{"status": "success", "data": {"description_md": "The average of a list of three consecutive odd integers is 7. When a fourth positive integer, $m$, different from the first three, is included in the list, the average of the list is an integer. What is the sum of the three smallest possible values of $m$?\n\n$\\text{(A)}\\ 6\\qquad\\text{(B)}\\ 9\\qquad\\text{(C)}\\ 21\\qquad\\text{(D)}\\ 29\\qquad\\text{(E)}\\ 33$\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 average of a list of three consecutive odd integers is 7. When a fourth positive integer, <span class=\"katex--inline\">m</span>, different from the first three, is included in the list, the average of the list is an integer. What is the sum of the three smallest possible values of <span class=\"katex--inline\">m</span>?</p>\n<p><span class=\"katex--inline\">\\text{(A)}\\ 6\\qquad\\text{(B)}\\ 9\\qquad\\text{(C)}\\ 21\\qquad\\text{(D)}\\ 29\\qquad\\text{(E)}\\ 33</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": "2015 Cayley Problem 21", "can_next": true, "can_prev": true, "nxt": "/problem/15_cayley_p22", "prev": "/problem/15_cayley_p20"}}