{"status": "success", "data": {"description_md": "Suppose that $S$ is a subset of $\\left\\{ 1, 2, 3, \\cdots , 25 \\right\\}$ such that the sum of any two (not necessarily distinct) elements of $S$ is never an element of $S.$ What is the maximum number of elements $S$ may contain?\n\n$\\textbf{(A)}\\ 12 \\qquad\\textbf{(B)}\\ 13 \\qquad\\textbf{(C)}\\ 14 \\qquad\\textbf{(D)}\\ 15 \\qquad\\textbf{(E)}\\ 16$", "description_html": "<p>Suppose that  <span class=\"katex--inline\">S</span>  is a subset of  <span class=\"katex--inline\">\\left\\{ 1, 2, 3, \\cdots , 25 \\right\\}</span>  such that the sum of any two (not necessarily distinct) elements of  <span class=\"katex--inline\">S</span>  is never an element of  <span class=\"katex--inline\">S.</span>  What is the maximum number of elements  <span class=\"katex--inline\">S</span>  may contain?</p>\n<p> <span class=\"katex--inline\">\\textbf{(A)}\\ 12 \\qquad\\textbf{(B)}\\ 13 \\qquad\\textbf{(C)}\\ 14 \\qquad\\textbf{(D)}\\ 15 \\qquad\\textbf{(E)}\\ 16</span> </p>\n<hr><p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2022 AMC 10B Problem 14", "can_next": true, "can_prev": true, "nxt": "/problem/22_amc10B_p15", "prev": "/problem/22_amc10B_p13"}}