{"status": "success", "data": {"description_md": "The digits of the positive integer $n$ include no 9s, exactly four 8s, exactly three 7s, exactly two 6s, and some other digits. If the sum of the digits of $n$ is 104 and the sum of the digits of $2n$ is 100, then the number of times that the digit 5 occurs in $n$ is\n\n$\\text{(A)}\\ 0\\qquad\\text{(B)}\\ 1\\qquad\\text{(C)}\\ 2\\qquad\\text{(D)}\\ 3\\qquad\\text{(E)}\\ 4$\n\n___\n\n**[Cayley](https://www.cemc.uwaterloo.ca/contests/past_contests.html#pcf), by [CEMC](https://cemc.uwaterloo.ca/), is licensed under the [CC BY-NC 3.0 DEED](https://creativecommons.org/licenses/by-nc/3.0/). They are not affiliated with or endorse TopsOJ in any way.**\n", "description_html": "<p>The digits of the positive integer <span class=\"katex--inline\">n</span> include no 9s, exactly four 8s, exactly three 7s, exactly two 6s, and some other digits. If the sum of the digits of <span class=\"katex--inline\">n</span> is 104 and the sum of the digits of <span class=\"katex--inline\">2n</span> is 100, then the number of times that the digit 5 occurs in <span class=\"katex--inline\">n</span> is</p>\n<p><span class=\"katex--inline\">\\text{(A)}\\ 0\\qquad\\text{(B)}\\ 1\\qquad\\text{(C)}\\ 2\\qquad\\text{(D)}\\ 3\\qquad\\text{(E)}\\ 4</span></p>\n<hr>\n<p><strong><a href=\"https://www.cemc.uwaterloo.ca/contests/past_contests.html#pcf\">Cayley</a>, by <a href=\"https://cemc.uwaterloo.ca/\">CEMC</a>, is licensed under the <a href=\"https://creativecommons.org/licenses/by-nc/3.0/\">CC BY-NC 3.0 DEED</a>. They are not affiliated with or endorse TopsOJ in any way.</strong></p>\n", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2012 Cayley Problem 25", "can_next": false, "can_prev": true, "nxt": "", "prev": "/problem/12_cayley_p24"}}