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

Home > Shapes
Zquare (Posted on 2004-10-10) Difficulty: 3 of 5

You have 5 squares joined by their sides in a Z pattern as shown. What is the fewest number of pieces and straight cuts neccesary so the pieces can form a single larger square if you can't use cuts that aren't straight, you can't move the pieces until all cuts have been done, you can't bend, fold or flex the squares, and you can't rotate or flip over the pieces when moving them to form the giant square?

No Solution Yet Submitted by Gamer    
Rating: 3.5000 (6 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
2 cuts. | Comment 11 of 23 |

I don't know if anyone already got this--I haven't read anyone else's answers.

The side of the new square must be sqrt(5), which happens to be the diagonal of a 1x2 rectangle.  After realizing that, it's not too hard to discover the following solution:

Letter the perimeter of the original figure starting at the upper left and working clockwise, placing a letter at every corner of every original square.  The lettering will look something like this

A  B  C
L   K  D
    J   E   F
    I   H  G

Cut from A to D then D to I.  Move the lower right segment to the left and up so that D on the lower right segment coincides with A of the original figure.  Move the upper right piece so that C coincides with J of the original figure.

Two cuts does it.

  Posted by Ken Haley on 2004-10-11 03:22:23
Please log in:
Remember me:
Sign up! | Forgot password

Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (5)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Copyright © 2002 - 2021 by Animus Pactum Consulting. All rights reserved. Privacy Information