var(–color-primary);float:right;font-family:nyt-franklin,Arial,helvetica,sans-serif!important;font-size:16px;font-weight:400;line-height:1.5;margin-right:10px;position:absolute;right:0}.quiz #dialogButton{font-family:nyt-cheltenham!important}.quiz .multiple-choice-question,.quiz .multiple-select-question{background-color:initial;border:none!important;margin-top:0;padding:30px 0}.quiz .multiple-choice-question p,.quiz .multiple-select-question p{color:var(–color-primary);font-family:nyt-cheltenham,georgia,times new roman,times,serif;font-size:26px;line-height:30px;margin:0 0 20px}.quiz .multiple-choice-question .counter,.quiz .multiple-select-question .counter{color:var(–color-primary);font-family:nyt-franklin,Arial,helvetica,sans-serif;font-size:16px;font-weight:700;line-height:18px;margin-top:0}.quiz .multiple-choice-question .answer,.quiz .multiple-select-question .answer{background-color:var(–color-bg-tertiary);margin-top:12px;padding:12px 50px 12px 16px}.quiz .multiple-choice-question .answer.question-unanswered:hover,.quiz .multiple-select-question .answer.question-unanswered:hover{background-color:var(–color-bg-quaternary)}.quiz .multiple-choice-question .answer.question-answered p,.quiz .multiple-select-question .answer.question-answered p{color:var(–color-quaternary)}.quiz .multiple-choice-question .answer p,.quiz .multiple-select-question .answer p{font-family:nyt-franklin,Arial,helvetica,sans-serif!important;font-size:16px;line-height:20px;margin:0}.quiz .multiple-choice-question .response,.quiz .multiple-select-question .response{border-left:initial;padding-left:0}.quiz .multiple-choice-question .response .text-block p,.quiz .multiple-select-question .response .text-block p{color:var(–color-primary);font-family:nyt-imperial,georgia,times new roman,times,serif;font-feature-settings:”liga” off,”clig” off;font-size:18px;font-weight:400;line-height:25px;margin:0 0 6px}.quiz .multiple-choice-question .response .text-block p [class$=-label],.quiz .multiple-select-question .response .text-block p [class$=-label]{font-family:nyt-franklin,Arial,helvetica,sans-serif;font-weight:700;line-height:130%}.quiz .multiple-choice-question .response .text-block p .correct-label,.quiz .multiple-select-question .response .text-block p .correct-label{color:var(–color-positive)}.quiz .multiple-choice-question .response .text-block p .incorrect-label,.quiz .multiple-select-question .response .text-block p .incorrect-label{color:var(–color-negative)}.quiz .multiple-choice-question .response .text-block blockquote,.quiz .multiple-select-question .response .text-block blockquote{color:var(–color-secondary);line-height:24px;margin:10px 0}.quiz .multiple-choice-question .response .text-block blockquote:first-of-type,.quiz .multiple-select-question .response .text-block blockquote:first-of-type{margin:20px 0 10px}.quiz .multiple-choice-question .response .text-block blockquote:last-of-type,.quiz .multiple-select-question .response .text-block blockquote:last-of-type{margin:10px 0 20px}.quiz .multiple-choice-question .response .stats,.quiz .multiple-select-question .response .stats{margin:0}.quiz .multiple-choice-question .response .stats p,.quiz .multiple-select-question .response .stats p{color:var(–color-quaternary);font-family:nyt-franklin,Arial,helvetica,sans-serif!important;font-size:12px;font-weight:500;text-align:initial}.quiz .multiple-choice-question .response:last-of-type,.quiz .multiple-select-question .response:last-of-type{margin:16px 0 0}.quiz .multiple-choice-question .done-button .text-block,.quiz .multiple-choice-question .email-signup-button .text-block,.quiz .multiple-select-question .done-button .text-block,.quiz .multiple-select-question .email-signup-button .text-block{border:1px solid var(–stroke-quaternary);padding:6px 12px}.quiz .multiple-choice-question .done-button .text-block p,.quiz .multiple-choice-question .email-signup-button .text-block p,.quiz .multiple-select-question .done-button .text-block p,.quiz .multiple-select-question .email-signup-button .text-block