bottleneck0111

If the set has only 1 odd number, its sum will be odd — not divisible by 2. But as soon as there are 2 numbers in the set (whether 2 odds or one even), then some subset will have an even sum.

So, the minimum number of elements needed in the set to guarantee a non-empty subset with a sum divisible by 2 is 2.

Answer: 2

Honestly bro, if there’s no limit on the grid, then it’s impossible to count — because even just two lattice points can form tons of different squares depending on size and rotation. So yeah, there would be infinite such squares.