MathDB
Dividing a 2n by 2n grid

Source: BxMO 2024 P2

April 27, 2024
combinatorics

Problem Statement

Let nn be a positive integer. In a coordinate grid, a path from (0,0)(0,0) to (2n,2n)(2n,2n) consists of 4n4n consecutive unit steps (1,0)(1,0) or (0,1)(0,1). Prove that the number of paths that divide the square with vertices (0,0),(2n,0),(2n,2n),(0,2n)(0,0),(2n,0),(2n,2n),(0,2n) into 2 regions with even areas is (4n2n)+(2nn)2\frac{{4n \choose 2n} + {2n \choose n}}{2}
Back to ProblemsView on AoPS