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A diamond (a parallelogram with equal sides) is given, and its sides are 2 cm long. The sharp angels are 60 degrees. If there are nine points inside the diamond, prove that there must be two of them so that the distance between them is at most 1 cm.

Ideas where to start from?

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    I believe that “a parallelogram with equal sides” is usually called a “rhombus”.2014-01-16

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Hint: Split the diamond into eight congruent equilateral triangles. The triangles are your pigeon holes.

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    @André, thanks for the thought, but it is two-dimensional diamond.Therefore, this hint will do the job.2012-06-10