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 OK, here goes nothing. by Juggler)

At first I thought you had it.  But no.  In order for this to work, you need to fit exactly 4 rectangles along one side exactly filling that side.  5 rectangles along the other sides, overlapping just enough to cover those 2 sides and the short edges of the two rectangles on the other 2 sides.  But by looking at the original tic-tac-toe cut, it only takes three rectangles to cover a side, and 4 to cover the other sides plus the short edges. 

You're going to have 4 rectangles left over.

Edited on October 20, 2004, 4:38 am

Posted by Ken Haley on 2004-10-20 04:33:50