The New Sudoku Players' Forum

by **coloin** » Thu Nov 07, 2024 10:37 pm

On its own a single BxB8

Code: Select all: .23.5....4.7....36.8........4..65.73....1.6.4.6....15...6.413.7...5.346...467..15 # BxB8

Morphed to show solving easier...

Code: Select all: +---+---+---+ |97.|.48|.6.| |4.6|5.9|...| |.58|67.|.4.| +---+---+---+ |.97|.65|..4| |8.5|...|..6| |64.|.8.|...| +---+---+---+ |.69|...|47.| |...|...|..2| |...|.5.|.91| +---+---+---+

Code: Select all: +----------------------+----------------------+----------------------+ | 9 7 123 | 123 4 8 | 1235 6 35 | | 4 123 6 | 5 123 9 | 12378 1238 378 | | 123 5 8 | 6 7 123 | 1239 4 39 | +----------------------+----------------------+----------------------+ | 123 9 7 | 123 6 5 | 1238 1238 4 | | 8 123 5 | 123479 1239 12347 | 12379 123 6 | | 6 4 123 | 12379 8 1237 | 123579 1235 3579 | +----------------------+----------------------+----------------------+ | 1235 6 9 | 1238 123 123 | 4 7 358 | | 1357 138 134 | 134789 139 13467 | 3568 358 2 | | 237 238 234 | 23478 5 23467 | 368 9 1 | +----------------------+----------------------+----------------------+

So I wonder how would you term/describe the guardian cells in box 5 at this stage ? ... not sure if its worthy to post in the puzzles section ...

Edit
Remorphed to this

Code: Select all: +---+---+---+ |.79|.48|.6.| |6.4|5.9|...| |85.|67.|.4.| +---+---+---+ |.46|.8.|...| |5.8|...|..6| |79.|.65|..4| +---+---+---+ |96.|...|47.| |...|...|..2| |...|.5.|.91| +---+---+---+ Mission Impossible

Website · by **denis_berthier** » Fri Nov 08, 2024 12:38 am

.
I have no special name for these guardians. Having only 2 guardians (or even only 1) doesn't generally make the puzzle easier.

Code: Select all: Trid-OR2-relation for digits 1, 2 and 3 in blocks: b1, with cells (marked #): r1c3, r2c2, r3c1 b2, with cells (marked #): r1c4, r2c5, r3c6 b4, with cells (marked #): r6c3, r5c2, r4c1 b5, with cells (marked #): r6c6, r5c5, r4c4 with 2 guardians (in cells marked @): n9r5c5 n7r6c6 +----------------------+----------------------+----------------------+ ! 9 7 123# ! 123# 4 8 ! 1235 6 35 ! ! 4 123# 6 ! 5 123# 9 ! 12378 1238 378 ! ! 123# 5 8 ! 6 7 123# ! 1239 4 39 ! +----------------------+----------------------+----------------------+ ! 123# 9 7 ! 123# 6 5 ! 1238 1238 4 ! ! 8 123# 5 ! 123479 1239#@ 12347 ! 12379 123 6 ! ! 6 4 123# ! 12379 8 1237#@ ! 123579 1235 3579 ! +----------------------+----------------------+----------------------+ ! 1235 6 9 ! 1238 123 123 ! 4 7 358 ! ! 1357 138 134 ! 134789 139 13467 ! 3568 358 2 ! ! 237 238 234 ! 23478 5 23467 ! 368 9 1 ! +----------------------+----------------------+----------------------+

It's an easy puzzle:

Code: Select all: Trid-OR2-whip[2]: OR2{{n9r5c5 | n7r6c6}} - b6n7{r6c7 .} ==> r5c7≠9 whip[1]: b6n9{r6c9 .} ==> r6c4≠9 Trid-OR2-ctr-whip[4]: c4n9{r8 r5} - c4n4{r5 r9} - c4n7{r9 r6} - OR2{{n7r6c6 n9r5c5 | .}} ==> r8c4≠8 Trid-OR2-ctr-whip[4]: c4n9{r8 r5} - c4n4{r5 r9} - c4n7{r9 r6} - OR2{{n7r6c6 n9r5c5 | .}} ==> r8c4≠3 Trid-OR2-ctr-whip[4]: c4n9{r8 r5} - c4n4{r5 r9} - c4n7{r9 r6} - OR2{{n7r6c6 n9r5c5 | .}} ==> r8c4≠1 whip[6]: c9n7{r6 r2} - c9n8{r2 r7} - c4n8{r7 r9} - c4n7{r9 r8} - c4n4{r8 r5} - c4n9{r5 .} ==> r6c6≠7 +----------------------+----------------------+----------------------+ ! 9 7 123 ! 123 4 8 ! 1235 6 35 ! ! 4 123 6 ! 5 123 9 ! 12378 1238 378 ! ! 123 5 8 ! 6 7 123 ! 1239 4 39 ! +----------------------+----------------------+----------------------+ ! 123 9 7 ! 123 6 5 ! 1238 1238 4 ! ! 8 123 5 ! 123479 1239 12347 ! 1237 123 6 ! ! 6 4 123 ! 1237 8 123 ! 123579 1235 3579 ! +----------------------+----------------------+----------------------+ ! 1235 6 9 ! 1238 123 123 ! 4 7 358 ! ! 1357 138 134 ! 479 139 13467 ! 3568 358 2 ! ! 237 238 234 ! 23478 5 23467 ! 368 9 1 ! +----------------------+----------------------+----------------------+ At least one candidate of a previous Trid-OR2-relation between candidates n9r5c5 n7r6c6 has just been eliminated. There remains a Trid-OR1-relation between candidates: n9r5c5 Trid-ORk-relation with only one candidate => r5c5=9 hidden-single-in-a-column ==> r8c4=9 naked-triplets-in-a-block: b8{r7c5 r7c6 r8c5}{n1 n2 n3} ==> r9c6≠3, r9c6≠2, r9c4≠3, r9c4≠2, r8c6≠3, r8c6≠1, r7c4≠3, r7c4≠2, r7c4≠1 singles ==> r7c4=8, r2c9=8, r2c7=7, r6c9=7, r6c7=9, r3c9=9, r6c8=5 whip[1]: b8n2{r7c6 .} ==> r7c1≠2 hidden-pairs-in-a-block: b5{n4 n7}{r5c4 r5c6} ==> r5c6≠3, r5c6≠2, r5c6≠1, r5c4≠3, r5c4≠2, r5c4≠1 naked-triplets-in-a-row: r8{c2 c5 c8}{n8 n1 n3} ==> r8c7≠8, r8c7≠3, r8c3≠3, r8c3≠1, r8c1≠3, r8c1≠1 naked-single ==> r8c3=4 finned-x-wing-in-columns: n1{c3 c4}{r1 r6} ==> r6c6≠1 whip[1]: b5n1{r6c4 .} ==> r1c4≠1 finned-swordfish-in-rows: n1{r8 r2 r5}{c2 c5 c8} ==> r4c8≠1 finned-swordfish-in-rows: n3{r8 r2 r5}{c2 c5 c8} ==> r4c8≠3 biv-chain[3]: c5n2{r7 r2} - r1c4{n2 n3} - c9n3{r1 r7} ==> r7c5≠3 biv-chain[4]: r1n1{c3 c7} - c7n5{r1 r8} - r7n5{c9 c1} - b7n1{r7c1 r8c2} ==> r2c2≠1 biv-chain[4]: r4c8{n2 n8} - r8n8{c8 c2} - c2n1{r8 r5} - c8n1{r5 r2} ==> r2c8≠2 whip[1]: c8n2{r5 .} ==> r4c7≠2, r5c7≠2 biv-chain[3]: r2c2{n3 n2} - r5n2{c2 c8} - c8n1{r5 r2} ==> r2c8≠3 singles ==> r2c8=1, r1c3=1, r3c6=1,r6c4=1 finned-x-wing-in-columns: n3{c6 c3}{r6 r7} ==> r7c1≠3 z-chain[2]: c4n3{r4 r1} - b3n3{r1c9 .} ==> r4c7≠3 whip[1]: b6n3{r5c8 .} ==> r5c2≠3 finned-swordfish-in-rows: n2{r7 r2 r6}{c6 c5 c2} ==> r5c2≠2 stte

