MathDB

P6

Part of 2010 Peru Iberoamerican Team Selection Test

Problems(1)

In how many ways can a 99-ladder be divided?

Source: 2010 Peru Iberoamerican TST problem 6

5/10/2023
On an nn × nn board, the set of all squares that are located on or below the main diagonal of the board is called then−laddern-ladder. For example, the following figure shows a 3−ladder3-ladder: [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 99−ladder99-ladder be divided into some rectangles, which have their sides on grid lines, in such a way that all the rectangles have distinct areas?
combinatorics