Rubik's Cube
The Rubik's Cube is a logic puzzle in the shape of a cube that is cut twice along each axis to allow the faces of the cube to be twisted. Each face is coloured differently so that when a face (or slice) is turned, part of the adjacent faces also turn. This "scrambles" the puzzle and sets up the player to rearrange the movable parts to restore the "solved state" where each of the coloured faces is complete.
NB: this is a huge subject and so from here I will concentrate on how we at Nottingham Hackspace have enjoyed the cube and how we teach solving the cube in our workshops.
The cube is full of mathematics and geek chic but is surprisingly easy to solve. We teach a semi-formal method that breaks down the large problem into a number of reasonable sub-steps. Depending on your frame of mind the method can be taught in a couple of hours, learned from the notes in a weekend, and memorised in a week or so. Armed with this knowledge, a successful learner can solve the cube from any of its 43 quintillion valid permutations within a couple of minutes and, with a little dedication and practice, quite consistently within 30-40 seconds.