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2011 AIME II Problems/Problem 14

Revision as of 10:46, 31 March 2011 by Joelinia (talk | contribs) (Created page with 'Problem: There are N permutations <math>(a_{1}, a_{2}, ... , a_{30})</math> of 1, 2, ... , 30 such that for <math>m \in \left\{{2, 3, 5}\right\}</math>, m divides <math>a_{n+m} …')
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Problem:

There are N permutations $(a_{1}, a_{2}, ... , a_{30})$ of 1, 2, ... , 30 such that for $m \in \left\{{2, 3, 5}\right\}$, m divides $a_{n+m} - a_{n}$ for all integers n with $1 \leq n < n+m \leq 30$. Find the remainder when N is divided by 1000.

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