Box Game |
There are two identical boxes. One of them contains n balls, while the other box contains one ball. Alice and Bob invented a game with the boxes and balls, which is played as follows:
Alice and Bob moves alternatively, Alice moves first. For each move, the player finds out the box having fewer number of balls inside, and empties that box (the balls inside will be removed forever), and redistribute the balls in the other box. After the redistribution, each box should contain at least one ball. If a player cannot perform a valid move, he loses. A typical game is shown below:
When both boxes contain only one ball, Bob cannot do anything more, so Alice wins.
Question: if Alice and Bob are both clever enough, who will win? Suppose both of them are very
smart and always follows a perfect strategy.
2 3 4 0
Alice Bob Alice
The Seventh Hunan Collegiate Programming Contest
Problemsetter: Rujia Liu, Special Thanks: Yiming Li & Jane Alam Jan