The Bandaged 2×2×2 is a 2×2×2 Rubik's Cube where two pairs of corners are fused together to become 2×1×1 blocks. The puzzle therefore has four normal corner cubes and two fused blocks. In the solved position the fused blocks are not parallel.
There are 7 arrangements that the two fused blocks can have relative to each other. The unbandaged corners can only be permuted in a 4-cycle, so have just 4 permutations. They can only be twisted by the same amount (though in alternating directions), and so have just 3 orientations. Together this gives 7·4·3 = 84 positions that can be reached.
The table below shows how many moves each position of the Bandaged 2×2×2 needs to solve. It shows the puzzle can be solved in no more than 10 moves (5.4167 on average) or 15 quarter turns (7.8095 on average).
|Face turn metric|
Hold the puzzle with one fused block along the bottom left edge of the cube. There are only two faces that might be able to be moved - the top face, denoted by U, and the right face, denoted by R. A clockwise quarter turn of a face is denoted by the letter of the face, i.e. U or R. Anti-clockwise turns are denoted by an apostrophe, i.e. U' or R', and half turns by a 2, i.e. U2 or R2.