By placing 27 squares with an area of 1 meter inside of a circle with the radius of 2 meters, prove that exist such a point that belongs to 3 different squares. (each one of the squares $\subseteq$ in the circle completely)
now I know that the combined area of the squares is 27 and 2 combined area of the circles is only $8\pi<27$ so the point that I need to prove that exist is indeed exist but I can't figure out how to do it formally with the Pigeonhole principle.
thanks in advance and sorry about the english
edited: I need a solution that involves the Pigeonhole principle
At first, packing like following image. $S_{rest}=2^2π-12=0.56$. This is limit packing. When full packing with 13 squares in one method, if rest one area of a square size, it's contradict against full packed. Therefore 13's packing of two type doesn't never lose one area of square size simultaneously. Therefore PHP prove.