An *n*-dimensional hypercube is the convex hull of the 2^{n} points
(*x*_{1}, *x*_{1}, ..., *x*_{n}), where
the *x*_{i} are 0 or 1. The hyperplanes
*x*_{1} + *x*_{1} + ... + *x*_{n} = *k*,
*k* = 1,2, ..., *n* − 1 divide the hypercube into *n* pieces. Find
the hypervolume of each piece.

For example, when *n*=2 we have a square divided into two isosceles right triangles
each of area 1/2. When *n*=3 we have a cube divided into two pyramids and an
octahedron. The pyramids each have volume 1/6 and the octahedron has volume 2/3.

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