MathDB

M2753

Part of Kvant 2023

Problems(1)

Find the number of equivalency classes under a weird operation on permutations

Source: All-Russian MO 2023 Final stage 11.3

4/23/2023
In every row of a grid 100×n100 \times n is written a permutation of the numbers 1,2…,1001,2 \ldots, 100. In one move you can choose a row and swap two non-adjacent numbers with difference 11. Find the largest possible nn, such that at any moment, no matter the operations made, no two rows may have the same permutations.
combinatorics