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 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.