p{color:var(–color-primary);font-family:nyt-franklin,Arial,helvetica,sans-serif!important;font-size:14px;font-weight:600;margin:0}.quiz .multiple-choice-question .freeform-answer,.quiz .multiple-select-question .freeform-answer{text-align:center}.quiz .multiple-choice-question .freeform-answer .complete-freeform-answer,.quiz .multiple-select-question .freeform-answer .complete-freeform-answer{margin:10px 0 0}.quiz .multiple-choice-question .freeform-answer .complete-freeform-answer .text-block,.quiz .multiple-select-question .freeform-answer .complete-freeform-answer .text-block{border:1px solid var(–stroke-quaternary);margin-top:0;padding:6px 12px}.quiz .multiple-choice-question .freeform-answer .complete-freeform-answer .text-block p,.quiz .multiple-select-question .freeform-answer .complete-freeform-answer .text-block p{color:var(–color-primary);font-family:nyt-franklin,Arial,helvetica,sans-serif;font-size:14px;font-weight:600}.quiz .multiple-choice-question .freeform-answer .complete-freeform-answer .text-block:hover,.quiz .multiple-select-question .freeform-answer .complete-freeform-answer .text-block:hover{border:3px solid var(–light-stroke-hover)}.quiz .multiple-choice-question.answered.has-correct-answers .answer.selected.correct,.quiz .multiple-select-question.answered.has-correct-answers .answer.selected.correct{background:var(–light-color-positive);background-image:url(https:\/\/static01.nytimes.com\/newsgraphics\/2024-metropolitan-diary-voting\/_images\/correct.svg);background-position:calc(100% – 20px);background-repeat:no-repeat;background-size:19px 19px;border:none!important;box-shadow:inset 0 0 0 1px var(–color-positive);-webkit-box-shadow:inset 0 0 0 1px var(–color-positive);-moz-box-shadow:inset 0 0 0 1px var(–color-positive)}.quiz .multiple-choice-question.answered.has-correct-answers .answer.selected.correct p,.quiz .multiple-select-question.answered.has-correct-answers .answer.selected.correct p{color:var(–color-positive)}.quiz .multiple-choice-question.answered.has-correct-answers .answer.selected.incorrect,.quiz .multiple-select-question.answered.has-correct-answers .answer.selected.incorrect{background:var(–light-color-negative);background-image:url(https:\/\/static01.nytimes.com\/newsgraphics\/2024-metropolitan-diary-voting\/_images\/incorrect.svg);background-position:calc(100% – 20px);background-repeat:no-repeat;background-size:19px 19px;border:none!important;box-shadow:inset 0 0 0 1px var(–color-negative);-webkit-box-shadow:inset 0 0 0 1px var(–color-negative);-moz-box-shadow:inset 0 0 0 1px var(–color-negative)}.quiz .multiple-choice-question.answered.has-correct-answers .answer.selected.incorrect p,.quiz .multiple-select-question.answered.has-correct-answers .answer.selected.incorrect p{color:var(–color-negative)}.quiz .multiple-choice-question.answered.has-correct-answers .answer.not-selected.correct,.quiz .multiple-select-question.answered.has-correct-answers .answer.not-selected.correct{background-image:url(https:\/\/static01.nytimes.com\/newsgraphics\/2024-metropolitan-diary-voting\/_images\/correct.svg);background-position:calc(100% – 20px);background-repeat:no-repeat;background-size:19px 19px}.quiz .multiple-choice-question.answered.has-correct-answers .answer.not-selected.correct p,.quiz .multiple-select-question.answered.has-correct-answers .answer.not-selected.correct p{color:var(–color-positive)}.quiz .multiple-choice-question.answered .done-button .text-block,.quiz .multiple-choice-question.answered .email-signup-button .text-block,.quiz .multiple-select-question.answered .done-button .text-block,.quiz .multiple-select-question.answered .email-signup-button .text-block{background:initial}.quiz .multiple-choice-question.unanswered .answer.selected,.quiz .multiple-select-question.unanswered .answer.selected{background-color:var(–color-bg-quaternary)}.quiz .multiple-choice-question.unanswered .done-button .text-block:hover,.quiz .multiple-choice-question.unanswered .email-signup-button .text-block:hover,.quiz .multiple-select-question.unanswered .done-button .text-block:hover,.quiz .multiple-select-question.unanswered .email-signup-button .text-block:hover{background-color:var(–default-button-background);box-shadow:inset 0 0 0 1px var(–light-stroke-hover);-webkit-box-shadow:inset 0 0 0 1px var(–light-stroke-hover);-moz-box-shadow:inset 0 0 0 1px var(–light-stroke-hover)}.quiz .multiple-choice-question.unanswered .done-button .text-block:hover p,.quiz .multiple-choice-question.unanswered .email-signup-button .text-block:hover p,.quiz .multiple-select-question.unanswered .done-button .text-block:hover p,.quiz .multiple-select-question.unanswered .email-signup-button .text-block:hover p{color:var(–color-primary);font-family:nyt-franklin,Arial,helvetica,sans-serif!important;margin:0}.quiz .scorecard{margin:20px auto}.quiz .scorecard .scorecard-kicker{color:var(–color-primary)}.quiz .scorecard .scorecard-inner{color:var(–color-primary);font-family:NYTCheltenham;font-feature-settings:”liga” off,”clig” off;font-size:26px;font-style:normal;font-weight:500;line-height:30px}.quiz .summary.conclusion{text-align:center}.quiz .summary.conclusion .text-block{text-align:left}.quiz .summary.conclusion .text-block p{color:var(–color-primary);font-family:nyt-imperial,georgia,times new roman,times,serif;font-feature-settings:”liga” off,”clig” off;font-size:18px;font-weight:400;line-height:25px;margin:0 auto 16px}.quiz .summary.conclusion .clear-saved{background-color:initial;margin:0}.quiz .summary.conclusion .clear-saved .text-block{background-color:initial;border:1px solid var(–stroke-quaternary);margin:2px;padding:6px 12px}.quiz .summary.conclusion .clear-saved .text-block p{color:var(–color-primary);font-family:nyt-franklin,Arial,helvetica,sans-serif;font-size:14px;font-weight:600;margin:0}.quiz .summary.conclusion .clear-saved .text-block:hover{border:3px solid var(–light-stroke-hover);margin:0}@media only screen and (min-width:480px){.quiz .intro-wrapper .text-block p{font-size:20px;line-height:30px}.quiz .email-signup-summary{font-family:nyt-franklin,Arial,helvetica,sans-serif;font-size:20px;line-height:24px}.quiz .multiple-choice-question,.quiz .multiple-select-question{padding:40px 0}.quiz .multiple-choice-question p,.quiz .multiple-select-question p{font-size:28px;line-height:34px}.quiz .multiple-choice-question .counter,.quiz .multiple-select-question .counter{font-size:20px;line-height:24px;position:static;text-align:initial}.quiz .multiple-choice-question .answer p,.quiz .multiple-select-question .answer p{font-size:20px;line-height:24px}.quiz .multiple-choice-question .response .text-block blockquote,.quiz .multiple-choice-question .response .text-block p,.quiz .multiple-select-question .response .text-block blockquote,.quiz .multiple-select-question .response .text-block p{font-size:20px;line-height:30px}.quiz .multiple-choice-question .response .stats,.quiz .multiple-select-question .response .stats{margin:0}.quiz .multiple-choice-question .response .stats p,.quiz .multiple-select-question .response .stats p{font-size:16px}.quiz .multiple-choice-question .response:last-of-type,.quiz .multiple-select-question .response:last-of-type{margin:20px 0 0}.quiz .multiple-choice-question .done-button .text-block,.quiz .multiple-choice-question .email-signup-button .text-block,.quiz .multiple-select-question .done-button .text-block,.quiz .multiple-select-question .email-signup-button .text-block{padding:6px 16px}.quiz .multiple-choice-question .done-button .text-block p,.quiz .multiple-choice-question .email-signup-button .text-block p,.quiz .multiple-select-question .done-button .text-block p,.quiz .multiple-select-question .email-signup-button .text-block p{font-family:nyt-franklin,Arial,helvetica,sans-serif!important;font-size:16px}.quiz .multiple-choice-question .done-button .text-block:hover p,.quiz .multiple-choice-question .email-signup-button .text-block:hover p,.quiz .multiple-select-question .done-button .text-block:hover p,.quiz .multiple-select-question .email-signup-button .text-block:hover p{font-size:16px}.quiz .multiple-choice-question .freeform-answer .complete-freeform-answer .text-block,.quiz .multiple-select-question .freeform-answer .complete-freeform-answer .text-block{padding:6px 16px}.quiz .multiple-choice-question .freeform-answer .complete-freeform-answer .text-block p,.quiz .multiple-choice-question .freeform-answer .complete-freeform-answer .text-block:hover p,.quiz .multiple-select-question .freeform-answer .complete-freeform-answer .text-block p,.quiz .multiple-select-question .freeform-answer .complete-freeform-answer .text-block:hover p{font-size:16px}.quiz .summary.conclusion .clear-saved .text-block{padding:6px 16px}.quiz .summary.conclusion .clear-saved .text-block p{font-size:16px}}@media screen and (min-width:600px){.quiz .full-width .caption{margin-left:20px}}@media screen and (min-width:1024px){.quiz .media .caption{margin:10px 20px 20px 0}}:root{–color-bg-elevated:#fff;–color-bg-primary:#fff;–color-bg-quaternary:#c7c7c7;–color-bg-secondary:#f8f8f8;–color-bg-tertiary:#ebebeb;–color-bg-inversePrimary:#121212;–color-bg-inverseSecondary:#363636;–color-overlay:#121212;–color-primary:#121212;–color-quaternary:#727272;–color-quintary:#8b8b8b;–color-secondary:#363636;–color-tertiary:#5a5a5a;–color-inversePrimary:#fff;–color-black:#000;–color-accent:#2671dc;–color-breaking:#d0021b;–color-developing:#e6540a;–color-editorial:#326891;–color-highlight:#fefad1;–color-negative:#a90111;–light-color-negative:rgba(169,1,17,.2);–color-positive:#267c30;–light-color-positive:rgba(38,124,48,.2);–stroke-primary:#121212;–stroke-quaternary:#dfdfdf;–stroke-secondary:#8b8b8b;–stroke-tertiary:#c7c7c7;–stroke-inversePrimary:#fff;–stroke-white:#fff;–stroke-gray100:#000;–light-stroke-hover:hsla(0,0%,7%,.12);–color-gold:#fccf0e;–color-silver:#b7b7b7;–color-bronze:#b78c79;–color-success:#40b29c;–color-failure:#dd5858;–viewport-xl:1366px;–viewport-lg:1245px;–viewport-md:975px;–viewport-sm:764px;–viewport-xs:374px;–viewport-xxs:340px;–viewport-switch-layout:$viewport-md;–viewport-hp-lg:1150px;–viewport-hp-md:740px}@media(prefers-color-scheme:dark){:root.NYTApp{–color-bg-elevated:var(–color-background-elevated,#fff);–color-bg-primary:var(–color-background-primary,#fff);–color-bg-quaternary:var(–color-background-quaternary,#c7c7c7);–color-bg-secondary:var(–color-background-secondary,#f8f8f8);–color-bg-tertiary:var(–color-background-tertiary,#ebebeb);–color-bg-inversePrimary:var(–color-background-inversePrimary,#121212);–color-bg-inverseSecondary:var( –color-background-inverseSecondary,#363636 );–color-overlay:var(–color-background-overlay,#121212);–color-primary:var(–color-content-primary,#121212);–color-quaternary:var(–color-content-quaternary,#727272);–color-quintary:var(–color-content-quintary,#8b8b8b);–color-secondary:var(–color-content-secondary,#363636);–color-tertiary:var(–color-content-tertiary,#5a5a5a);–color-inversePrimary:var(–color-content-inversePrimary,#fff);–color-black:var(–color-overlay-black,#000);–color-accent:var(–color-signal-accent,#2671dc);–color-breaking:var(–color-signal-breaking,#d0021b);–color-developing:var(–color-signal-developing,#e6540a);–color-editorial:var(–color-signal-editorial,#326891);–color-highlight:var(–color-signal-highlight,#fefad1);–color-negative:var(–color-signal-negative,#a90111);–color-positive:var(–color-signal-positive,#267c30);–stroke-primary:var(–color-stroke-primary,#121212);–stroke-quaternary:var(–color-stroke-quaternary,#dfdfdf);–stroke-secondary:var(–color-stroke-secondary,#8b8b8b);–stroke-tertiary:var(–color-stroke-tertiary,#c7c7c7);–stroke-inversePrimary:var(–color-stroke-inversePrimary,#fff);–stroke-white:var(–color-static-white,#fff);–stroke-gray100:var(–color-static-gray100,#000)}}.question >.text-block p{font-size:1.5rem;font-weight:500;letter-spacing:-.5px;line-height:1.2;text-wrap:pretty}.question >.text-block p a{text-decoration:1px underline;text-underline-offset:2px}.question >.text-block p a:hover{text-decoration:none}.question{margin-bottom:30px}.quiz figcaption .credit{display:none}.summary.response p a{text-decoration:1px underline;text-underline-offset:2px}.summary.response p a:hover{text-decoration:none}@media only screen and (min-width:480px){.scorecard .scorecard-kicker{float:none;font-size:24px;margin:0;position:relative;text-align:left}}span.equation{display:block;font-family:nyt-franklin;font-size:20px;font-weight:400;margin-top:18px;text-align:center}@media