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2013 HMMT Guts #27: Intersection of Hypercube and Hyperplane

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March 26, 2013
HMMT

Problem Statement

Let WW be the hypercube {(x1,x2,x3,x4) ∣ 0≤x1,x2,x3,x4≤1}\{(x_1,x_2,x_3,x_4)\,|\,0\leq x_1,x_2,x_3,x_4\leq 1\}. The intersection of WW and a hyperplane parallel to x1+x2+x3+x4=0x_1+x_2+x_3+x_4=0 is a non-degenerate 33-dimensional polyhedron. What is the maximum number of faces of this polyhedron?
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