Pigeon principle question: Nine points in a diamond 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?

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