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by **coloin** » Fri Nov 08, 2024 3:19 pm

Thanks ... thats clear.

With only one guardian ... the initial step is definitely easy, as eleven will vouch !

In the above puzzle the other [123] clues in r5c4 ,r4c6 andr 5c4 mean that its not certain that this puzzle even has a tridagon....
I guess its all about proving r6c6≠7 in which case there is a tridagon pattern and therefore r5c5=9 ... [which you have demonstrated]

If you have noticed i tend to post puzzles with the 123 pattern as the tridagon clues in boxes 1,2 and 4,5.
So there are puzzles with
one guardian [v common]
two obvious guardians
two potential guardians with other clues in box 5 [as above]
here as in MJ with a hexagon of 123x [3 pairs of guardians]

Code: Select all: +-------------------+-------------------+-------------------+ | 5 7 123 | 123 8 9 | 12346 1346 2346 | | 4 123 6 | 5 123 7 | 8 139 239 | | 123 8 9 | 6 4 123 | 5 137 237 | +-------------------+-------------------+-------------------+ | 123 6 5 | 8 1237 1234 | 12347 13479 23479 | | 8 123 4 | 1237 9 1235 | 12367 1367 23567 | | 7 9 123 | 1234 1235 6 | 1234 1348 23458 | +-------------------+-------------------+-------------------+ | 6 4 7 | 123 123 1238 | 9 5 38 | | 139 135 138 | 13479 13567 13458 | 3467 2 34678 | | 239 235 238 | 23479 23567 23458 | 3467 34678 1 | +-------------------+-------------------+-------------------+

I guess there must be other different patterns of potential tridagon eliminations ...

Website · by **denis_berthier** » Fri Nov 08, 2024 3:57 pm

coloin wrote:With only one guardian ... the initial step is definitely easy, as eleven will vouch !

Of course, but this exhausts all the potentialities of the tridagon. And the puzzle may be very hard after this first step.

coloin wrote:In the above puzzle the other [123] clues in r5c4 ,r4c6 andr 5c4 mean that its not certain that this puzzle even has a tridagon....
I guess its all about proving r6c6≠7 in which case there is a tridagon pattern and therefore r5c5=9 ... [which you have demonstrated]

What counts is the position of the cells in the blocks. There's nothing to prove; there's just a pattern of cells to identify in the blocks.
See the tridagon thread for details: http://forum.enjoysudoku.com/the-tridagon-rule-t39859.html
What may confuse you is, there may be several tridagons in the same resolution state, each with different guardians (as in your example below).

coloin wrote:If you have noticed i tend to post puzzles with the 123 pattern as the tridagon clues in boxes 1,2 and 4,5.
So there are puzzles with
one guardian [v common]
two obvious guardians
two potential guardians with other clues in box 5 [as above]

I don't understand your difference between "obvious guardians" and "potential guardians".
In a tridagon, we call guardians all the non-tridagon digits in any of the 12 tridagon cells.

coloin wrote:here as in MJ with a hexagon of 123x [3 pairs of guardians]
Code: Select all
+-------------------+-------------------+-------------------+ | 5 7 123 | 123 8 9 | 12346 1346 2346 | | 4 123 6 | 5 123 7 | 8 139 239 | | 123 8 9 | 6 4 123 | 5 137 237 | +-------------------+-------------------+-------------------+ | 123 6 5 | 8 1237 1234 | 12347 13479 23479 | | 8 123 4 | 1237 9 1235 | 12367 1367 23567 | | 7 9 123 | 1234 1235 6 | 1234 1348 23458 | +-------------------+-------------------+-------------------+ | 6 4 7 | 123 123 1238 | 9 5 38 | | 139 135 138 | 13479 13567 13458 | 3467 2 34678 | | 239 235 238 | 23479 23567 23458 | 3467 34678 1 | +-------------------+-------------------+-------------------+

I guess there must be other different patterns of potential tridagon eliminations ...

In this example, there are two tridagons for the same digits (and therefore in the same 4 blocks), each with 3 guardians.
They coincide in blocks b1, b2 and b4; they differ in block b5.
As I've shown in the tridagon thread, once you fix the cells in 3 of the blocks, there are 3 possibilities for the cells in the 4th block.

Code: Select all: Trid-OR3-relation for digits 1, 2 and 3 in blocks: b1, with cells (marked #): r1c3, r2c2, r3c1 b2, with cells (marked #): r1c4, r2c5, r3c6 b4, with cells (marked #): r6c3, r5c2, r4c1 b5, with cells (marked #): r6c4, r5c6, r4c5 with 3 guardians (in cells marked @): n7r4c5 n5r5c6 n4r6c4 +----------------------+----------------------+----------------------+ ! 5 7 123# ! 123# 8 9 ! 12346 1346 2346 ! ! 4 123# 6 ! 5 123# 7 ! 8 139 239 ! ! 123# 8 9 ! 6 4 123# ! 5 137 237 ! +----------------------+----------------------+----------------------+ ! 123# 6 5 ! 8 1237#@ 1234 ! 12347 13479 23479 ! ! 8 123# 4 ! 1237 9 1235#@ ! 12367 1367 23567 ! ! 7 9 123# ! 1234#@ 1235 6 ! 1234 1348 23458 ! +----------------------+----------------------+----------------------+ ! 6 4 7 ! 123 123 1238 ! 9 5 38 ! ! 139 135 138 ! 3479 3567 3458 ! 3467 2 34678 ! ! 239 235 238 ! 3479 3567 3458 ! 3467 34678 1 ! +----------------------+----------------------+----------------------+

