

The Flexatube's layout is a
foursquare strip. 



It is a great and unique puzzle
discovered in 1939. Martin Gardner in his Second
Scientific American Book of Mathematical Puzzles and
Diversions (1961),^{1 }writes that Arthur
Stone discovered the Flexatube somewhat accidentally
working on a flexagon, and was very surprised with this
discovery.
The one hardly can imagine a puzzle which is so simple
to make, and so interesting and hard to solve as the
Flexatube is. Actually, this is a simple paper tube  a
paper cube without top and bottom faces. It can be
folded along its edges and its faces' diagonals; all
these lines should be previously precreased to have
smooth folding. The object of the puzzle is to turn the
tube inside out, folding it only along the lines between
the triangles, and without any other bends, folds or
other deformations of paper.
There are several different correct solutions to the
Flexatube found in different years by Arthur Stone, T.
S. Ransom, Hugo Steinhaus,
David Mitchell,^{2}
Stefan Louw, and
myself,^{3}
but anybody who managed to find even one solution to it
can say how interesting and hard at the same time the
solving process is.
A very surprising fact is that the very first solution
of the Flexatube has an intermediate step (exactly in
the midway) where the Flexatube changes into... its
smaller copy  a small cubical tube! Great tubereducing
trick!
Because of its external and internal elegancy and
mathematical harmony the Flexatube can be considered as
one of the best puzzles ever.
To solve the Flexatube you can easy make it, using
provided image of the unfolded puzzle. First, print the
Flexatube layout. For this, click the image at left;
it's marked with our special "printable puzzle"
pictogram. You will go to a new window with the
Flexatube layout; then you can print and cut it out.
Then carefully precrease and prefold the puzzle strip
along all dotted lines. And, finally, paste together two
opposite ends of the strip; the gray flap is the place
for glue.
Note that you can print the puzzle for your own use
only, and not for any kind of commercial profit. 
