MathDB

Probability of Two Selected Squares are Adjacent

Source: 2015 AIME 2 Problem 5

March 26, 2015

probability

Problem Statement

Two unit squares are selected at random without replacement from an

n\times n

grid of unit squares. Find the least positive integer

n

such that the probability that the two selected squares are horizontally or vertically adjacent is less than

\frac{1}{2015}