and

Code: Select all: Trid-OR3-relation for digits 1, 2 and 3 in blocks: b1, with cells (marked #): r1c3, r2c2, r3c1 b2, with cells (marked #): r1c4, r2c5, r3c6 b4, with cells (marked #): r6c3, r5c2, r4c1 b5, with cells (marked #): r6c5, r5c4, r4c6 with 3 guardians (in cells marked @): n4r4c6 n7r5c4 n5r6c5 +----------------------+----------------------+----------------------+ ! 5 7 123# ! 123# 8 9 ! 12346 1346 2346 ! ! 4 123# 6 ! 5 123# 7 ! 8 139 239 ! ! 123# 8 9 ! 6 4 123# ! 5 137 237 ! +----------------------+----------------------+----------------------+ ! 123# 6 5 ! 8 1237 1234#@ ! 12347 13479 23479 ! ! 8 123# 4 ! 1237#@ 9 1235 ! 12367 1367 23567 ! ! 7 9 123# ! 1234 1235#@ 6 ! 1234 1348 23458 ! +----------------------+----------------------+----------------------+ ! 6 4 7 ! 123 123 1238 ! 9 5 38 ! ! 139 135 138 ! 3479 3567 3458 ! 3467 2 34678 ! ! 239 235 238 ! 3479 3567 3458 ! 3467 34678 1 ! +----------------------+----------------------+----------------------+

Note that there are much more complex examples, with up to 15 tridagons (or more - I don't remember the max number I've seen) and/or guardians per tridagon. In each of the 4 blocks, there may be several combinations of cells, each entering a full tridagon pattern.
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by **coloin** » Fri Nov 08, 2024 5:46 pm

denis_berthier wrote:I don't understand your difference between "obvious guardians" and "potential guardians".

I say potential because you dont know that the tridagon pattern is in the puzzle

Code: Select all: +-------------------+-------------------+-------------------+ | 5 7 123 | 123 8 9 | 12346 1346 2346 | | 4 123 6 | 5 123 7 | 8 139 239 | | 123 8 9 | 6 4 123 | 5 137 237 | +-------------------+-------------------+-------------------+ | 123 6 5 | 8 1237 1234 | 12347 13479 23479 | | 8 123 4 | 1237 9 1235 | 12367 1367 23567 | | 7 9 123 | 1234 1235 6 | 1234 1348 23458 | +-------------------+-------------------+-------------------+ | 6 4 7 | 123 123 1238 | 9 5 38 | | 139 135 138 | 13479 13567 13458 | 3467 2 34678 | | 239 235 238 | 23479 23567 23458 | 3467 34678 1 | +-------------------+-------------------+-------------------+

At the beginning stage this pattern is possible, so the tridagon pattern is not assured to be in the path

Code: Select all: +---+---+---+ |..1|3..|...| |.2.|.1.|...| |3..|..2|...| +---+---+---+ |2..|.3.|...| |.1.|...|...| |..3|12.|...| +---+---+---+ |...|...|...| |...|...|...| |...|...|...| +---+---+---+

denis_berthier wrote:Note that there are much more complex examples, with up to 15 tridagons

I cant see any of these examples in the tridagon thread though, which is why im trying to outline the types ...apologies if not in your thread...

Website · by **denis_berthier** » Fri Nov 08, 2024 7:14 pm

coloin wrote:
denis_berthier wrote:Note that there are much more complex examples, with up to 15 tridagons

I cant see any of these examples in the tridagon thread though, which is why im trying to outline the types

Usually, most of them are not used in the resolution path (e.g. because they have too many guardians) and I don't keep them in the resolution path.
I haven't keep track of them but if I fall upon one, I'll publish it.

by **eleven** » Sat Nov 09, 2024 12:48 am

coloin wrote:
Code: Select all
.23.5....4.7....36.8........4..65.73....1.6.4.6....15...6.413.7...5.346...467..15 # BxB8

...
... not sure if its worthy to post in the puzzles section ...

The tridagon has 2 externals, 7r5c7 and 3r6c5

Code: Select all: +-------------------------+---------------------------+---------------------------+ | 169 2 3 | d14789 5 46789 | 789 489 189 | | 4 159 7 | 1289 289 289 | 2589 3 6 | | 1569 8 159 | d123479 239 24679 | 2579 249 129 | +-------------------------+---------------------------+---------------------------+ | 1289 4 1289 | *289 6 5 | *289 7 3 | | b235789 b3579 2589 | c23789 1 a*289+7 | 6 *289 4 | | c23789 6 289 | ec234789 *289+3 24789 | 1 5 #*289 | +-------------------------+---------------------------+---------------------------+ | 2589 59 6 | *289 4 1 | 3 *289 7 | | 12789 179 1289 | 5 #*289 3 | 4 6 #*289 | | 2389 39 4 | 6 7 *289 | *289 1 5 | +-------------------------+---------------------------+---------------------------+

7r5c7 - r5c12 = (7-3)r6c1
7r5c7 - r56c4 = (17-4)r13c4 = (4-3)r6c4
=> 3r6c5

Then there is a UR47 => 6r1c6, after which is solvable with normal advanced techniques (ER 4.3).
Maybe notable is an impossible pattern (which still needs other techniques)

Code: Select all: +-------------------+-------------------+-------------------+ | 19 2 3 | 4 5 6 | 7 89 189 | | 4 5 7 | 1 289 289 | 29 3 6 | | 6 8 19 | 3 29 7 | 5 4 129 | +-------------------+-------------------+-------------------+ | 1289 4 *289+1 |*289 6 5 |*289 7 3 | | 3 7 5 |*289 1 28 | 6 *289 4 | | 289 6 *289 | 7 3 4 | 1 5 *289 | +-------------------+-------------------+-------------------+ | 5 9 6 |*28 4 1 | 3 *28 7 | | 7 1 *28 | 5 289 3 | 4 6 *289 | |*28 3 4 | 6 7 289 |*289 1 5 | +-------------------+-------------------+-------------------+

Hidden Text: Show

Website · by **denis_berthier** » Sat Nov 09, 2024 4:37 am

.

