In how many ways can a 99-ladder be divided?
Source: 2010 Peru Iberoamerican TST problem 6
May 10, 2023
combinatorics
Problem Statement
On an × board, the set of all squares that are located on or below the main diagonal of the board is called the. For example, the following figure shows a :
[asy]
draw((0,0)--(0,3));
draw((0,0)--(3,0));
draw((0,1)--(3,1));
draw((1,0)--(1,3));
draw((0,2)--(2,2));
draw((2,0)--(2,2));
draw((0,3)--(1,3));
draw((3,0)--(3,1));
[/asy]
In how many ways can a be divided into some rectangles, which have their sides on grid lines, in such a way that all the rectangles have distinct areas?