Enro Rubik invented the puzzle which is now known as Rubik’s Cube in the 1970's. More than
100 million cubes have been sold worldwide. The mathematics behind solutions to the cube
have been extensively studied by mathematicians and puzzle enthusiasts alike. See the book by
Joyner  for example. Though I like puzzles, my history with the cube was one of failure. I
found it too difficult for me to solve a mixed-up puzzle and memorizing a long complicated
algorithm to solve the cube was not appealing to me. My youngest son became intrigued with
the cube and asked for one of his own. He played for a while with a cube I gave to him and, like
father - like son, discovered that the puzzle was too tough for him and asked me to solve the
I decided to see what tools for restoring the puzzle were available on the internet and found that
there are many sites devoted to online animated versions of the cube and automated cube solvers.
Several such programs allow the user to input the initial mixed-up state of the cube and then
provide a sequence of cube twists to restore the cube to the solved state. The program we used is
called Cube Explorer . A few months later, I gave the puzzle known as Rubik’s UFO to my
son for Christmas. Though he played with the puzzle longer than he had played with the Rubik’s
Cube, the result was the same. He returned the mixed-up puzzle to me to solve.
Solving Rubik’s UFO
Though I suspected that an internet search for a solution to Rubik’s UFO would be successful,
this time I did not want to take that route. I wanted discover a procedure for solving the puzzle
on my own. The first challenge was the fact that I wasn’t even certain what the solved state of
the puzzle looked like. In the holiday crush, the package the puzzle came in and the “hints
booklet” could not be found. Here is a picture of a mixed up UFO puzzle.
Twelve pieces are arranged in two "hexagons" forming the top and bottom of