{"status": "success", "data": {"description_md": "Let $ K$ be the product of all factors $ (b-a)$ (not necessarily distinct) where $ a$ and $ b$ are integers satisfying $ 1\\le a < b \\le 20$. Find the greatest positive integer $ n$ such that $ 2^n$ divides $ K$.\n___\nLeading zeroes must be inputted, so if your answer is `34`, then input `034`. Full credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>Let $ K$ be the product of all factors $ (b-a)$ (not necessarily distinct) where $ a$ and $ b$ are integers satisfying $ 1\\le a &lt; b \\le 20$. Find the greatest positive integer $ n$ such that $ 2^n$ divides $ K$.</p>&#10;<hr><p>Leading zeroes must be inputted, so if your answer is <code>34</code>, then input <code>034</code>. 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": "2010 AIME II Problem 3", "can_next": true, "can_prev": true, "nxt": "/problem/10_aime_II_p04", "prev": "/problem/10_aime_II_p02"}}