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Make two copies of this puzzle.  Make the second copy the mirror image of the first.  That gives you twelve pieces rather than six.  It gives you twelve puzzles rather than one.

Five of the six pieces have mirror images which are different from themselves.  When you substitute a mirror image for one of these five, you have a new puzzle.  The new puzzle has a different solution.  One of the twleve different puzzles has seven solutions: it's the easiest to solve. 

One of the twleve has no solution.



These puzzles are rather difficult to solve, and when someone finds a solution to one it can be rather difficult to remember that solution.  Changing just one piece in the puzzle might make it the impossible puzzle.  A person who has just discovered a solution will usually not realize when a substitute is made (mirror images look pretty much alike).  If the new puzzle is the impossible puzzle, the solution has mysteriously disappeared.