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Groups of Three Collinear Points

Source: 1998 National High School Mathematics League, Exam One, Problem 6

March 9, 2020
geometry3D geometry

Problem Statement

In the 27 points of a cube: 8 vertexes, 12 midpoints of edges, 6 centers of surfaces, and the center of the cube, the number of groups of three collinear points is (A)57(B)49(C)43(D)37\text{(A)}57\qquad\text{(B)}49\qquad\text{(C)}43\qquad\text{(D)}37
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