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It's possible if and only if n=1 or n is even

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September 20, 2010
geometry3D geometrycombinatoricspackingIMO Shortlist

Problem Statement

Prove that it is possible to place 2n(2n+1)2n(2n + 1) parallelepipedic (rectangular) pieces of soap of dimensions 1×2×(n+1)1 \times 2 \times (n + 1) in a cubic box with edge 2n+12n + 1 if and only if nn is even or n=1n = 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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