This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

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Found problems: 2

2017 Kürschák Competition, 3
Tags: latin square , table , permutation , sudoku , combinatorics
An $n$ by $n$ table has an integer in each cell, such that no two cells within a row share the same number. Prove that it is possible to permute the elements within each row to obtain a table that has $n$ distinct numbers in each column.

2020 Iran MO (3rd Round), 3
Tags: latin square , combinatorics
Consider a latin square of size $n$. We are allowed to choose a $1 \times 1$ square in the table, and add $1$ to any number on the same row and column as the chosen square (the original square will be counted aswell) , or we can add $-1$ to all of them instead. Can we with doing finitly many operation , reach any latin square of size $n?$