🔢 IMO 2025 Problem 6 Visualizer

Visualization tool for IMO 2025 Problem 6 - Analyzing non-overlapping rectangular zero blocks in permutation matrices

📋 IMO 2025 Problem 6

Problem Statement:

"Consider a 2025 × 2025 grid of unit squares. Matlida wishes to place on the grid some rectangular tiles, possibly of different sizes, such that each side of every tile lies on a grid line and every unit square is covered by at most one tile.

Determine the minimum number of tiles Matlida needs to place so that each row and each column of the grid has exactly one unit square that is not covered by any tile."

🔍 How this tool helps

This visualization tool helps understand the problem by analyzing smaller n×n grids (permutation matrices) where:

    1s represent uncovered squares (one per row and column)
    0s represent squares covered by tiles
    Rectangular blocks of 0s represent the tiles Matlida places

Note: This tool visualizes the problem for smaller values of n to help understand the pattern. The actual IMO problem asks for n = 2025, which is computationally intractable to visualize completely.

⚠️ Note: For n > 8, the number of matrices becomes very large (n! = 40320 for n=8), which may cause browser performance issues. The limit is set to n ≤ 8.

Calculating permutation matrices and analyzing zero blocks...

📊 Results

Total Number of Permutation Matrices

0

🔍 Tile Analysis (Rectangular Zero Blocks)

📊 All Possible Grid Configurations