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?

(In reply to Bad solution by Sam)

Indeed, if cuts are not required to go allt he way through, you could do the same thing in four cuts:

Taking 1 to be the length of the side of one small square

1 - Make a horizontal cut .25 of the way up
2 - Make a horizontal cut another .25 of the way up, thus making two strips, .25 x 2
3 - Make a horizontal cut separating the bottom two squares from the group
4 - Make a vertical cut separating the two bottom squares, starting above them and going down only half way.

This leaves you with two rectangles .5 x 1 and two strips .25 x 2.

Put the first two rectangles together to make a square. Place  this with the other three to make a 2x2 square. Put the two long strips on the sides of this square, making a 2.25 x 2.25 square.


I expect that this won't be the best solution either.

Posted by Sam on 2004-10-10 10:32:51