Show that if any seven points am chosen in a regular hexagon whose sides are of 1 unit, then two of them must be no further apart than 1 unit.

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written 7.9 years ago by

teamques10 ★ 68k

modified 2.9 years ago by

sagarkolekar ★ 11k

discrete mathematics

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written 7.9 years ago by

teamques10 ★ 68k

From the center of the hexagon, draw a line to each vertex. This will partition the hexagon into 6 equilateral triangles, each with side of length 1. If 7 points are chosen, then there must be 2 points being in a same triangle according to pigeonhole principle and the distance between these two points should not be greater than 1. Consider the figure shown below.

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