Parity Grid

Parity Grid is a small grid of numbers. Pressing any tile adds 1 to that tile and to each tile directly above, below, left and right of it. Your goal is to make every number on the board divisible by the target — 2 on the easier boards, meaning every number ends up even, and 3 on the harder ones.

The catch is that you can never change one number alone. Press a tile in the middle of a 3x3 board and five numbers move at once, so a press that fixes the number you were looking at will usually break a neighbour. Some tiles are locked: you cannot press them, but they still receive +1 from the presses around them, which means you have to reach them indirectly. Pressing the same tile twice on a divisible-by-2 board undoes itself, so the useful question is not which tiles to press but how many times each one needs pressing.

It suits students who have just learned about even and odd numbers or multiples of 3 and are ready to use that knowledge rather than recite it. Older students meet a genuine piece of mathematics here: the board is a system of linear equations in disguise, and the fastest solutions come from spotting that structure.