[Up] [Map] [Eryk's home page] (Feedback)

Chain cube puzzles go by a number of different names. I have three different ones.

Description with example

What you have are twenty-seven small cubes joined by an elastic thread running through all of them. The thread either passes straight though the cube or makes a right angled turn. Because the join is flexible you can turn it at will. Here is a picture of one unwound all the way. chain cube unwound

The object is to fold the structure into a large 3x3x3 cube. Here is the same cube partially folded. chain cube half-solved

And completely solved.
chain cube solved

There are 11,487 puzzles of this type. So, clearly most of them haven't been manufactured.

Counts of chains of various types

Here is a table I made a long time ago. The first column is the number of unique ways of folding the chain into a cube (ignoring rotations and reflections). The columns labelled '2' through '11' categorize chains based on the number of straight cubies. Each entry is the number of chains with that many straights and that many unique solutions. The last column is the sum of that row. The last row is the sum of the columns. For example, the chain pictured has 9 straight cubies and a unique solution so is one of the 187 chains with 9 straights that have a unique solutions.

        2    3    4    5    6    7    8    9   10   11
   1        15  144  589 1053 1078  556  187   34    2  3658
   2        26  145  502  862  770  325   65    9       2704
   3        25  118  326  393  255  104   21            1242
   4    1   14   98  242  340  203   89   14    1       1002
   5        12   56  140  168   86   12    1             475
   6    1   11   57  123  181   97   23    3             496
   7    2    6   36  101   71   30                       246
   8         8   35   89   83   43   22    7    1        288
   9    3    9   23   51   61   17    5                  169
  10        10   33   57   34   16    6                  156
  11         6   28   39   22   11    1    1             108
  12    2    4   30   39   35   17    9    1             137
  13    2    2   20   31    9    5    1                   70
  14         6   23   25   24   10                        88
  15         2   16   28   12    3                        61
  16         3   15   24   11    7    5    3    1         69
  17    1    9   14   16    9    3                        52
  18    1    3    9    6   10    7    1                   37
  19         6   12   16    6    2                        42
  20         1   11   18   11    1                        42
  21    3    4    8   10    3    1                        29
  22    1    6   10    7    2    1                        27
  23    1    5    8    6    2                             22
  24         2    8    7    6    3                        26
  25         5    5    5    1    1                        17
  26    1         8    5    3    1                        18
  27    1    2    6    5    4                             18
  28    1    1   10    2    1    1                        16
  29         1    4    5                                  10
  30              4    3    1    4                        12
  31         3    1    7    1                             12
  32         2    4    6    2                             14
  33         1    3    3    3    1                        11
  34         2    3         4                              9
  35         1    1    2                                   4
  36                   2                                   2
  37         2    1    1                                   4
  38         1    1    1                                   3
  39              4    2                                   6
  40                   1    3                              4
  41              1         1                              2
  42              1         3                              4
  43    1    2              1                              4
  44         1         3    1                              5
  45                   2    1                              3
  46         1    1                                        2
  47         1    1    2    2                              6
  48         2              1                              3
  49                   1                                   1
  50         1    1    1                                   3
  51              1    1                                   2
  52              1         1                              2
  53              1    1                                   2
  54         2                                             2
  55         2                                             2
  56    1         1                                        2
  57              2         1                              3
  58              1                                        1
* 61         1    1                                        2
  62    1    1         3                                   5
* 64              1                                        1
* 67                   1                                   1
* 70         1         1    1                              3
  71         1                                             1
* 73              1                                        1
* 81              1                                        1
* 85                   1                                   1
  86              1                                        1
  87              1                                        1
  88              2    2                                   4
* 90              1    1                                   2
*104         1    1                                        2
*112         1                                             1
*115                   1                                   1
*119              1                                        1
*123         1                                             1
*126              1                                        1
*142              1                                        1
       24  235 1037 2563 3444 2674 1159  303   46    2 11487

Last Updated: 2003-04-16