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6+6=CUBE

6+6=CUBE Design and Copyright : 北島孝二 (Koji Kitajima) (1993).

A#0 B#51 C#102
D#119 E#187 F#255
G#791 H#927 I#959
J#991 K#1023 L#1023
Pieces 12 K-L are congruent.
Selection random notchable
Length 6
Goal 6×6×6
Holes 8
Solutions 1,896
642 without notches on the edge
0 without notches on the face

Goal 6 Piece Burr ×1
Holes 0
Solutions 17 / 27

Goal 6 Piece Burr ×2
Holes 0
Solutions 1 / 1

There are 18,940 kinds of possible combination which can construct 2 Nothcable Solid 6 Piece Burr without internal holes. The combinations which have a unique solution are 7,820 kinds.

6PB×2 CombiPiece Set Combi
114,582
23,527
3550
4212
541
615
76
85
102
18,940

The following combinations (mirror each other) are 10 kinds of combination, that have 26 solutions.

1. 0 51×2 255 791 823 927 959 974 991 1006 1023 0 51×2 255 823 887 910 927 959 974 991 1023

The following combination is 2 kinds of combination, that has 45 solutions, it is the maximum.

1. 51×2 791×2 823×2 910×2 974×2 1023×2

There are 114 kinds of possible combination with which 6PB×2 can be constructed by using 12 kinds of piece. The combinations which have a unique solution are the following 28 kinds (mirror 14 kinds), that have no solution of 6×6×6 without notches on the face.

1. 0 17 51 255 823 855 887 927 959 991 1006 1023 0 17 51 255 887 927 942 959 974 991 1006 1023
2. 0 51 102 823 855 870 887 927 959 991 1006 1023 0 51 102 870 887 927 942 959 974 991 1006 1023
3. 0 51 119 187 791 823 855 927 959 991 1006 1023 0 51 119 187 887 910 927 942 959 974 991 1023
4. 0 51 119 187 823 855 870 887 927 959 991 1023 0 51 119 187 870 927 942 959 974 991 1006 1023
5. 0 51 187 255 791 823 887 927 959 974 991 1006 0 51 187 255 823 887 910 927 959 974 991 1006
6. 0 51 187 358 823 887 927 942 959 974 991 1023 0 51 187 614 823 855 927 959 974 991 1006 1023
7. 0 51 187 358 823 927 942 959 974 991 1006 1023 0 51 187 614 823 855 887 927 959 974 991 1023
8. 0 51 187 791 823 855 887 927 959 974 1006 1023 0 51 187 823 887 910 927 942 974 991 1006 1023
9. 0 51 187 823 855 870 887 927 959 974 1006 1023 0 51 187 823 870 887 927 942 974 991 1006 1023
10. 0 51 255 358 823 910 927 942 959 974 991 1023 0 51 255 614 791 823 855 927 959 974 991 1023
11. 0 51 358 791 823 855 927 942 959 991 1006 1023 0 51 614 855 887 910 927 942 959 974 991 1023
12. 0 51 358 791 823 887 927 942 959 974 991 1023 0 51 614 823 855 910 927 959 974 991 1006 1023
13. 0 51 358 823 855 870 887 927 942 959 991 1023 0 51 614 855 870 927 942 959 974 991 1006 1023
14. 0 51 358 823 870 887 927 942 959 974 991 1023 0 51 614 823 855 870 927 959 974 991 1006 1023

The following combination has 6 kinds of 6PB×2 using 12 kinds of piece. There are 2 solutions of 6×6×6 without notches on the face.

1. 0 17 51 255 823 887 927 959 974 991 1006 1023

There are 402 kinds of combination with which 6PB×2 that has unique solution can be constructed by using 11 kinds of piece. There are 2 combinations (mirror each other) that have 2 solutions of 6×6×6 without notches on the face. ☞ 6+6=CUBE Improved

1. 0 51 255 358 823 870 910 927 959 974 1023×2 0 51 255 614 791 823 870 927 974 991 1023×2

 

When using Millable burrs, there are 39,450 kinds of possible combination. The combinations which have a unique solution are 16,035 kinds.

6PB×2 CombiPiece Set Combi
129,562
27,520
31,591
4534
5149
649
730
810
92
102
121
39,450

The following combination is 12 kinds of combination, that have 42 solutions.

1. 0 51×2 191 223 255 823 927 959 974 991 1023

The following combination is 8 kinds of combination, that has 48 solutions, it is the maximum.

1. 0×2 187 191 223 255 823 959 974 991 1023×2

There are 351 kinds of possible combination with which 6PB×2 can be constructed by using 12 kinds of piece. The combinations which have a unique solution are 190 kinds.

The following combinations can assemble 6PB×2, but 2 6PBs are different.

1. 0×2 191×2 255×2 823×2 991×4 0×2 223×2 255×2 959×4 974×2

 

Feb 21, 2006 by k16@chiba.email.ne.jp