/sci/ - Science & Math

>>12615823
Suppose it were row 4. By Lemma 1, A1, A2, and A3 must be occupied by red or green. In order for red and green to be congruent, D1, D2, and D3 must be occupied by the opposite color of A3, A2, and A1 respectively. However, if D1, D2, and D3 are occupied by red and green, then blue cannot occupy the necessary eight squares. Then it cannot be row 4.

Therefore, it is impossible to remove a square from a 5x5 grid and cut the remaining squares into three congruent parts. QED.