# 10 Dots, 10 Coins

If you have 10 dots on the ground, can you always cover them with 10 pennies without the coins overlapping?

**SOLUTION**

Assume the dots lie in a plane and the radius of a penny is 1. Make an infinite grid of circles with radii 1, as shown on the picture, and place it randomly in the plane.

If we choose any point in the plane, the probability that it will end up inside some circle of the grid is equal to S(C)/S(H), where S(C) is the area of a coin and S(H) is the area of a regular hexagon circumscribed around it.

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