Code: Select all: Resolution state after Singles and whips[1]: +----------------------+----------------------+----------------------+ ! 169 2 3 ! 14789 5 46789 ! 789 489 189 ! ! 4 159 7 ! 1289 289 289 ! 2589 3 6 ! ! 1569 8 159 ! 123479 239 24679 ! 2579 249 129 ! +----------------------+----------------------+----------------------+ ! 1289 4 1289 ! 289 6 5 ! 289 7 3 ! ! 235789 3579 2589 ! 23789 1 2789 ! 6 289 4 ! ! 23789 6 289 ! 234789 2389 24789 ! 1 5 289 ! +----------------------+----------------------+----------------------+ ! 2589 59 6 ! 289 4 1 ! 3 289 7 ! ! 12789 179 1289 ! 5 289 3 ! 4 6 289 ! ! 2389 39 4 ! 6 7 289 ! 289 1 5 ! +----------------------+----------------------+----------------------+ 178 candidates.

I hadn't tried your 630 impossible patterns, but this puzzle is a champion for them. I don't have enough fingers to count them. Note that most of them appear several time (on different cells). I've limited the guardians count to 8.
I tried to hide the list, but the forum software doesn't agree. Instead, I'll split this post into two parts. Jump to the next post to see the application of these patterns.

Code: Select all: Trid-OR2-relation for digits 2, 8 and 9 in blocks: b5, with cells (marked #): r4c4, r5c6, r6c5 b6, with cells (marked #): r4c7, r5c8, r6c9 b8, with cells (marked #): r7c4, r9c6, r8c5 b9, with cells (marked #): r7c8, r9c7, r8c9 with 2 guardians (in cells marked @): n7r5c6 n3r6c5 +----------------------+----------------------+----------------------+ ! 169 2 3 ! 14789 5 46789 ! 789 489 189 ! ! 4 159 7 ! 1289 289 289 ! 2589 3 6 ! ! 1569 8 159 ! 123479 239 24679 ! 2579 249 129 ! +----------------------+----------------------+----------------------+ ! 1289 4 1289 ! 289# 6 5 ! 289# 7 3 ! ! 235789 3579 2589 ! 23789 1 2789#@ ! 6 289# 4 ! ! 23789 6 289 ! 234789 2389#@ 24789 ! 1 5 289# ! +----------------------+----------------------+----------------------+ ! 2589 59 6 ! 289# 4 1 ! 3 289# 7 ! ! 12789 179 1289 ! 5 289# 3 ! 4 6 289# ! ! 2389 39 4 ! 6 7 289# ! 289# 1 5 ! +----------------------+----------------------+----------------------+ Trid-OR2-whip[2]: OR2{{n3r6c5 | n7r5c6}} - b4n7{r5c1 .} ==> r6c1≠3 whip[1]: r6n3{c5 .} ==> r5c4≠3 EL13c290-OR4-relation for digits: 2, 8 and 9 in cells (marked #): (r8c9 r9c1 r9c6 r9c7 r7c1 r7c4 r7c8 r5c6 r5c8 r4c4 r4c7 r6c1 r6c9) with 4 guardians (in cells marked @) : n3r9c1 n5r7c1 n7r5c6 n7r6c1 +----------------------+----------------------+----------------------+ ! 169 2 3 ! 14789 5 46789 ! 789 489 189 ! ! 4 159 7 ! 1289 289 289 ! 2589 3 6 ! ! 1569 8 159 ! 123479 239 24679 ! 2579 249 129 ! +----------------------+----------------------+----------------------+ ! 1289 4 1289 ! 289# 6 5 ! 289# 7 3 ! ! 235789 3579 2589 ! 2789 1 2789#@ ! 6 289# 4 ! ! 2789#@ 6 289 ! 234789 2389 24789 ! 1 5 289# ! +----------------------+----------------------+----------------------+ ! 2589#@ 59 6 ! 289# 4 1 ! 3 289# 7 ! ! 12789 179 1289 ! 5 289 3 ! 4 6 289# ! ! 2389#@ 39 4 ! 6 7 289# ! 289# 1 5 ! +----------------------+----------------------+----------------------+ EL13c290-OR4-relation for digits: 2, 8 and 9 in cells (marked #): (r6c9 r5c3 r5c6 r5c8 r4c3 r4c4 r4c7 r9c6 r9c7 r7c4 r7c8 r8c3 r8c9) with 4 guardians (in cells marked @) : n5r5c3 n7r5c6 n1r4c3 n1r8c3 +----------------------+----------------------+----------------------+ ! 169 2 3 ! 14789 5 46789 ! 789 489 189 ! ! 4 159 7 ! 1289 289 289 ! 2589 3 6 ! ! 1569 8 159 ! 123479 239 24679 ! 2579 249 129 ! +----------------------+----------------------+----------------------+ ! 1289 4 1289#@ ! 289# 6 5 ! 289# 7 3 ! ! 235789 3579 2589#@ ! 2789 1 2789#@ ! 6 289# 4 ! ! 2789 6 289 ! 234789 2389 24789 ! 1 5 289# ! +----------------------+----------------------+----------------------+ ! 2589 59 6 ! 289# 4 1 ! 3 289# 7 ! ! 12789 179 1289#@ ! 5 289 3 ! 4 6 289# ! ! 2389 39 4 ! 6 7 289# ! 289# 1 5 ! +----------------------+----------------------+----------------------+ EL13c290-OR7-relation for digits: 2, 8 and 9 in cells (marked #): (r6c9 r5c1 r5c6 r5c8 r4c1 r4c4 r4c7 r9c6 r9c7 r7c4 r7c8 r8c1 r8c9) with 7 guardians (in cells marked @) : n3r5c1 n5r5c1 n7r5c1 n7r5c6 n1r4c1 n1r8c1 n7r8c1 +----------------------------+----------------------------+----------------------------+ ! 169 2 3 ! 14789 5 46789 ! 789 489 189 ! ! 4 159 7 ! 1289 289 289 ! 2589 3 6 ! ! 1569 8 159 ! 123479 239 24679 ! 2579 249 129 ! +----------------------------+----------------------------+----------------------------+ ! 1289#@ 4 1289 ! 289# 6 5 ! 289# 7 3 ! ! 235789#@ 3579 2589 ! 2789 1 2789#@ ! 6 289# 4 ! ! 2789 6 289 ! 234789 2389 24789 ! 1 5 289# ! +----------------------------+----------------------------+----------------------------+ ! 2589 59 6 ! 289# 4 1 ! 3 289# 7 ! ! 12789#@ 179 1289 ! 5 289 3 ! 4 6 289# ! ! 2389 39 4 ! 6 7 289# ! 