The colour of a square from its coordinates

Every square is light or dark, and you can tell which without looking at a board. Number the files $1$ to $8$ (a = 1) and use the rank number as it is. Add them. If $\text{file} + \text{rank}$ is even the square is dark; if it is odd the square is light. On a1 the sum is $1 + 1 = 2$, which is even, so a1 is dark.

This is parity: only whether the sum is odd or even matters, not its size. Two squares share a colour exactly when their coordinate sums have the same parity. One rule replaces memorising the whole pattern.