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find the number of rhombi

Source: Austria 1986

July 7, 2009
analytic geometrygeometryrectanglefloor functionceiling functiongeometry unsolved

Problem Statement

For s,tāˆˆN s,t \in \mathbb{N}, consider the set M\equal{}\{ (x,y) \in \mathbb{N} ^2 | 1 \le x \le s, 1 \le y \le t \}. Find the number of rhombi with the vertices in M M and the diagonals parallel to the coordinate axes.
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