How many non-attacking pawns can be placed on a $n \times n$ chessboard?
Source: 2019 Pan-African Shortlist - C1
January 18, 2021
combinatorics
Problem Statement
A pawn is a chess piece which attacks the two squares diagonally in front if it. What is the maximum number of pawns which can be placed on an chessboard such that no two pawns attack each other?