i haven't read it, but wikipedia tells me that the eric frank russell short story now inhale refers to the tower of hanoi game as "arkymalarky." myself, i think tower of hanoi, or even tower of brahma or tower of benares, is a much more dignified name for this compelling little math game.
the object is to move a set of graduated spherical solids from one position to another, usually indicated by pegs. there must be at least one empty peg on which to hold the spheres, a sphere may not be placed atop another with a smaller diameter, and the final tower must exactly mimic the starting configuration.
naturally, there are algorithmic ways to approach the puzzle and it gets more challenging as the number of spheres increases. here's a fun little virtual tower to play with.