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Discussion of Problem 1092. Transversal

I cant understand the problems!!!!
Posted by Xudong_LI 4 Jun 2016 12:47
Could someone tell me what's the meaning of this problem?my english is noot good.The google translation is bad.
Re: I cant understand the problems!!!!
Posted by c_pp 2 Jan 2017 23:36

let:
2D array[N][N],   and transversal is a cells of N , which for each row and each column has one cell in the transversal.
for example:
2D array:
    1) 2)  3)
=============
1)| 1  2   3
2)| 4  5   6
3)| 7  8   9

transversal-1: { (1;1) , (2;2) , (3;3) }  // (row, col) -- coordinate of a cell, .
transversal-2: { (1;1) , (2;3) , (3;2) }
transversal-3: { (1;2) , (2;1) , (3;3) }
transversal-4: { (1;2) , (2;3) , (3;1) }
transversal-5: { (1;3) , (2;1) , (3;2) }
transversal-6: { (1;3) , (2;2) , (3;1) }

Note that, there 1*2*3...*N = N!  different transversals exist.

Now, about problem: 2D array with 2N+1 x 2N+1 size , elements '+' or '-'.
And allowed  operation: can change sign to opposite in all cells in a transversal.

You are asked to determine if it is possible to obtain a table containing not more than 2N cells with the sign "+" by a sequence of such operations
Good Luck!