289# 1 5 ! +----------------------------+----------------------------+----------------------------+ EL13c290-OR7-relation for digits: 2, 8 and 9 in cells (marked #): (r5c8 r6c4 r6c1 r6c9 r4c4 r4c3 r4c7 r9c1 r9c7 r8c3 r8c9 r7c4 r7c8) with 7 guardians (in cells marked @) : n3r6c4 n4r6c4 n7r6c4 n7r6c1 n1r4c3 n3r9c1 n1r8c3 +----------------------------+----------------------------+----------------------------+ ! 169 2 3 ! 14789 5 46789 ! 789 489 189 ! ! 4 159 7 ! 1289 289 289 ! 2589 3 6 ! ! 1569 8 159 ! 123479 239 24679 ! 2579 249 129 ! +----------------------------+----------------------------+----------------------------+ ! 1289 4 1289#@ ! 289# 6 5 ! 289# 7 3 ! ! 235789 3579 2589 ! 2789 1 2789 ! 6 289# 4 ! ! 2789#@ 6 289 ! 234789#@ 2389 24789 ! 1 5 289# ! +----------------------------+----------------------------+----------------------------+ ! 2589 59 6 ! 289# 4 1 ! 3 289# 7 ! ! 12789 179 1289#@ ! 5 289 3 ! 4 6 289# ! ! 2389#@ 39 4 ! 6 7 289 ! 289# 1 5 ! +----------------------------+----------------------------+----------------------------+ EL13c290-OR7-relation for digits: 2, 8 and 9 in cells (marked #): (r4c7 r6c6 r6c1 r6c9 r5c6 r5c3 r5c8 r7c1 r7c8 r8c3 r8c9 r9c6 r9c7) with 7 guardians (in cells marked @) : n4r6c6 n7r6c6 n7r6c1 n7r5c6 n5r5c3 n5r7c1 n1r8c3 +-------------------------+-------------------------+-------------------------+ ! 169 2 3 ! 14789 5 46789 ! 789 489 189 ! ! 4 159 7 ! 1289 289 289 ! 2589 3 6 ! ! 1569 8 159 ! 123479 239 24679 ! 2579 249 129 ! +-------------------------+-------------------------+-------------------------+ ! 1289 4 1289 ! 289 6 5 ! 289# 7 3 ! ! 235789 3579 2589#@ ! 2789 1 2789#@ ! 6 289# 4 ! ! 2789#@ 6 289 ! 234789 2389 24789#@ ! 1 5 289# ! +-------------------------+-------------------------+-------------------------+ ! 2589#@ 59 6 ! 289 4 1 ! 3 289# 7 ! ! 12789 179 1289#@ ! 5 289 3 ! 4 6 289# ! ! 2389 39 4 ! 6 7 289# ! 289# 1 5 ! +-------------------------+-------------------------+-------------------------+ EL14c159s-OR6-relation for digits: 2, 8 and 9 in cells (marked #): (r2c7 r2c6 r2c4 r4c7 r5c8 r6c9 r6c5 r6c4 r9c7 r9c6 r7c8 r7c4 r8c9 r8c5) with 6 guardians (in cells marked @) : n5r2c7 n1r2c4 n3r6c5 n3r6c4 n4r6c4 n7r6c4 +----------------------------+----------------------------+----------------------------+ ! 169 2 3 ! 14789 5 46789 ! 789 489 189 ! ! 4 159 7 ! 1289#@ 289 289# ! 2589#@ 3 6 ! ! 1569 8 159 ! 123479 239 24679 ! 2579 249 129 ! +----------------------------+----------------------------+----------------------------+ ! 1289 4 1289 ! 289 6 5 ! 289# 7 3 ! ! 235789 3579 2589 ! 2789 1 2789 ! 6 289# 4 ! ! 2789 6 289 ! 234789#@ 2389#@ 24789 ! 1 5 289# ! +----------------------------+----------------------------+----------------------------+ ! 2589 59 6 ! 289# 4 1 ! 3 289# 7 ! ! 12789 179 1289 ! 5 289# 3 ! 4 6 289# ! ! 2389 39 4 ! 6 7 289# ! 289# 1 5 ! +----------------------------+----------------------------+----------------------------+ EL14c159-OR3-relation for digits: 2, 8 and 9 in cells (marked #): (r7c4 r7c8 r9c6 r9c7 r8c3 r8c5 r8c9 r5c4 r5c8 r6c3 r6c9 r4c3 r4c4 r4c7) with 3 guardians (in cells marked @) : n1r8c3 n7r5c4 n1r4c3 +----------------------+----------------------+----------------------+ ! 169 2 3 ! 14789 5 46789 ! 789 489 189 ! ! 4 159 7 ! 1289 289 289 ! 2589 3 6 ! ! 1569 8 159 ! 123479 239 24679 ! 2579 249 129 ! +----------------------+----------------------+----------------------+ ! 1289 4 1289#@ ! 289# 6 5 ! 289# 7 3 ! ! 235789 3579 2589 ! 2789#@ 1 2789 ! 6 289# 4 ! ! 2789 6 289# ! 234789 2389 24789 ! 1 5 289# ! +----------------------+----------------------+----------------------+ ! 2589 59 6 ! 289# 4 1 ! 3 289# 7 ! ! 12789 179 1289#@ ! 5 289# 3 ! 4 6 289# ! ! 2389 39 4 ! 6 7 289# ! 289# 1 5 ! +----------------------+----------------------+----------------------+ EL14c159-OR5-relation for digits: 2, 8 and 9 in cells (marked #): (r7c4 r7c8 r9c6 r9c7 r8c1 r8c5 r8c9 r5c4 r5c8 r6c1 r6c9 r4c1 r4c4 r4c7) with 5 guardians (in cells marked @) : n1r8c1 n7r8c1 n7r5c4 n7r6c1 n1r4c1 +-------------------------+-------------------------+-------------------------+ ! 169 2 3 ! 14789 5 46789 ! 789 489 189 ! ! 4 159 7 ! 1289 289 289 ! 2589 3 6 ! ! 1569 8 159 ! 123479 239 24679 ! 2579 249 129 ! +-------------------------+-------------------------+-------------------------+ ! 1289#@ 4 1289 ! 289# 6 5 ! 289# 7 3 ! ! 235789 3579 2589 ! 2789#@ 1 2789 ! 6 289# 4 ! ! 2789#@ 6 289 ! 234789 2389 24789 ! 1 5 289# ! +-------------------------+-------------------------+-------------------------+ ! 2589 59 6 ! 289# 4 1 ! 3 289# 7 ! ! 12789#@ 179 1289 ! 5 289# 3 ! 4 6 289# ! ! 2389 39 4 ! 6 7 289# ! 