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?

I think I can do it in 4 cuts.

Label the squares ABCD and E, where A is the upper left,, C is the middle, and E is the lower right.

Cut AB from lower left to upper right.
Cut between B and C.
Cut CD from upper left to lower right.
Cut between D and E.

Block E will be a square in the center of the new larger square.
There are now 4 other pieces, each is a triangle 1 by 2 by sqrt(5).  Simply look at where the hypotenuse is facing to know which of the 4 sides of the new squrare that triangle will become.

For example, the upper half of AB has a hypotenuse facing kind of southeast.   So move it to the bottom of E, so that its left edge aligns with E's left edge and the point is sticking out to the right.

Now take the left half of CD, whose hypotenuse points up and to the right, move it to the left side of square E.  Note that the bottom edge of this triangle (left half of CD) will rest on the pointed part of the first triangle that was sticking out to the right.

Posted by Larry on 2004-10-10 13:29:52