To understand the question better
Isn't for 2x2
a valid answer?
2. For 3x3
1 1 0
0 1 1
1 0 1
1 1 0
1 1 0
0 0 0
the problem is to count how many binary matrices there are with following properties
i. every column must have even number of 's
ii. every row must have even number of 's
For matrices there is none. For matrices there is one:
I think for 3x3 there isn't any. Atleast I couldn't construct one, but I suck at Sudoku's.
The number of square binary matrices is calculated with . So, I though maybe substracting the matrices without even number of 's from that number would help, but then we come the problem, how to pick out the correct matrices.
Any help is appreciated. Thank you!
Yeah, you are right, those cases should be included too. Fooled myself to think, when there's no [tex]1[/tex]'s in row/column, the amount is not even or odd (kinda undecidable or something). That's clearly wrong. I think I can make inductive proof for your formula. Thanks very much for help! It clarified my thoughts very well.
Hmm. There's one problem with your formula. For it gives . But I think there's only of those matrices. All matrices:
Only 0. and 15. qualify, I think. So, we need new equation or I'm completely lost. Thanks.