Piles of stones in a row. Players alternate taking piles from the front, where . After taking, becomes . Initially . Both play optimally.
What's the max stones Player 1 can get? Example: piles , . Player 1 can take or piles. Taking gives stones and sets . Now Player 2 can take to piles... The variable adds a new dimension to the state. This problem combines interval-style thinking with an extra parameter.