In a 10*10 matrix there are 92 ones and the rest is zeroes and twos.

Prove (not by simulation) that the value of the determinant of the above matrix is divisible by 3.

The eight positions that are not 1's can occupy at most 8 rows, and at most 8 columns. That leaves at least 2 rows and 2 columns that are all 1's, and are therefore identical.

With 2 identical rows, the determinant must be zero, which is divisible by 3.