Tian on Nostr: Use integer coordinates in the obvious way. (The non-obvious details don't matter.) ...

Use integer coordinates in the obvious way. (The non-obvious details don't matter.) For a position at (x,y) call (x mod 2,y mod 2) its parity type. There are four different parity types, so five different positions have at least one pair of positions with the same parity type. Such a pair has an even difference in both the x- and the y-coordinate, so their midpoint has integer coordinates and therefore is another point on the grid.