denis_berthier wrote:eleven wrote:I have generated now 680 non equivalent 3-digit patterns in 6 boxes (10 cells: 31, 12: 38, 13: 290, 14: 159, 15: 102, 16: 10).

Added: i have copied a zip file to my old google drive:

here (list).

Instead of one pattern potentially in T&E(3) - i.e. that can't be proven contradictory in the simplified version of T&E(2), restricted to cells in the pattern - we now have 10:

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`000001001000010010000100100000001001000010100000100010000000000000000000000000000 #38 12-cells`

000000000001001001001010010000001010000010001001100100000000000000000000000000000 #171 13-cells

000000000001001001001010010001000000010001010010010001000000000000000000000000000 #180 13-cells

000000000001001001001010010001000000010001010100010001000000000000000000000000000 #181 13-cells

000000001000011010001100100001000001010100001100100010000000000000000000000000000 #56 15-cells

000000001001001010010010100001001000010100001100010001000000000000000000000000000 #66 15-cells

000001001001000010010010100000010001001001100010100010000000000000000000000000000 #97 15-cells (ex #37)

000001001001010010001010010001000001010001100010001100000000000000000000000000000 #5 16-cells

000001001001010010001010010001000001010001100100001100000000000000000000000000000 #6 16-cells

000001001001010010001010100001001000010100001100100001000000000000000000000000000 #9 16-cells

So, from 680 3-digit contradictory patterns produced by eleven, quick calculations in CSP-Rules have led to the above list of 10 patterns that cannot be proven contradictory in the restricted form of T&E(2) (which considers only candidates in the pattern). In and of itself, this is an interesting result:

- if you want to prove contradiction for them, you must either remain in T&E(2) and use some candidate(s) not in the pattern or jump to T&E(3);

- restricted T&E(2) is a very fast procedure and this pre-selection allows drastic improvements wrt a selection in full T&E(2).

Now, the question remains: are these 10 patterns contradictory in T&E(2) - i.e. in the full version of T&E(2) that allows using any candidate(s).

Until now, I have been busy other things.

But I have now done the full calculations for the 10 patterns. And the results are worth mentioning IMO.

1)

The 10 patterns are contradictory in restricted T&E(3).2)

Only one pattern (#38 in 12 cells) is not contradictory in the full T&E(2); it is isomorphic to the tridagon pattern, with no condition on a target cell.

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`+-------+-------+-------+ `

! . . . ! . . 1 ! . . 1 !

! . . . ! . 1 . ! . 1 . !

! . . . ! 1 . . ! 1 . . !

+-------+-------+-------+

! . . . ! . . 1 ! . . 1 !

! . . . ! . 1 . ! 1 . . !

! . . . ! 1 . . ! . 1 . !

+-------+-------+-------+

! . . . ! . . . ! . . . !

! . . . ! . . . ! . . . !

! . . . ! . . . ! . . . !

+-------+-------+-------+

000001001000010010000100100000001001000010100000100010000000000000000000000000000 #38 12-cells

isomorphic to something closer to the trivalue oddagon:

+-------+-------+-------+

! . . . ! . . 1 ! . . 1 !

! . . . ! . 1 . ! . 1 . !

! . . . ! 1 . . ! 1 . . !

+-------+-------+-------+

! . . . ! . . 1 ! . . 1 !

! . . . ! 1 . . ! . 1 . !

! . . . ! . 1 . ! 1 . . !

+-------+-------+-------+

! . . . ! . . . ! . . . !

! . . . ! . . . ! . . . !

! . . . ! . . . ! . . . !

+-------+-------+-------+

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`Reminder:`

trivalue oddagon pattern:

+-------+-------+-------+

! . . . ! . . 1 ! . . 1 !

! . . . ! . 1 . ! . 1 . !

! . . . ! 1 . . ! 1 . . !

+-------+-------+-------+

! . . . ! 1 . . ! . . 1 !

! . . . ! . 1 . ! . 1 . !

! . . . ! . . 1 ! 1 . . !

+-------+-------+-------+

! . . . ! . . . ! . . . !

! . . . ! . . . ! . . . !

! . . . ! . . . ! . . . !

+-------+-------+-------+

[Edit]: in order to be complete: none of the 630 patterns can be proven contradictory in full T&E(1).