Your paper is too...
This question can be solved by 0,1, Matrix.I think You are smart enough to get a very strict verification from nest example:
there 4 piles : 3 , 5, 8, 10. We transfer them to binary numbers 11,101,1000,1010.We get 0,1 matrix
0 0 1 1
0 1 0 1
1 0 0 0
1 0 1 0
We call it is odd,cos we can find the sum of second column(any column) is odd the first win,she(or he) take 4 (100) from 5 (101).she(or he) get a even matrix in which the sum of all column is even.The key point is no matter the second how to do she(or he)can not get even matrix.The first always can keep the even to end.If the matrix is even, the first is loser.Math is beautiful, but kills a funny game.
This question can be solved by 0,1, Matrix.I think You are smart enough to get a very strict verification from nest example:
there 4 piles : 3 , 5, 8, 10. We transfer them to binary numbers 11,101,1000,1010.We get 0,1 matrix
0 0 1 1
0 1 0 1
1 0 0 0
1 0 1 0
We call it is odd,cos we can find the sum of second column(any column) is odd the first win,she(or he) take 4 (100) from 5 (101).she(or he) get a even matrix in which the sum of all column is even.The key point is no matter the second how to do she(or he)can not get even matrix.The first always can keep the even to end.If the matrix is even, the first is loser.Math is beautiful, but kills a funny game.
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