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Subject: Ranking the Puzzles
From: mark.longridge@canrem.com (Mark Longridge)
Message-Id: <60.1223.5834.0C1F29E7@canrem.com>
Date: Sat, 2 Sep 1995 03:48:00 -0400
Organization: CRS Online  (Toronto, Ontario)

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 <-