MathDB

Permutations [2011.II.14]

Source:

March 31, 2011

AIME2011 AIME II

Problem Statement

There are

N

permutations

(a_1,a_2,\dots,a_{30})

1,2,\dots,30

such that for

m\in\{2,3,5\}

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.