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?

The final square will be 5 square units.
Each side will be sqrt(5).
You can get that length by taking a 2 x 1 rectangle, and cutting its diagonal.   Then the diagonal will be a side of the new square.

I assume that since we can't rotate, the final square will look rotated by the angle whose tangent is either 2 or 1/2.

But I haven't figured out the cuts yet.

Posted by Larry on 2004-10-10 13:10:28