MathDB
a_i + j = n + 1 where i = a_j, permutations of 1,2,...,n , when 4 divides n

Source: Dutch IMO TST1 2012 p4

January 10, 2020
combinatoricspermutations

Problem Statement

Let nn be a positive integer divisible by 44. We consider the permutations (a1,a2,...,an)(a_1, a_2,...,a_n) of (1,2,...,n)(1,2,..., n) having the following property: for each j we have ai+j=n+1a_i + j = n + 1 where i=aji = a_j . Prove that there are exactly (12n)!(14n)!\frac{ (\frac12 n)!}{(\frac14 n)!} such permutations.
Back to ProblemsView on AoPS