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ways of filling the 2xn grid with numbers 1,2,..., 2n under one condition

Source: Mexican Mathematical Olympiad 2006 P3

July 31, 2018
combinatoricsgrid

Problem Statement

Let nn be an integer greater than 11. In how many ways can we fill all the numbers 1,2,...,2n1, 2,..., 2n in the boxes of a grid of 2×n2\times n, one in each box, so that any two consecutive numbers are they in squares that share one side of the grid?
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