Segments Perpendicular to a Diagonal

★ 8/10combinatorics Counting solid geometry Casework

Problem

Let $l$ be a space diagonal of a cube, and let $S$ be the set consisting of the cube's vertices and the midpoints of its edges. How many segments joining two points of $S$ are perpendicular to $l$ ?

Answer

Solution

Difficulty	8/10
Topics	combinatorics, Counting, solid geometry, Casework

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