screen and (min-width:895px){.scorecard{position:relative}.scorecard .scorecard-kicker{font-size:28px;left:calc(50% – 390px);line-height:1;margin:0;position:absolute;top:-2px}span.equation{font-size:22px}}Jens Mortensen for The New York Times1. In taxicab geometry, circles don\u2019t look round \u2014 they form sharp, angular shapes. What shape do they resemble?2. In taxicab geometry, even the value of pi is a surprise. What is it?Jens Mortensen for The New York Times3. Mathematicians have long been fascinated by a special number that describes self-similar proportions. What is the approximate value of this \u201cgolden ratio\u201d?Jens Mortensen for The New York Times4. Leonardo da Vinci\u2019s \u201cVitruvian Man\u201d has been analyzed endlessly for hidden patterns. According to a 2015 study, does the navel divide the figure according to the golden ratio?5. In the densest possible arrangement of soda cans standing on a flat surface, each can in the middle touches the same number of neighbors. How many is it?Jens Mortensen for The New York Times6. In 2022, a mathematician won a Fields Medal for solving a problem about how to pack spheres tightly in eight dimensions. Who did it?Jens Mortensen for The New York Times7. The first four triangular numbers are 1, 3, 6 and 10. Why is 10 considered a triangular number?Jens Mortensen for The New York Times8. In 1672, Gottfried Wilhelm Leibniz found a clever way to add the reciprocals of all the triangular numbers. What sum did he get? 1 + 1\/3 + 1\/6 + 1\/10 + …The New York Times, photo via Alamy9. At a wedding reception, the bride seats eight of her ex-boyfriends together at a table. (This actually happened to me once.) If each ex-boyfriend shakes hands with each of the others, how many handshakes occur in total?Photo illustration by The New York Times, source photos by Balarama Heller for The New York Times10. Four bugs start in the corners of a square that measures 1 foot by 1 foot. Each bug chases its clockwise neighbor, always crawling directly toward the neighbor\u2019s current position. If they all crawl at the same speed, how far does each bug travel before they all meet at the center?<\/p>\n

Questions and answers 1 through 8: photo illustrations by Jens Mortensen for The New York Times; answer 6: photo by Brendan Hoffman for The New York Times; question 9: photo illustration by The New York Times, source photo via Alamy; question 10: photo illustration by The New York Times, source photos by Balarama Heller for The New York Times.Produced by<\/p>\n","protected":false},"author":1,"featured_media":31583,"comment_status":"close","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[34],"tags":[],"class_list":["post-31581","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-science"],"_links":{"self":[{"href":"https:\/\/medexperts.pro\/index.php?rest_route=\/wp\/v2\/posts\/31581","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/medexperts.pro\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/medexperts.pro\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/medexperts.pro\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/medexperts.pro\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=31581"}],"version-history":[{"count":3,"href":"https:\/\/medexperts.pro\/index.php?rest_route=\/wp\/v2\/posts\/31581\/revisions"}],"predecessor-version":[{"id":31594,"href":"https:\/\/medexperts.pro\/index.php?rest_route=\/wp\/v2\/posts\/31581\/revisions\/31594"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/medexperts.pro\/index.php?rest_route=\/wp\/v2\/media\/31583"}],"wp:attachment":[{"href":"https:\/\/medexperts.pro\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=31581"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/medexperts.pro\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=31581"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/medexperts.pro\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=31581"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}