Ranking the Puzzles by Number of Combinations ---------------------------------------------
Name Combinations Mechanism ---- ------------ ---------
1. Rubik's Wahn (5x5x5) 2.8*10^74 Udo Krell 2. Megaminx 10^68 Kersten Meier, Ben Halpern 3. Rubik's Revenge (4x4x4) 7.4*10^45 Unknown 4. Pyraminx Hexagon (A) 2.9*10^30 No known mechanism 5. VIP Sphere 4.4*10^26 Unknown 6. Impossi-ball 2.4*10^25 Wolfgang Kuppers 7. Picture Cube (3x3x3) (E) 8.8*10^22 Erno Rubik, Dan Hoey 8. Calendar Cube (3x3x3)(F) 4.4*10^22 Marvin Silbermintz 9. Rubik's Cube 4th Dim.(D) 1.1*10^22 Erno Rubik 10. Rubik's Cube (3x3x3) 4.3*10^19 Erno Rubik 11. Pyraminx Octahedron 8.2*10^18 Unknown 12. Octagon 5.4*10^18 Unknown 13. Christoph's Jewel (B) 2.0*10^15 Christoph Bandelow 14. Master Pyraminx (C) 4.5*10^14 Uwe Meffert 15. Barrel 2.7*10^14 Gumpei Yokoi 16. 15 Puzzle 1.3*10^12 Sam Lloyd 17. Missing Link 8.2*10^10 Marvin Glass & Associates 18. Trillion 1.0*10^9 Unknown 19. Rubik's Domino (3x3x2) 4.0*10^8 Erno Rubik 20. Picture Skewb 1.0*10^8 Tony Durham, Uwe Meffert 21. Pyraminx 7.6*10^7 Uwe Meffert 22. Pocket Cube (2x2x2) 3.6*10^6 Enro Rubik 23. Skewb 3.1*10^6 Tony Durham 24. Snub Pyraminx 9.3*10^5 Uwe Meffert 25. Simple Octahedron 5.0*10^4 No known mechanism
(A) This assumes 90 degree turns for the faces adjacent to the top face
(B) This is a snub Pyraminx Octahedron (Octahedron minus the tips)
(C) This assumes a Pyraminx visually the same as a regular pyraminx
with rotations about the 4 vertices AND 6 edges.
(D) Yet another picture cube that does not have 4 orientations for
each of it's 6 centres.
(E) This assumes a cube with centres which can show 4 distinct
orientations for all 6 centres, and the only example I know
of is Dan Hoey's Tartan Cube.
(F) Interestingly, due to the 'O' character on one of the centres
of the Calendar Cube having only 2 distinct orientations,
this picture cube has only half of the number of combinations
of the Tartan Cube.
-> Mark <-