All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Shapes
Imperfect Square (Posted on 2004-10-14) Difficulty: 3 of 5
       _
   ___|_|_
 _|_|_|_|_|
|_|_|_|_|_|_
  |_|_|_|_|_|
  |_|_|_|_|
    |_|
The above piece of chocolate looks like a square with 4 pieces stuck on to it. How can you divide it with 4 straight cuts that they may form four congruent squares when moved? (You may not move the pieces until all cuts have been made, and you may not rotate or flip over any of the pieces when moving them. Also, all the chocolate must be used to make the squares.)

No Solution Yet Submitted by Gamer    
Rating: 3.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Method for solving this type of dissection problem | Comment 2 of 8 |

This shape tessellates.  If you draw a few copies on a sheet of graph paper you can make your cuts as continuous lines across many copies of the shape.

If these cuts are parallel to lines connecting the centers of neighboring shapes, they will cut all shapes the same.

Note for this shape, the lines connecting neighboring centers have slopes of 1/2 and -2 (or -1/2 and 2)

This is just the slope you need to get sides = 5

The only thing left is to find four such lines that fit inside one shape.  They are two perpendicular sets.

nikki described the placement of these lines well, I think.

The tesselation shows how the pieces will re-form into squares.

-Jer

(sorry if that made no sense at the end)


  Posted by Jer on 2004-10-14 16:15:13
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (2)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information