MEMO 2008 pojedinačno problem 2

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April 28, 2012
Consider a n \times n checkerboard with n > 1, n \in \mathbb{N}. How many possibilities are there to put 2n - 2 identical pebbles on the checkerboard (each on a different field/place) such that no two pebbles are on the same checkerboard diagonal. Two pebbles are on the same checkerboard diagonal if the connection segment of the midpoints of the respective fields are parallel to one of the diagonals of the n \times n square.
Source: Srednjoeuropska matematička olimpijada 2008, pojedinačno natjecanje, problem 2