Chomp! Game (combinatorial Games)

Http://blog.csdn.net/acdreamers/article/details/17021095

There is an N * m chessboard, each time you can take a square and take away all the squares on its right and above. Get the lattice () in the lower-left corner, if it is 8*3

The status after (6, 2) AND (2, 3) are removed from the board.

Conclusion: the answer is that apart from the one-to-one board, the first-hand can win a board of other sizes.

Analysis: There is a clever proof that there is a winning strategy for the first hand. Unfortunately, this proof is not constructive, that is, it does not show how to win the first hand.

The proof is as follows:

If the latter hand wins, that is to say, the latter hand has a winning strategy, so that no matter which stone the first hand gets, the latter hand can win the final victory. Now let's assume that

FetchIn the top-right corner of the stone (n, m), the next hand through some method to make yourself into a winning situation. But in fact, the first hand can match

The latter took the same result this time and entered a winning situation, which is in conflict with assumptions.

Deformation of chocolate games:

About number games: 1 ~ N numbers. Two people take turns to select a number and erase it from its approximate number. Wipe the last number of people to win and ask who will win.

Analysis: similar to the chocolate game, the conclusion is that no matter the number of N is the first choice. (Assume that "1" is selected first ").

Chomp! Game (combinatorial Games)