The New Sudoku Players' Forum

Website · by **denis_berthier** » Tue Jan 17, 2023 2:06 pm

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The following puzzle was proposed by mith somewhere (I can't find where) as one with (almost) the two impossible patterns:
- tridagon
- #37 in eleven's 15-cell list of impossible patterns

Code: Select all: +-------+-------+-------+ ! . . 7 ! . 9 . ! 4 5 . ! ! . 9 . ! . . . ! 6 . 7 ! ! 4 . 5 ! 6 7 . ! . 8 9 ! +-------+-------+-------+ ! . . . ! 4 5 . ! 7 6 . ! ! 7 . 4 ! 9 . 6 ! 8 . 5 ! ! . . . ! . 8 7 ! . 9 4 ! +-------+-------+-------+ ! . . . ! 8 . . ! . 7 . ! ! 3 . . ! 7 . . ! . . . ! ! 2 7 . ! . . . ! . . 8 ! +-------+-------+-------+ ..7.9.45..9....6.74.567..89...45.76.7.49.68.5....87.94...8...7.3..7.....27......8 SER =10.1

Code: Select all: Resolution state after Singles and whips[1]: +----------------------+----------------------+----------------------+ ! 168 12368 7 ! 123 9 1238 ! 4 5 123 ! ! 18 9 1238 ! 1235 1234 123458 ! 6 123 7 ! ! 4 123 5 ! 6 7 123 ! 123 8 9 ! +----------------------+----------------------+----------------------+ ! 189 1238 12389 ! 4 5 123 ! 7 6 123 ! ! 7 123 4 ! 9 123 6 ! 8 123 5 ! ! 156 12356 1236 ! 123 8 7 ! 123 9 4 ! +----------------------+----------------------+----------------------+ ! 1569 1456 169 ! 8 12346 123459 ! 12359 7 1236 ! ! 3 14568 1689 ! 7 1246 12459 ! 1259 124 126 ! ! 2 7 169 ! 135 1346 13459 ! 1359 134 8 ! +----------------------+----------------------+----------------------+ 176 candidates.

In addition to the solution(s), I'm interested in:
- other puzzles with eleven's pattern
- other T&E(3) patterns

by **eleven** » Tue Jan 17, 2023 4:50 pm

Code: Select all: +-------------------------+-------------------------+-------------------------+ | 168 12368 7 |*123 9 1238 | 4 5 *123 | | 18 9 1238 | 1235 *123+4 123458 | 6 *123 7 | | 4 123 5 | 6 7 *123 |*123 8 9 | +-------------------------+-------------------------+-------------------------+ | 189 1238 12389 | 4 5 *123 | 7 6 *123 | | 7 123 4 | 9 *123 6 | 8 *123 5 | | 156 12356 1236 |*123 8 7 |*123 9 4 | +-------------------------+-------------------------+-------------------------+ | 1569 1456 169 | 8 12346 123459 | 12359 7 1236 | | 3 14568 1689 | 7 1246 12459 | 1259 124 126 | | 2 7 169 | 135 1346 13459 | 1359 134 8 | +-------------------------+-------------------------+-------------------------+

TH (*) => 4r2c5

Code: Select all: +-------------------------+-------------------------+-------------------------+ | 168 *123+68 7 |*123 9 1238 | 4 5 *123 | | 18 9 1238 | 1235 4 12358 | 6 *123 7 | | 4 *123 5 | 6 7 *123 |*123 8 9 | +-------------------------+-------------------------+-------------------------+ | 189 1238 12389 | 4 5 *123 | 7 6 *123 | | 7 *123 4 | 9 *123 6 | 8 *123 5 | | 156 12356 1236 |*123 8 7 |*123 9 4 | +-------------------------+-------------------------+-------------------------+ | 1569 1456 169 | 8 1236 123459 | 12359 7 1236 | | 3 14568 1689 | 7 126 12459 | 1259 124 126 | | 2 7 169 | 135 136 13459 | 1359 134 8 | +-------------------------+-------------------------+-------------------------+

