I have a cross in the form of one square with four identical squares surrounding it

   _
 _|_|_
|_|_|_|
  |_|

Cut it into the fewest number of pieces possible such that, when rearranged the pieces form two smaller crosses of identical size.

I've gotten it to 9 pieces.

The trick was to realize that to get two similarly shape crosses of half the size (area), then the linear dimension shrinks to sqrt(2)*original.  Then start cutting on the diagonals.

    __
   | /|
 __|/\|__
|\   /   |
|/_  \ /\|
   |\/|
   |/\|

I'll leave the assembly of the pieces as an exercise for the reader

Posted by Bob Smith on 2006-03-06 14:59:14