289# 1 5 ! +-------------------------+-------------------------+-------------------------+ EL14c159-OR7-relation for digits: 2, 8 and 9 in cells (marked #): (r7c4 r7c8 r8c5 r8c9 r9c1 r9c6 r9c7 r5c4 r5c8 r4c1 r4c7 r6c1 r6c4 r6c9) with 7 guardians (in cells marked @) : n3r9c1 n7r5c4 n1r4c1 n7r6c1 n3r6c4 n4r6c4 n7r6c4 +----------------------------+----------------------------+----------------------------+ ! 169 2 3 ! 14789 5 46789 ! 789 489 189 ! ! 4 159 7 ! 1289 289 289 ! 2589 3 6 ! ! 1569 8 159 ! 123479 239 24679 ! 2579 249 129 ! +----------------------------+----------------------------+----------------------------+ ! 1289#@ 4 1289 ! 289 6 5 ! 289# 7 3 ! ! 235789 3579 2589 ! 2789#@ 1 2789 ! 6 289# 4 ! ! 2789#@ 6 289 ! 234789#@ 2389 24789 ! 1 5 289# ! +----------------------------+----------------------------+----------------------------+ ! 2589 59 6 ! 289# 4 1 ! 3 289# 7 ! ! 12789 179 1289 ! 5 289# 3 ! 4 6 289# ! ! 2389#@ 39 4 ! 6 7 289# ! 289# 1 5 ! +----------------------------+----------------------------+----------------------------+ EL14c1-OR5-relation for digits: 2, 8 and 9 in cells (marked #): (r6c9 r5c6 r5c8 r4c1 r4c4 r4c7 r9c6 r9c7 r7c1 r7c4 r7c8 r8c1 r8c5 r8c9) with 5 guardians (in cells marked @) : n7r5c6 n1r4c1 n5r7c1 n1r8c1 n7r8c1 +-------------------------+-------------------------+-------------------------+ ! 169 2 3 ! 14789 5 46789 ! 789 489 189 ! ! 4 159 7 ! 1289 289 289 ! 2589 3 6 ! ! 1569 8 159 ! 123479 239 24679 ! 2579 249 129 ! +-------------------------+-------------------------+-------------------------+ ! 1289#@ 4 1289 ! 289# 6 5 ! 289# 7 3 ! ! 235789 3579 2589 ! 2789 1 2789#@ ! 6 289# 4 ! ! 2789 6 289 ! 234789 2389 24789 ! 1 5 289# ! +-------------------------+-------------------------+-------------------------+ ! 2589#@ 59 6 ! 289# 4 1 ! 3 289# 7 ! ! 12789#@ 179 1289 ! 5 289# 3 ! 4 6 289# ! ! 2389 39 4 ! 6 7 289# ! 289# 1 5 ! +-------------------------+-------------------------+-------------------------+ EL14c1-OR7-relation for digits: 2, 8 and 9 in cells (marked #): (r6c9 r4c4 r4c7 r5c1 r5c6 r5c8 r7c4 r7c8 r9c1 r9c6 r9c7 r8c1 r8c5 r8c9) with 7 guardians (in cells marked @) : n3r5c1 n5r5c1 n7r5c1 n7r5c6 n3r9c1 n1r8c1 n7r8c1 +----------------------------+----------------------------+----------------------------+ ! 169 2 3 ! 14789 5 46789 ! 789 489 189 ! ! 4 159 7 ! 1289 289 289 ! 2589 3 6 ! ! 1569 8 159 ! 123479 239 24679 ! 2579 249 129 ! +----------------------------+----------------------------+----------------------------+ ! 1289 4 1289 ! 289# 6 5 ! 289# 7 3 ! ! 235789#@ 3579 2589 ! 2789 1 2789#@ ! 6 289# 4 ! ! 2789 6 289 ! 234789 2389 24789 ! 1 5 289# ! +----------------------------+----------------------------+----------------------------+ ! 2589 59 6 ! 289# 4 1 ! 3 289# 7 ! ! 12789#@ 179 1289 ! 5 289# 3 ! 4 6 289# ! ! 2389#@ 39 4 ! 6 7 289# ! 289# 1 5 ! +----------------------------+----------------------------+----------------------------+ EL14c13-OR5-relation for digits: 2, 8 and 9 in cells (marked #): (r6c9 r5c6 r5c4 r5c8 r4c1 r4c4 r4c7 r7c4 r7c8 r9c6 r9c7 r8c1 r8c5 r8c9) with 5 guardians (in cells marked @) : n7r5c6 n7r5c4 n1r4c1 n1r8c1 n7r8c1 +-------------------------+-------------------------+-------------------------+ ! 169 2 3 ! 14789 5 46789 ! 789 489 189 ! ! 4 159 7 ! 1289 289 289 ! 2589 3 6 ! ! 1569 8 159 ! 123479 239 24679 ! 2579 249 129 ! +-------------------------+-------------------------+-------------------------+ ! 1289#@ 4 1289 ! 289# 6 5 ! 289# 7 3 ! ! 235789 3579 2589 ! 2789#@ 1 2789#@ ! 6 289# 4 ! ! 2789 6 289 ! 234789 2389 24789 ! 1 5 289# ! +-------------------------+-------------------------+-------------------------+ ! 2589 59 6 ! 289# 4 1 ! 3 289# 7 ! ! 12789#@ 179 1289 ! 5 289# 3 ! 4 6 289# ! ! 2389 39 4 ! 6 7 289# ! 289# 1 5 ! +-------------------------+-------------------------+-------------------------+ EL10c28-OR7-relation for digits: 2, 8 and 9 in cells (marked #): (r8c1 r8c9 r7c4 r7c1 r7c8 r5c4 r4c4 r6c6 r6c1 r6c9) with 7 guardians (in cells marked @) : n1r8c1 n7r8c1 n5r7c1 n7r5c4 n4r6c6 n7r6c6 n7r6c1 +-------------------------+-------------------------+-------------------------+ ! 169 2 3 ! 14789 5 46789 ! 789 489 189 ! ! 4 159 7 ! 1289 289 289 ! 2589 3 6 ! ! 1569 8 159 ! 123479 239 24679 ! 2579 249 129 ! +-------------------------+-------------------------+-------------------------+ ! 1289 4 1289 ! 289# 6 5 ! 289 7 3 ! ! 235789 3579 2589 ! 2789#@ 1 2789 ! 6 289 4 ! ! 2789#@ 6 289 ! 234789 2389 24789#@ ! 1 5 289# ! +-------------------------+-------------------------+-------------------------+ ! 2589#@ 59 6 ! 289# 4 1 ! 3 289# 7 ! ! 12789#@ 179 1289 ! 5 289 3 ! 4 6 289# ! ! 2389 39 4 ! 6 7 289 ! 289 1 5 ! +-------------------------+-------------------------+-------------------------+ EL10c28-OR6-relation for digits: 2, 8 and 9 in cells (marked #): (r8c1 r8c9 r7c4 r7c1 r7c8 r5c4 r4c4 r6c5 r6c1 r6c9) with 6 guardians (in cells marked @) : n1r8c1 n7r8c1 n5r7c1 n7r5c4 n3r6c5 n7r6c1 +-------------------------+-------------------------+-------------------------+ ! 