Math Insight (short)
- Key idea: Look for something that stays the same after each move (an invariant).
- Why it works: When you flip exactly 2 switches, the parity (even/odd) of the number of black switches never changes.
- What it teaches: Some states are impossible not because of “lack of moves,” but because a hidden quantity blocks you.
Try both rules:
- Flip 2: parity can block you. If black count is odd, you can never reach 0.
- Flip 3: parity flips each move, so you need a different strategy.