Draw a square ABCD with center M. Cut out the
triangle T= BMC.
Rotate and reattach T to an adjacent side of
whats left of the square
by lining up side BC with either CD or
AB.
Now you've got a six-sided figure. Suppose
you want to cut this
figure into two pieces that can reassembled into
the original square shape.
Of course, one way to do it is to lop of the
original triangle and put it back
where it came from.
Find another solution.
* * * * *
In Klarner's files there are some notes that credit
this highly addictive little
problem to some unknown person in Eindhoven. Does anyone know anything
more about it?
For more on Klarner's files (he died in
1999)