Problem

Source: (2022-) 2023 XVI 16th Dürer Math Competition Finals Day 2 E11

Tags: combinatorics



The binary sudoku is a puzzle in which a table should be filled with digits $0$ and $1$ such that in each row and column, the number of 0s is equal to the number of $1$s. Furthermore, there cannot exist three adjacent cells in a row or in a column such that they have the same digit written in them. Solving the given binary sudoku, what is the sum of the numbers in the two diagonals?