Ranking the Puzzles by Number of Combinations --------------------------------------------- In general, puzzles without a known mechanism exist as an "idea" only. Ideas for puzzles are welcome, and with GAP's help it is not difficult to find the number of combinations. The list is admittedly mixing puzzles of different types, e.g. Rubik's type and sliding tile type, but we are also interested in the computibility of finding God's Algorithm. Hopefully this list will provide a checklist of the feasibility of using a computer to sift through all the 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. Alexander's Star 7.2*10^34 Adam Alexander 5. Pyraminx Hexagon (A) 2.9*10^30 No known mechanism 6. VIP Sphere 4.4*10^26 Unknown 7. Impossi-ball 2.4*10^25 Wolfgang Kuppers 8. Picture Cube (3x3x3) (E) 8.8*10^22 Erno Rubik, Dan Hoey 9. Calendar Cube (3x3x3)(F) 4.4*10^22 Marvin Silbermintz 10. Rubik's Cube 4th Dim.(D) 1.1*10^22 Erno Rubik 11 Rubik's World (G) 2.7*10^21 Erno Rubik 12. Rubik's Cube (3x3x3) 4.3*10^19 Erno Rubik 13. Pyraminx Octahedron 8.2*10^18 Unknown 14. Octagon 5.4*10^18 Unknown 15. Christoph's Jewel (B) 2.0*10^15 Christoph Bandelow 16. Master Pyraminx (C) 4.5*10^14 Uwe Meffert 17. Barrel 2.7*10^14 Gumpei Yokoi 18. Square 1 1.2*10^13 Dr. Vojtech Kopsky 19. 15 Puzzle 1.0*10^13 Sam Lloyd 20. Missing Link 8.2*10^10 Marvin Glass & Associates 21. Trillion 1.0*10^9 Unknown 22. Rubik's Domino (3x3x2) 4.0*10^8 Erno Rubik 23. Picture Skewb 1.0*10^8 Tony Durham, Uwe Meffert 24. Pyraminx 7.6*10^7 Uwe Meffert 25. Dino Cube #1 (H) 1.9*10^7 Erno Rubik?? 26. Halpern's Tetrahedron 3.7*10^6 Ben Halpern, Kersten Meier 27. Pocket Cube (2x2x2) 3.6*10^6 Erno Rubik 28. Skewb 3.1*10^6 Tony Durham 29. Snub Pyraminx 9.3*10^5 Uwe Meffert 30. Simple Octahedron 5.0*10^4 No known mechanism 31. Dino Cube #2 (I) 4.2*10^4 Erno Rubik?? 32. Rubik's Layer (3x3x1) 192 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. (G) This one has 3 blank centres and 3 centres with 4 orientations. (H) Standard Dino Cube colouring with each side with a different colour. (I) Easy Dino Cube colouring has each tetrad with a different colour. Collated by Mark Longridge, March 22, 1996.