169 2 3 ! 14789 5 46789 ! 789 489 189 ! ! 4 159 7 ! 1289 289 289 ! 2589 3 6 ! ! 1569 8 159 ! 123479 239 24679 ! 2579 249 129 ! +-------------------------+-------------------------+-------------------------+ ! 1289 4 1289 ! 289# 6 5 ! 289 7 3 ! ! 235789 3579 2589 ! 2789#@ 1 2789 ! 6 289 4 ! ! 2789#@ 6 289 ! 234789 2389#@ 24789 ! 1 5 289# ! +-------------------------+-------------------------+-------------------------+ ! 2589#@ 59 6 ! 289# 4 1 ! 3 289# 7 ! ! 12789#@ 179 1289 ! 5 289 3 ! 4 6 289# ! ! 2389 39 4 ! 6 7 289 ! 289 1 5 ! +-------------------------+-------------------------+-------------------------+ EL13c179-OR8-relation for digits: 2, 8 and 9 in cells (marked #): (r6c1 r6c9 r6c6 r5c1 r5c8 r5c4 r8c9 r8c5 r9c7 r9c6 r7c1 r7c8 r7c4) with 8 guardians (in cells marked @) : n7r6c1 n4r6c6 n7r6c6 n3r5c1 n5r5c1 n7r5c1 n7r5c4 n5r7c1 +----------------------------+----------------------------+----------------------------+ ! 169 2 3 ! 14789 5 46789 ! 789 489 189 ! ! 4 159 7 ! 1289 289 289 ! 2589 3 6 ! ! 1569 8 159 ! 123479 239 24679 ! 2579 249 129 ! +----------------------------+----------------------------+----------------------------+ ! 1289 4 1289 ! 289 6 5 ! 289 7 3 ! ! 235789#@ 3579 2589 ! 2789#@ 1 2789 ! 6 289# 4 ! ! 2789#@ 6 289 ! 234789 2389 24789#@ ! 1 5 289# ! +----------------------------+----------------------------+----------------------------+ ! 2589#@ 59 6 ! 289# 4 1 ! 3 289# 7 ! ! 12789 179 1289 ! 5 289# 3 ! 4 6 289# ! ! 2389 39 4 ! 6 7 289# ! 289# 1 5 ! +----------------------------+----------------------------+----------------------------+ EL13c179-OR3-relation for digits: 2, 8 and 9 in cells (marked #): (r4c3 r4c7 r4c4 r6c3 r6c9 r6c5 r9c7 r9c6 r7c8 r7c4 r8c3 r8c9 r8c5) with 3 guardians (in cells marked @) : n1r4c3 n3r6c5 n1r8c3 +----------------------+----------------------+----------------------+ ! 169 2 3 ! 14789 5 46789 ! 789 489 189 ! ! 4 159 7 ! 1289 289 289 ! 2589 3 6 ! ! 1569 8 159 ! 123479 239 24679 ! 2579 249 129 ! +----------------------+----------------------+----------------------+ ! 1289 4 1289#@ ! 289# 6 5 ! 289# 7 3 ! ! 235789 3579 2589 ! 2789 1 2789 ! 6 289 4 ! ! 2789 6 289# ! 234789 2389#@ 24789 ! 1 5 289# ! +----------------------+----------------------+----------------------+ ! 2589 59 6 ! 289# 4 1 ! 3 289# 7 ! ! 12789 179 1289#@ ! 5 289# 3 ! 4 6 289# ! ! 2389 39 4 ! 6 7 289# ! 289# 1 5 ! +----------------------+----------------------+----------------------+ EL13c179-OR5-relation for digits: 2, 8 and 9 in cells (marked #): (r4c1 r4c7 r4c4 r6c1 r6c9 r6c5 r9c7 r9c6 r7c8 r7c4 r8c1 r8c9 r8c5) with 5 guardians (in cells marked @) : n1r4c1 n7r6c1 n3r6c5 n1r8c1 n7r8c1 +-------------------------+-------------------------+-------------------------+ ! 169 2 3 ! 14789 5 46789 ! 789 489 189 ! ! 4 159 7 ! 1289 289 289 ! 2589 3 6 ! ! 1569 8 159 ! 123479 239 24679 ! 2579 249 129 ! +-------------------------+-------------------------+-------------------------+ ! 1289#@ 4 1289 ! 289# 6 5 ! 289# 7 3 ! ! 235789 3579 2589 ! 2789 1 2789 ! 6 289 4 ! ! 2789#@ 6 289 ! 234789 2389#@ 24789 ! 1 5 289# ! +-------------------------+-------------------------+-------------------------+ ! 2589 59 6 ! 289# 4 1 ! 3 289# 7 ! ! 12789#@ 179 1289 ! 5 289# 3 ! 4 6 289# ! ! 2389 39 4 ! 6 7 289# ! 289# 1 5 ! +-------------------------+-------------------------+-------------------------+ EL13c30-OR8-relation for digits: 2, 8 and 9 in cells (marked #): (r5c4 r5c8 r6c1 r6c4 r6c9 r7c4 r7c8 r8c1 r8c5 r8c9 r9c1 r9c6 r9c7) with 8 guardians (in cells marked @) : n7r5c4 n7r6c1 n3r6c4 n4r6c4 n7r6c4 n1r8c1 n7r8c1 n3r9c1 +----------------------------+----------------------------+----------------------------+ ! 169 2 3 ! 14789 5 46789 ! 789 489 189 ! ! 4 159 7 ! 1289 289 289 ! 2589 3 6 ! ! 1569 8 159 ! 123479 239 24679 ! 2579 249 129 ! +----------------------------+----------------------------+----------------------------+ ! 1289 4 1289 ! 289 6 5 ! 289 7 3 ! ! 235789 3579 2589 ! 2789#@ 1 2789 ! 6 289# 4 ! ! 2789#@ 6 289 ! 234789#@ 2389 24789 ! 1 5 289# ! +----------------------------+----------------------------+----------------------------+ ! 2589 59 6 ! 289# 4 1 ! 3 289# 7 ! ! 12789#@ 179 1289 ! 5 289# 3 ! 4 6 289# ! ! 2389#@ 39 4 ! 6 7 289# ! 289# 1 5 ! +----------------------------+----------------------------+----------------------------+ EL13c30-OR5-relation for digits: 2, 8 and 9 in cells (marked #): (r5c4 r5c8 r4c1 r4c4 r4c7 r7c4 r7c8 r9c1 r9c6 r9c7 r8c1 r8c5 r8c9) with 5 guardians (in cells marked @) : n7r5c4 n1r4c1 n3r9c1 n1r8c1 n7r8c1 +-------------------------+-------------------------+-------------------------+ ! 169 2 3 ! 14789 5 46789 ! 789 489 189 ! ! 4 159 7 ! 1289 289 289 ! 2589 3 6 ! ! 1569 8 159 ! 123479 239 24679 ! 