{"status": "success", "data": {"description_md": "**POTD Challenge December 19, 2023**\n**Author:** munch\n\nIf $a,b,c,d$ are non-negative real numbers such that$\\frac{(a+b+c+d)^3}{3} + (a+b+c+d)(a^2+b^2+c^2+d^2) = \\frac{4(a^3+b^3+c^3+d^3)}{3},$ find the sum of all values of $ab+ac+ad+bc+bd+cd$.", "description_html": "<p><strong>POTD Challenge December 19, 2023</strong><br/>&#10;<strong>Author:</strong> munch</p>&#10;<p>If <span class=\"katex--inline\">a,b,c,d</span> are non-negative real numbers such that<span class=\"katex--inline\">\\frac{(a+b+c+d)^3}{3} + (a+b+c+d)(a^2+b^2+c^2+d^2) = \\frac{4(a^3+b^3+c^3+d^3)}{3},</span> find the sum of all values of <span class=\"katex--inline\">ab+ac+ad+bc+bd+cd</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 5, "problem_name": "Problem of the Day #30 (Challenge)", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}