- Fire game is a game in which you have a ring with n candles ( n usually greater than 5).
- Each candle has two statuses: burn or not burn.
- With each move you can change the status of a candle, the two next to candles of this one will change together.
- When changing the status of a candle from not burn to burn, the cost is 1. But from burn to not burn cost is 0.
Ex: The ring has eight candles. The first, second and eighth have the status is burned. When we change the status of the first candle to not burn, the second and the eighth one will change to not burn together. After this move, the statuses of the three candles change to not burn.
- The purpose of this game is from the start status of the ring after x moves, all candles will burn. The cost and the move are minimal.