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\(A\) and \(B\) are two opposite corners of an \(n \times n\) board \((n \geq 1)\) divided into \(n^2\) unit squares. Each square is divided into two triangles by a diagonal parallel to \(A B\), giving \(2 n^2\) triangles in total. A piece moves from \(A\) to \(B\) going along the sides of the triangles and, whenever it moves along a segment, it places a seed in each of the triangles having that segment as a side. The piece never moves along the same segment twice. It turns out that after the trip every triangle contains exactly two seeds. For which values of \(n\) is this possible?
in Mathematics by Platinum (138,598 points) | 25 views

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