Consider the region shown below. It is bounded by a regular hexagon whose sides are the length 1 units.

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written 8.2 years ago by

krrish • 360

modified 2.9 years ago by

sagarkolekar ★ 11k

Show that if any seven points are chosen in this region then two of them must be no further apart than 1 unit. enter image description here

discrete mathematics

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written 8.2 years ago by

krrish • 360

Now we must ﬁnd the pigeons and the pigeonholes...So divide the hexagon into six equal regions.Each will be an equilateral trangle of length of each side as one unit.Now these are our pigeonholes and the points as our pigeons. So by Pigeon Hole Principle two points will be in the same triangle. Thus they will be at a distance less than one unit.Hence Proved

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