# Mock AIME 5 2005-2006 Problems/Problem 7

## Problem

A coin of radius $1$ is flipped onto an $500 \times 500$ square grid divided into $2500$ equal squares. Circles are inscribed in $n$ of these $2500$ squares. Let $P_n$ be the probability that, given that the coin lands completely within one of the smaller squares, it also lands completely within one of the circles. Let $P$ be the probability that, when flipped onto the grid, the coin lands completely within one of the smaller squares. Let $n_0$ smallest value of $n$ such that $P_n > P$. Find the value of $\left\lfloor \frac{n_0}{3} \right\rfloor$.