Impossible pattern (*) => 68r1c2 (second here)

Hidden Text: Show

Code: Select all: +-------------------------+-------------------------+-------------------------+ | 168 68 7 |*123 9 1238 | 4 5 *123 | | 18 9 *23 | 1235 4 12358 | 6 *123 7 | | 4 *23 5 | 6 7 *123 |*123 8 9 | +-------------------------+-------------------------+-------------------------+ | 89 1238 12389 | 4 5 *123 | 7 6 *123 | | 7 *123 4 | 9 *123 6 | 8 *123 5 | | 56 12356 *123+6 |*123 8 7 |*123 9 4 | +-------------------------+-------------------------+-------------------------+ | 569 1456 169 | 8 1236 123459 | 12359 7 1236 | | 3 14568 1689 | 7 126 12459 | 1259 124 126 | | 2 7 169 | 135 136 13459 | 1359 134 8 | +-------------------------+-------------------------+-------------------------+

15-cell pattern (*) => 6r6c3 (see here and next post)

Code: Select all: +-------------------------+-------------------------+-------------------------+ | 18 6 7 | 123 9 1238 | 4 5 23-1 | | 18 9 23 | 1235 4 12358 | 6 123 7 | | 4 23 5 | 6 7 #123 |#123 8 9 | +-------------------------+-------------------------+-------------------------+ | 9 8 23 | 4 5 #123 | 7 6 #123 | | 7 123 4 | 9 123 6 | 8 123 5 | | 5 123 6 | 123 8 7 | 23-1 9 4 | +-------------------------+-------------------------+-------------------------+ | 6 45 19 | 8 123 123459 | 12359 7 123 | | 3 45 8 | 7 12 12459 | 1259 124 6 | | 2 7 19 | 135 6 13459 | 1359 134 8 | +-------------------------+-------------------------+-------------------------+

skyscraper 1r3c67,r4c69 => -1r1c9,r6c7

Code: Select all: +-------------------------+-------------------------+-------------------------+ | 18 6 7 | 123 9 1238 | 4 5 *23 | | 18 9 *23 | 1235 4 12358 | 6 *123 7 | | 4 23 5 | 6 7 123 | 123 8 9 | +-------------------------+-------------------------+-------------------------+ | 9 8 *23 | 4 5 123 | 7 6 *123 | | 7 123 4 | 9 123 6 | 8 23-1 5 | | 5 123 6 | 123 8 7 | 23 9 4 | +-------------------------+-------------------------+-------------------------+ | 6 45 19 | 8 123 123459 | 12359 7 123 | | 3 45 8 | 7 12 12459 | 1259 124 6 | | 2 7 19 | 135 6 13459 | 1359 134 8 | +-------------------------+-------------------------+-------------------------+

oddagon 23 (*): 1r2c8 = 1r4c9 => -1r5c8

Code: Select all: +-------------------------+-------------------------+-------------------------+ | 18 6 7 | 123 9 1238 | 4 5 23 | | 18 9 a23 | 1235 4 12358 | 6 123 7 | | 4 *a23 5 | 6 7 a23+1 |*23-1 8 9 | +-------------------------+-------------------------+-------------------------+ | 9 8 a23 | 4 5 a23 | 7 6 1 | | 7 *23+1 4 | 9 123 6 | 8 *23 5 | | 5 123 6 | 123 8 7 |*23 9 4 | +-------------------------+-------------------------+-------------------------+ | 6 45 19 | 8 123 123459 | 12359 7 23 | | 3 45 8 | 7 12 12459 | 1259 124 6 | | 2 7 19 | 135 6 13459 | 1359 134 8 | +-------------------------+-------------------------+-------------------------+

