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Prove that it is possible to place 2n(2n + 1) parallelepipedic (rectangular) pieces of soap of dimensions 1 \times  2 \times  (n + 1) in a cubic box with edge 2n + 1 if and only if n is even or n = 1.

Remark. It is assumed that the edges of the pieces of soap are parallel to the edges of the box.

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