MathDB

3

Part of IMSC 2023

Problems(1)

Grid 9x9 with 0 and 1

Source: IMSC 2023 Mock IMO P3

7/13/2023
A binoku is a 9×99 \times 9 grid that is divided into nine 3×33 \times 3 subgrids with the following properties: - each cell contains either a 00 or a 11, - each row contains at least one 00 and at least one 11, - each column contains at least one 00 and at least one 11, and - each of the nine subgrids contains at least one 00 and at least one 11.
An incomplete binoku is obtained from a binoku by removing the numbers from some of the cells. What is the largest number of empty cells that an incomplete binoku can contain if it can be completed into a binoku in a unique way?
Proposed by Stijn Cambie, South Korea