oddagon 23 (a) => 1r3c6, then (-1r3c7) oddagon 23 (*) => 1r5c2, singles

Code: Select all: +----------------------+----------------------+----------------------+ | 1 6 7 | 23 9 8 | 4 5 *23 | | 8 9 *23 | 235 4 235 | 6 1 7 | | 4 *23 5 | 6 7 1 |*23 8 9 | +----------------------+----------------------+----------------------+ | 9 8 *23 | 4 5 *23 | 7 6 1 | | 7 1 4 | 9 *23 6 | 8 23 5 | | 5 23 6 | 1 8 7 | 23 9 4 | +----------------------+----------------------+----------------------+ | 6 45 19 | 8 *23+1 23459 | 12359 7 *23 | | 3 45 8 | 7 12 2459 | 1259 24 6 | | 2 7 19 | 35 6 3459 | 1359 34 8 | +----------------------+----------------------+----------------------+

oddagon 23 (*) => 1r7c5, ste

Website · by **denis_berthier** » Wed Jan 18, 2023 7:25 am

eleven, thanks
I was busy with defining and coding ORk-chains and I haven't followed the "chromatic" discussions very closely.
Could you update your lists of contradictory patterns there?

For #37, I've found a morph (maybe already known) that looks better IMO than #37 itself (I tried to make as many parallel 3-cell lines as possible):

Code: Select all: #37: +-------+-------+-------+ ! . . . ! . . X ! . . X ! ! . . X ! . . . ! . X . ! ! . X . ! . X . ! X . . ! +-------+-------+-------+ ! . . . ! . X . ! . . X ! ! . . X ! . . X ! X . . ! ! . X . ! X . . ! . X . ! +-------+-------+-------+ ! . . . ! . . . ! . . . ! ! . . . ! . . . ! . . . ! ! . . . ! . . . ! . . . ! +-------+-------+-------+ morph: +-------+-------+-------+ ! . . . ! X . . ! . . X ! ! . . X ! . . . ! . X . ! ! . X . ! . . X ! X . . ! +-------+-------+-------+ ! . . . ! . . X ! . . X ! ! . X . ! . X . ! . X . ! ! . . X ! X . . ! X . . ! +-------+-------+-------+ ! . . . ! . . . ! . . . ! ! . . . ! . . . ! . . . ! ! . . . ! . . . ! . . . ! +-------+-------+-------+

[Edit]: errr, it's the pattern in the above puzzle :oops:

Website · by **denis_berthier** » Wed Jan 18, 2023 8:03 am

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I have coded eleven's impossible pattern #37 in his 15-cell list (see previous post).
As an automatic result, I can use it with ORk-chains (Elev-ORk-chains)

There's a solution combining the basic tridagon elimination rule and the new Elev-ORk-chains. But the tridagon is almost useless in the solution. Here's an easy one using only Elev-ORk-chains (in addition to standard chains).

SudoRules identifies two different instances of the pattern (only one will be used). It may be that my (largely untested) code for detecting the pattern is not selective enough.

Code: Select all: +----------------------+----------------------+----------------------+ ! 168 12368 7 ! 123 9 1238 ! 4 5 123 ! ! 18 9 1238 ! 1235 1234 123458 ! 6 123 7 ! ! 4 123 5 ! 6 7 123 ! 123 8 9 ! +----------------------+----------------------+----------------------+ ! 189 1238 12389 ! 4 5 123 ! 7 6 123 ! ! 7 123 4 ! 9 123 6 ! 8 123 5 ! ! 156 12356 1236 ! 123 8 7 ! 123 9 4 ! +----------------------+----------------------+----------------------+ ! 1569 1456 169 ! 8 12346 123459 ! 12359 7 1236 ! ! 3 14568 1689 ! 7 1246 12459 ! 1259 124 126 ! ! 2 7 169 ! 135 1346 13459 ! 1359 134 8 ! +----------------------+----------------------+----------------------+ OR3-anti-eleven[15] for digits 2, 3 and 1 anti-block: 7 anti-column: 1 blocks: b6, with cells: r4c9, r5c8, r6c7 b2, with cells: r1c4, r2c5, r3c6 b3, with cells: r1c9, r2c8, r3c7 b4, with cells: r5c2, r6c3 b5, with cells: r4c6, r6c4 b1, with cells: r2c3, r3c2 with 3 guardians: n8r2c3 n4r2c5 n6r6c3 OR2-anti-eleven[15] for digits 2, 3 and 1 anti-block: 7 anti-column: 1 blocks: b3, with cells: r1c9, r2c8, r3c7 b5, with cells: r4c6, r5c5, r6c4 b6, with cells: r4c9, r5c8, r6c7 b1, with cells: r2c3, r3c2 b2, with cells: r1c4, r3c6 b4, with cells: r5c2, r6c3 with 2 guardians: n8r2c3 n6r6c3

