Blue and red cells on a board
Source: Kvant Magazine No. 5 2023 M2748
January 9, 2024
boardcombinatorics
Problem Statement
In a board, some of the cells are blue, and the rest are red. No blue cells borders another blue cell on the side. The red cells, on the other hand, form a connected component (one may get from any red cell to any other red cell only by traversing edge-adjacent red cells). Prove that less than one third of the cells on the board are blue.Proposed by B. Frenkin