{"status": "success", "data": {"description_md": "If $wxyz$ is a four-digit positive integer with $w \\neq 0$, the *layer sum* of this integer equals $wxyz + xyz + yz + z$. For example, the layer sum of $4089$ is $4089 + 089 + 89 + 9 = 4276$. If the layer sum of $wxyz$ equals $2014$, what is the value of $w + x + y + z$?\n\n$\\text{(A)}\\ 12\\qquad\\text{(B)}\\ 15\\qquad\\text{(C)}\\ 11\\qquad\\text{(D)}\\ 13\\qquad\\text{(E)}\\ 10$\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>If <span class=\"katex--inline\">wxyz</span> is a four-digit positive integer with <span class=\"katex--inline\">w \\neq 0</span>, the *layer sum* of this integer equals <span class=\"katex--inline\">wxyz + xyz + yz + z</span>. For example, the layer sum of <span class=\"katex--inline\">4089</span> is <span class=\"katex--inline\">4089 + 089 + 89 + 9 = 4276</span>. If the layer sum of <span class=\"katex--inline\">wxyz</span> equals <span class=\"katex--inline\">2014</span>, what is the value of <span class=\"katex--inline\">w + x + y + z</span>?</p>\n<p><span class=\"katex--inline\">\\text{(A)}\\ 12\\qquad\\text{(B)}\\ 15\\qquad\\text{(C)}\\ 11\\qquad\\text{(D)}\\ 13\\qquad\\text{(E)}\\ 10</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": 2, "problem_name": "2014 Cayley Problem 20", "can_next": true, "can_prev": true, "nxt": "/problem/14_cayley_p21", "prev": "/problem/14_cayley_p19"}}