Abstract
We answer a problem posed recently by Knuth: an n-dimensional box, with edges lying on the positive coordinate axes and generic edge lengths W 1 < W 2 < ⋯ < W n , is dissected into n! pieces along the planes x i = x j . We describe which pieces have the same volume, and show that there are C n distinct volumes, where C n denotes the nth Catalan number.
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