The Professor's Cube is a fiendshly difficult puzzle based on the Rubik's Cube.

As opposed to the Rubik's Cube's 3x3x3 construction, the Professor's Cube is 5x5x5.

It is the sequel to a puzzle known as Rubik's Revenge which had.......yes you've guessed is, 4x4x4 construction.

The Professor's Cube is also known as Rubik's Delusion and is known to be one of toughest puzzles of it's type.

The following info is from Jaap's Puzzle Page:

The number of positions:
There are 8 corner pieces with 3 orientations each, 24 side edge pieces and 12 central edge pieces with 2 orientations each, 24 inside corner pieces, and 24 inside edge pieces, giving a maximum of 8! * 24!^3 * 12! * 3^8 * 2^36 positions.

This limit is not reached because:

The total twist of the corners is fixed (3)
The side edge orientation is dependent on its position (2^24)
The number of central edge flips is even (2)
There are indistinguishable inside face pieces (4!^12)
The permutation of corners and central edges is even (2)
This leaves 8! * 24!^3 * 12! * 3^7 *2^10 /4!^12= 282,870,942,277,741,856,536,180,333,107,150,328,293,127,731,985,672,134,721,536,000,000,000,000,000 or 2.8*10^74 positions.

Jaap's puzzle page can be found at

Another nodeshell rescue!