The ORk-chains part:

Elev-OR2-whip[3]: OR2{{n8r2c3 | n6r6c3}} - c3n2{r6 r4} - c3n3{r4 .} ==> r2c3≠1
Elev-OR2-whip[3]: OR2{{n8r2c3 | n6r6c3}} - c3n2{r6 r2} - c3n3{r2 .} ==> r4c3≠8
biv-chain[3]: r4n9{c3 c1} - r4n8{c1 c2} - b7n8{r8c2 r8c3} ==> r8c3≠9
Elev-OR2-whip[3]: OR2{{n6r6c3 | n8r2c3}} - r1c1{n8 n1} - r2c1{n1 .} ==> r6c1≠6
Elev-OR2-whip[3]: OR2{{n6r6c3 | n8r2c3}} - c3n2{r2 r4} - c3n3{r4 .} ==> r6c3≠1

Code: Select all: z-chain[4]: c3n1{r9 r4} - r6c1{n1 n5} - c2n5{r6 r7} - c2n4{r7 .} ==> r8c2≠1 z-chain[4]: c3n1{r9 r4} - r6c1{n1 n5} - c2n5{r6 r8} - c2n4{r8 .} ==> r7c2≠1 z-chain[4]: r4n8{c2 c1} - c1n9{r4 r7} - b7n5{r7c1 r7c2} - c2n4{r7 .} ==> r8c2≠8 hidden-single-in-a-block ==> r8c3=8 +----------------------+----------------------+----------------------+ ! 168 12368 7 ! 123 9 1238 ! 4 5 123 ! ! 18 9 23 ! 1235 1234 123458 ! 6 123 7 ! ! 4 123 5 ! 6 7 123 ! 123 8 9 ! +----------------------+----------------------+----------------------+ ! 189 1238 1239 ! 4 5 123 ! 7 6 123 ! ! 7 123 4 ! 9 123 6 ! 8 123 5 ! ! 15 12356 236 ! 123 8 7 ! 123 9 4 ! +----------------------+----------------------+----------------------+ ! 1569 456 169 ! 8 12346 123459 ! 12359 7 1236 ! ! 3 456 8 ! 7 1246 12459 ! 1259 124 126 ! ! 2 7 169 ! 135 1346 13459 ! 1359 134 8 ! +----------------------+----------------------+----------------------+

At least one candidate of a previous Elev-OR2-relation has just been eliminated.
There remains a Elev-OR1-relation between candidates: n6r6c3

Elev-ORk-relation with only one candidate => r6c3=6

The end is easy, in W4:

