{"status": "success", "data": {"description_md": "There are many positive integers $N$ with the following properties:\n\n- the digits of $N$ include at least one of each of the digits 3, 4, 5, and 6,\n- the digits of $N$ include no digits other than 3, 4, 5, and 6, and\n- the sum of the digits of $N$ is 900 and the sum of the digits of $2N$ is 900.\n\nWhen the largest and smallest possible values of $N$ are multiplied together, the number of digits in the resulting product is\n\n$\\text{(A)}\\ 408\\qquad\\text{(B)}\\ 400\\qquad\\text{(C)}\\ 432\\qquad\\text{(D)}\\ 416\\qquad\\text{(E)}\\ 424$\n\n___\n\n**[Fermat](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>There are many positive integers <span class=\"katex--inline\">N</span> with the following properties:</p>\n<p>- the digits of <span class=\"katex--inline\">N</span> include at least one of each of the digits 3, 4, 5, and 6,\n- the digits of <span class=\"katex--inline\">N</span> include no digits other than 3, 4, 5, and 6, and\n- the sum of the digits of <span class=\"katex--inline\">N</span> is 900 and the sum of the digits of <span class=\"katex--inline\">2N</span> is 900.</p>\n<p>When the largest and smallest possible values of <span class=\"katex--inline\">N</span> are multiplied together, the number of digits in the resulting product is</p>\n<p><span class=\"katex--inline\">\\text{(A)}\\ 408\\qquad\\text{(B)}\\ 400\\qquad\\text{(C)}\\ 432\\qquad\\text{(D)}\\ 416\\qquad\\text{(E)}\\ 424</span></p>\n<hr>\n<p><strong><a href=\"https://www.cemc.uwaterloo.ca/contests/past_contests.html#pcf\">Fermat</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 Fermat Problem 25", "can_next": false, "can_prev": true, "nxt": "", "prev": "/problem/12_fermat_p24"}}