What Jan Burse did not note in the original question and why this is of interest is that while the specific case is to find the answer for 6 items in a set, the more general problem of finding the minimum of a superpermutation is an unanswered question in maths. What makes this of value to a Prolog community is that while the answers for the values 1,2,3,4, and 5 are known.

there is also a proof for a lower bound (4chan proof)

```
n! + (n − 1)! + (n − 2)! + n − 3.
```

and it is suspected (YouTube) (Site) (paper) that this is an upper bound

```
L₂(n) = n! + (n − 1)! + (n − 2)! + (n − 3)! + n − 3
```

and possibly even (YouTube) (link)

```
L₃(n) = n! + (n − 1)! + (n − 2)! + (n − 3)! + n − 4
```

and that amateur people in math and computer science can work on this by finding examples that are equal to or lower than the value predicted in the proof.

n |
4chan lower bound |
L₂(n) |
Current Best Minimal Superpermutation Length |
Known to be minimum |
Current Best Minimal Superpermutation |

1 |
- |
- |
1 |
Yes |
1 |

2 |
- |
- |
3 |
Yes |
121 |

3 |
9 |
- |
9 |
Yes |
123121321 |

4 |
33 |
34 |
33 |
Yes |
123412314231243121342132413214321 |

5 |
152 |
154 |
153 |
Yes |
123451234152341253412354123145231425314235142315423124531243512431524312543121345213425134215342135421324513241532413524132541321453214352143251432154321 |

6 |
867 |
873 |
872 |
No |
12345612345162345126345123645132645136245136425136452136451234651234156234152634
15236415234615234165234125634125364125346125341625341265341235641235461235416235
41263541236541326543126453162435162431562431652431625431624531642531462531426531
42563142536142531645231465231456231452631452361452316453216453126435126431526431
25643215642315462315426315423615423165423156421356421536241536214536215436215346
21354621345621346521346251346215364215634216534216354216345216342516342156432516
43256143256413256431265432165432615342613542613452613425613426513426153246513246
53124635124631524631254632154632514632541632546132546312456321456324156324516324
56132456312465321465324165324615326415326145326154326514362514365214356214352614
35216435214635214365124361524361254361245361243561243651423561423516423514623514
263514236514326541362541365241356241352641352461352416352413654213654123 |

7 |
5884 |
5,908 |
5,906 |
No |
5906 |
link |

8 |
46,085 |
46,205 |
46,205 |
No |
46,205 |

9 |
408,246 |
408,966 |
408,966 |
No |
408,966 |

EDIT 09/17/2019

In the StackOverflow discussion Jan B. asked

could be a nice example for tabling maybe?

While I don’t actively work on the problem, like many other problems I read up enough on it to have a working vocabulary so that when I read more about it I understand the problem, then I put the problem on the so called back burner of the brain.

When I think about this as a Hamilton path and the kernel/extensions structures it seems there could be a correspondence between the kernel/extensions and tabling.

Also when I recently watched this video about about neural networks, it seemed there was a similarity to simplifying a problem by reducing the given set to a more canonical form, but what and how they are related I don’t know.

Posting here not to start a discussion, but to give feedback for others who read this and say that yes I agree that looking at tabling to help solve the problem is a path I would put on my short list.