{"status": "success", "data": {"description_md": "Call a permutation $a_1,a_2,\\ldots,a_n$ quasi-increasing if $a_k\\le a_{k+1}+2$ for each $1\\le k\\le n-1$. For example, $54321$ and $14253$ are quasi-increasing permutations of the integers $1,2,3,4,5$, but $45123$ is not. Find the number of quasi-increasing permutations of the integers $1,2,\\ldots,7$.\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": "

Call a permutation a_1,a_2,\\ldots,a_n quasi-increasing if a_k\\le a_{k+1}+2 for each 1\\le k\\le n-1. For example, 54321 and 14253 are quasi-increasing permutations of the integers 1,2,3,4,5, but 45123 is not. Find the number of quasi-increasing permutations of the integers 1,2,\\ldots,7.

Leading zeroes must be inputted, so if your answer is 34, then input 034. Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.

", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 5, "problem_name": "2015 AIME II Problem 10", "can_next": true, "can_prev": true, "nxt": "/problem/15_aime_II_p11", "prev": "/problem/15_aime_II_p09"}}