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?

2 Cuts, 3 pieces:

 __ __
|__| /|        /|'-., 
   |/ |__  => / |__  /
   |`'+.,|     `'-.|/

And that's my messy drawing.

More specific cutting instructions:  Label  all the intersections left to right, top to bottom as A-L.  Cut from C to G, and G to L.

I have no proof of maximization, but it seems impossible to get any better.

A note on maximization, how are we supposed to maximize both pieces and cuts?  Do we maximize them separately (perhaps there is a case with only two pieces but nine cuts) or maximize their sum, etc.  I think, however that no matter the answer, this solution will be best.

Posted by Tristan on 2004-10-10 18:34:13