Tower Cube is a puzzle that is like a 2×2×3 Rubik's cube. The two 2×2 faces can be turned by quarter or half turns, but the four 2×3 faces only allow half turns. It is made by Gentosha.
Taking one of the piece in the middle layer as a reference point, the three other middle layer pieces can be arranged in 3! ways, and the 8 corner pieces can be rearranged in 8! ways. This gives a total of 8!·3! = 241,920 positions.
A computer search gave the following result:
|Face turn metric|
This shows that at most 14 moves are needed to solve the puzzle (9.7372 on average), or 15 (10.603 on average) if half turns of the square faces count as two moves.
Hold the puzzle with the square faces at the top and bottom. Clockwise quarter turns of the top or bottom layer will be denoted by U and D respectively, half turns by U2 and D2, and finally counter-clockwise turns by U' and D'. For a half turn of a side the notation F, B, L, and R represent turns of the front, back, left and right face respectively.
Phase 1: Solve the top and bottom layers.
Phase 2: Solve the middle layer.