January 2nd, 2017, 08:08 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, 08:25 AM  #2 
Senior Member Joined: May 2016 From: USA Posts: 632 Thanks: 257 
"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, 08:42 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, 09:30 AM  #4 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 9,441 Thanks: 640 
Is zigzagging allowed?

January 2nd, 2017, 09:41 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, 10:15 AM  #6 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 9,441 Thanks: 640 
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, 10:26 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, 10:36 AM  #8 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 9,441 Thanks: 640  
January 2nd, 2017, 10:41 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, 11:42 AM  #10 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 9,441 Thanks: 640 
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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