2023 Combinatorics #4
Source:
April 17, 2023
Problem Statement
The cells of a grid are each colored red, white, or blue. Sam starts at the bottom-left cell of the grid and walks to the top-right cell by taking steps one cell either up or to the right. Thus, he passes through cells on his path, including the start and end cells. Compute the number of colorings for which Sam is guaranteed to pass through a total of exactly red cells, exactly white cells, and exactly blue cells no matter which route he takes.