The Counting Game is a game played between two players. The first player starts
counting at 1, and can say no more than maxAdd numbers. The second player continues
counting from where the first player left off. The two players alternate, each one
contributing at least one but no more than maxAdd numbers. The player who says
the goal number is the winner.
For example, if maxAdd is 3 and the goal is 20, then a game (between bad players A and B) might
go like this:
A: 1,2,3 ... B: 4,5 ... A: 6 ... B: 7,8,9 ... A: 10,11,12 ... B: 13
... A: 14 ... B: 15,16 ... A: 17,18 ... B: 19,20
Since player B said the goal number, she was the winner.
There is a perfect strategy for this game. When maxAdd is 3, if you end your turn by saying 16, then no
matter whether your opponent contributes 1, 2, or 3 numbers you will be able to
count to 20 on your next turn. Similarly, if you end your turn by saying 12, then no matter
what your opponent
does you can end your next turn by saying 16, and thus win on your following turn.
Create a class CountGame to help you play this game. It should contain a method
howMany that is given maxAdd, the
most numbers you may say on each turn, goal, the goal number, and next, the number
that you must start counting on. The method
should return how many numbers you should say. If there is no way for you to force
a win, then the method should return 1.
