_
   ___|_|_
 _|_|_|_|_|
|_|_|_|_|_|_
  |_|_|_|_|_|
  |_|_|_|_|
    |_|

The above piece of chocolate looks like a square with 4 pieces stuck on to it. How can you divide it with 4 straight cuts that they may form four congruent squares when moved? (You may not move the pieces until all cuts have been made, and you may not rotate or flip over any of the pieces when moving them. Also, all the chocolate must be used to make the squares.)

            b---+
            |   |
    a---+---+   +---c
    |               |
+---+               +
|                   |
+---c               +---d
    |                   |
    +               b---+
    |               |
    +---d   a---+---+
        |   |
        +---+

One solution is to make the four cuts from a to a, b to b, c to c and d to d.  The pieces may be relocated to form four squares with each SQRT(5) units to a side.  The four squares, in comparison to the present figure, should appear tilted at an approximate 26.565 degree angle.

Edited on November 2, 2008, 5:50 am

Posted by Dej Mar on 2008-11-01 09:24:06