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 January 2nd, 2017, 07:08 AM #1 Newbie   Joined: Dec 2016 From: España Posts: 11 Thanks: 0 Math Focus: Logic 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!
 January 2nd, 2017, 07:25 AM #2 Senior Member   Joined: May 2016 From: USA Posts: 1,038 Thanks: 423 "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?
 January 2nd, 2017, 07:42 AM #3 Newbie   Joined: Dec 2016 From: España Posts: 11 Thanks: 0 Math Focus: Logic Along the grid lines, sorry for my english. Is like a 4x4 chessboard, with 16 regular squares. Thanks for your answer
 January 2nd, 2017, 08:30 AM #4 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 12,610 Thanks: 845 Is zigzagging allowed?
 January 2nd, 2017, 08:41 AM #5 Newbie   Joined: Dec 2016 From: España Posts: 11 Thanks: 0 Math Focus: Logic Yes Denis, if you do it in a single cut
 January 2nd, 2017, 09:15 AM #6 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 12,610 Thanks: 845 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?
 January 2nd, 2017, 09:26 AM #7 Newbie   Joined: Dec 2016 From: España Posts: 11 Thanks: 0 Math Focus: Logic 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
January 2nd, 2017, 09:36 AM   #8
Math Team

Joined: Oct 2011

Posts: 12,610
Thanks: 845

Quote:
 Originally Posted by relativo94 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?

 January 2nd, 2017, 09:41 AM #9 Newbie   Joined: Dec 2016 From: España Posts: 11 Thanks: 0 Math Focus: Logic No, I suppose is the same cut
 January 2nd, 2017, 10:42 AM #10 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 12,610 Thanks: 845 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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