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The game criteria is intentionally very open-ended. The goal is to make a game that incorporates logic into a fun challenge. Thus far, many students are opting to adapt a game that already exists, but one could design a game from scratch if they so desired.
For refresher, there are seven logic operations one will want to make use of. This includes:
AND OR XOR
NOT
NAND NOR XNOR
A B | Y ----|-- 0 0 | 0 1 0 | 0 0 1 | 0 1 1 | 1