KöMaL 2026 C1898

We would like to select some of the nine lattice points of a $2\times 2$ square lattice such that no three of them form a right triangle. a) Prove that it's not possible to select five points with the property above. b) How many ways are there to select four points satisfying the above property? (Two selections are considered different if there is a point that is selected in one of them and not selected in the other.)