Grasshopper jumps to adjacent cells
Source: Azerbaijan NMO 2022, Senior P2
August 12, 2023
combinatorics
Problem Statement
Each cell of the 4x4 board has a grasshopper. When a grasshopper jumps, it moves to one of the adjacent cells (down, up, right, or left). The grasshopper cannot move diagonally or go off the board. At most how many cells can remain empty after each grasshopper jumps once?