Staircase problem
Source: India TST III-Problem 3
May 23, 2011
rectangleinductionLaTeXcombinatorics unsolvedcombinatorics
Problem Statement
Consider a square grid which is divided into unit squares(think of a chess-board). The set of all unit squares intersecting the main diagonal of the square or lying under it is called an -staircase. Find the number of ways in which an -stair case can be partitioned into several rectangles, with sides along the grid lines, having mutually distinct areas.