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January 2nd, 2017, 08:08 AM   #1
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How to divide a board

I have a problem that says:
We want to divide a 4x4 board into two parts with the same area with a single cut through the grid lines. How many ways can I do it?

I don't know how to solve this problem. Any suggestion? Thanks!
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January 2nd, 2017, 08:25 AM   #2
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"Through" the grid lines or "along" the grid lines? In either case, how many grid lines are there, where are they placed relative to the edges, and how are they oriented relative to the edges?
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January 2nd, 2017, 08:42 AM   #3
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Along the grid lines, sorry for my english. Is like a 4x4 chessboard, with 16 regular squares.

Thanks for your answer
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January 2nd, 2017, 09:30 AM   #4
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Is zigzagging allowed?
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January 2nd, 2017, 09:41 AM   #5
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Yes Denis, if you do it in a single cut
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January 2nd, 2017, 10:15 AM   #6
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1 1 1 1
2 2 1 1
2 2 2 1
2 2 2 1

Are different resulting shapes (like above) allowed?
Or must shapes be identical?
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January 2nd, 2017, 10:26 AM   #7
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There are more. For example

1 1 2 2
1 1 2 2
1 1 2 2
1 1 2 2

or

1 1 1 1
1 2 2 2
1 2 2 2
1 1 2 2
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January 2nd, 2017, 10:36 AM   #8
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Quote:
Originally Posted by relativo94 View Post
1 1 1 1
1 2 2 2
1 2 2 2
1 1 2 2
1 1 1 1
2 2 2 1
2 2 2 1
2 2 1 1

That one is same as the one you're showing above;
it is the one you're showing after being "flipped":
do you consider them as 2 different cuts?
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January 2nd, 2017, 10:41 AM   #9
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No, I suppose is the same cut
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January 2nd, 2017, 11:42 AM   #10
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Well, make up your mind...; if so:

1 1 1 1
1 1 1 1
2 2 2 2
2 2 2 2

is same as:

1 1 2 2
1 1 2 2
1 1 2 2
1 1 2 2

is same as:

2 2 2 2
2 2 2 2
1 1 1 1
1 1 1 1

is same as:

2 2 1 1
2 2 1 1
2 2 1 1
2 2 1 1
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