If you have 10 dots on a table, can you always cover them with 10 pennies without overlapping?
Remark: You can assume the dots are not too close to the edge of the table.
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 stands for “area”.