Take a square and cut it as you wish into a finite number of pieces. Rearrange the pieces without rotating or flipping any of them to form an new square that is rotated 45-degrees compared to the original.

(In reply to One possible Solution (visual) by SteveH)

I tried putting this together and it doesn't work.  (Am I wrong here?  I'd like to see a second picture.)

There are no 45 degree segments which are rational with the sides of the square.  This means you can't fit them.

I fooled myself a couple of times when I started with a 12x12 square on graph paper.  The target square is close 8.5 digonals on a side.  In fact, the area of this 'rotated' square is 144.5 units.

-Jer

Posted by Jer on 2004-10-20 11:36:29