Code: Select all: hidden-single-in-a-row ==> r9c5=6 naked-pairs-in-a-block: b7{r7c3 r9c3}{n1 n9} ==> r7c1≠9, r7c1≠1 singles ==> r4c1=9, r4c2=8 whip[1]: b7n1{r9c3 .} ==> r4c3≠1 z-chain[3]: b4n1{r6c2 r5c2} - r3n1{c2 c6} - r4n1{c6 .} ==> r6c7≠1 whip[4]: c3n3{r4 r2} - r3n3{c2 c7} - c9n3{r1 r7} - c5n3{r7 .} ==> r4c6≠3 z-chain[4]: r6c7{n3 n2} - r6c4{n2 n1} - r4c6{n1 n2} - r4c3{n2 .} ==> r6c2≠3 z-chain[4]: c4n2{r2 r6} - b5n3{r6c4 r5c5} - b4n3{r5c2 r4c3} - c3n2{r4 .} ==> r2c6≠2, r2c5≠2 t-whip[4]: r2c3{n2 n3} - r4n3{c3 c9} - b6n1{r4c9 r5c8} - r2c8{n1 .} ==> r2c4≠2 z-chain[3]: b2n2{r1c6 r3c6} - r4n2{c6 c3} - r2n2{c3 .} ==> r1c9≠2 z-chain[3]: b3n2{r3c7 r2c8} - c3n2{r2 r4} - c9n2{r4 .} ==> r8c7≠2, r7c7≠2 finned-x-wing-in-columns: n2{c7 c4}{r6 r3} ==> r3c6≠2 whip[1]: b2n2{r1c6 .} ==> r1c2≠2 biv-chain[3]: r1n2{c4 c6} - r4c6{n2 n1} - r3c6{n1 n3} ==> r1c4≠3 biv-chain[3]: r3c6{n3 n1} - r4n1{c6 c9} - r1c9{n1 n3} ==> r1c6≠3, r3c7≠3 finned-x-wing-in-rows: n3{r4 r1}{c9 c3} ==> r2c3≠3 singles ==> r2c3=2, r4c3=3, r3c7=2, r6c7=3, r5c5=3 whip[1]: c5n2{r8 .} ==> r7c6≠2, r8c6≠2 whip[1]: c7n1{r9 .} ==> r7c9≠1, r8c8≠1, r8c9≠1, r9c8≠1 naked-pairs-in-a-column: c4{r1 r6}{n1 n2} ==> r9c4≠1, r2c4≠1 x-wing-in-columns: n3{c4 c8}{r2 r9} ==> r9c6≠3, r2c6≠3 finned-x-wing-in-columns: n1{c4 c1}{r6 r1} ==> r1c2≠1 finned-x-wing-in-columns: n1{c9 c4}{r1 r4} ==> r4c6≠1 stte

by **shye** » Wed Jan 18, 2023 12:11 pm

hadnt seen elevens pattern before, but didnt seem to need it, only some fancy oddagon stuff

1) trivalue oddagon (& RT)

Hidden Text: Show

2) AHS bivalue oddagon

Hidden Text: Show

3) bivalue oddagon

Hidden Text: Show

by **eleven** » Wed Jan 18, 2023 4:08 pm

Nice find, shye !

denis_berthier wrote:Could you update your lists of contradictory patterns there?

The list can be found here.

Website · by **denis_berthier** » Thu Jan 19, 2023 7:51 am

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shye wrote:hadnt seen elevens pattern before, but didnt seem to need it, only some fancy oddagon stuff
1) trivalue oddagon (& RT)

My purpose was to show that eleven's pattern was enough (among the T&E(3) patterns) for this puzzle. It provides an example of a puzzle in T&E(3) whose solution doesn't depend on the tridagon pattern. AFAIK, it's the first such example.

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Website · by **denis_berthier** » Thu Jan 19, 2023 8:01 am

eleven wrote:
denis_berthier wrote:Could you update your lists of contradictory patterns there?

The list can be found here.

Actually, after scanning the "chromatic" thread in more detail, I fell upon an update of these lists: http://forum.enjoysudoku.com/chromatic-patterns-t39885-71.html
I had completely missed it.
What's interesting is, 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. See the "chromatic" thread for details.
There is indeed only 1 in T&E(3) - see the next posts of the above thread.

Website · by **denis_berthier** » Sat Jan 21, 2023 11:40 pm

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There was some mistake in the original title of this thread.
The eleven's contradictory pattern appearing here is not in restricted T&E(2) but it is in T&E(2). Mea culpa for not checking this before.
How then can this puzzle be solved by a pattern in T&E(2)? Contrary to what I thought without checking, the puzzle is in T&E(2).

Of course, this doesn't change the validity of the solution based on eleven's pattern. But it explains why tridagon rules are not necessary.
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