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 $\left\lfloor \frac{n_0}{3} \right\rfloor$ .

Mock AIME 5 2005-2006 (Problems, Source)
Preceded by Problem 6	Followed by Problem 8
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15

Page

Toolbox

Search

Mock AIME 5 2005-2006 Problems/Problem 7

Contents

Problem

Solution

Solution

See also