2579 249 129 ! +-------------------------+-------------------------+-------------------------+ ! 1289#@ 4 1289 ! 289# 6 5 ! 289# 7 3 ! ! 235789 3579 2589 ! 2789#@ 1 2789 ! 6 289# 4 ! ! 2789 6 289 ! 234789 2389 24789 ! 1 5 289 ! +-------------------------+-------------------------+-------------------------+ ! 2589 59 6 ! 289# 4 1 ! 3 289# 7 ! ! 12789#@ 179 1289 ! 5 289# 3 ! 4 6 289# ! ! 2389#@ 39 4 ! 6 7 289# ! 289# 1 5 ! +-------------------------+-------------------------+-------------------------+ EL13c234-OR7-relation for digits: 2, 8 and 9 in cells (marked #): (r9c7 r8c3 r8c9 r7c4 r7c8 r5c3 r5c8 r4c4 r4c3 r4c7 r6c4 r6c1 r6c9) with 7 guardians (in cells marked @) : n1r8c3 n5r5c3 n1r4c3 n3r6c4 n4r6c4 n7r6c4 n7r6c1 +----------------------------+----------------------------+----------------------------+ ! 169 2 3 ! 14789 5 46789 ! 789 489 189 ! ! 4 159 7 ! 1289 289 289 ! 2589 3 6 ! ! 1569 8 159 ! 123479 239 24679 ! 2579 249 129 ! +----------------------------+----------------------------+----------------------------+ ! 1289 4 1289#@ ! 289# 6 5 ! 289# 7 3 ! ! 235789 3579 2589#@ ! 2789 1 2789 ! 6 289# 4 ! ! 2789#@ 6 289 ! 234789#@ 2389 24789 ! 1 5 289# ! +----------------------------+----------------------------+----------------------------+ ! 2589 59 6 ! 289# 4 1 ! 3 289# 7 ! ! 12789 179 1289#@ ! 5 289 3 ! 4 6 289# ! ! 2389 39 4 ! 6 7 289 ! 289# 1 5 ! +----------------------------+----------------------------+----------------------------+ EL13c234-OR6-relation for digits: 2, 8 and 9 in cells (marked #): (r8c9 r9c6 r9c7 r7c1 r7c8 r5c6 r5c8 r6c1 r6c6 r6c9 r4c1 r4c4 r4c7) with 6 guardians (in cells marked @) : n5r7c1 n7r5c6 n7r6c1 n4r6c6 n7r6c6 n1r4c1 +-------------------------+-------------------------+-------------------------+ ! 169 2 3 ! 14789 5 46789 ! 789 489 189 ! ! 4 159 7 ! 1289 289 289 ! 2589 3 6 ! ! 1569 8 159 ! 123479 239 24679 ! 2579 249 129 ! +-------------------------+-------------------------+-------------------------+ ! 1289#@ 4 1289 ! 289# 6 5 ! 289# 7 3 ! ! 235789 3579 2589 ! 2789 1 2789#@ ! 6 289# 4 ! ! 2789#@ 6 289 ! 234789 2389 24789#@ ! 1 5 289# ! +-------------------------+-------------------------+-------------------------+ ! 2589#@ 59 6 ! 289 4 1 ! 3 289# 7 ! ! 12789 179 1289 ! 5 289 3 ! 4 6 289# ! ! 2389 39 4 ! 6 7 289# ! 289# 1 5 ! +-------------------------+-------------------------+-------------------------+ EL13c176-OR7-relation for digits: 2, 8 and 9 in cells (marked #): (r7c1 r7c4 r7c8 r9c1 r9c6 r9c7 r4c4 r4c7 r6c5 r6c9 r5c1 r5c4 r5c8) with 7 guardians (in cells marked @) : n5r7c1 n3r9c1 n3r6c5 n3r5c1 n5r5c1 n7r5c1 n7r5c4 +----------------------------+----------------------------+----------------------------+ ! 169 2 3 ! 14789 5 46789 ! 789 489 189 ! ! 4 159 7 ! 1289 289 289 ! 2589 3 6 ! ! 1569 8 159 ! 123479 239 24679 ! 2579 249 129 ! +----------------------------+----------------------------+----------------------------+ ! 1289 4 1289 ! 289# 6 5 ! 289# 7 3 ! ! 235789#@ 3579 2589 ! 2789#@ 1 2789 ! 6 289# 4 ! ! 2789 6 289 ! 234789 2389#@ 24789 ! 1 5 289# ! +----------------------------+----------------------------+----------------------------+ ! 2589#@ 59 6 ! 289# 4 1 ! 3 289# 7 ! ! 12789 179 1289 ! 5 289 3 ! 4 6 289 ! ! 2389#@ 39 4 ! 6 7 289# ! 289# 1 5 ! +----------------------------+----------------------------+----------------------------+ EL10c6-OR7-relation for digits: 2, 8 and 9 in cells (marked #): (r7c4 r7c8 r7c1 r6c1 r5c4 r5c8 r5c1 r4c4 r4c7 r4c3) with 7 guardians (in cells marked @) : n5r7c1 n7r6c1 n7r5c4 n3r5c1 n5r5c1 n7r5c1 n1r4c3 +----------------------------+----------------------------+----------------------------+ ! 169 2 3 ! 14789 5 46789 ! 789 489 189 ! ! 4 159 7 ! 1289 289 289 ! 2589 3 6 ! ! 1569 8 159 ! 123479 239 24679 ! 2579 249 129 ! +----------------------------+----------------------------+----------------------------+ ! 1289 4 1289#@ ! 289# 6 5 ! 289# 7 3 ! ! 235789#@ 3579 2589 ! 2789#@ 1 2789 ! 6 289# 4 ! ! 2789#@ 6 289 ! 234789 2389 24789 ! 1 5 289 ! +----------------------------+----------------------------+----------------------------+ ! 2589#@ 59 6 ! 289# 4 1 ! 3 289# 7 ! ! 12789 179 1289 ! 5 289 3 ! 4 6 289 ! ! 2389 39 4 ! 6 7 289 ! 289 1 5 ! +----------------------------+----------------------------+----------------------------+ EL10c6-OR7-relation for digits: 2, 8 and 9 in cells (marked #): (r7c1 r7c8 r7c4 r4c4 r5c1 r5c8 r5c4 r6c1 r6c9 r6c5) with 7 guardians (in cells marked @) : n5r7c1 n3r5c1 n5r5c1 n7r5c1 n7r5c4 n7r6c1 n3r6c5 +----------------------------+----------------------------+----------------------------+ ! 169 2 3 ! 14789 5 46789 ! 789 489 189 ! ! 4 159 7 ! 1289 289 289 ! 2589 3 6 ! ! 1569 8 159 ! 123479 239 24679 ! 2579 249 129 ! +----------------------------+----------------------------+----------------------------+ ! 1289 4 1289 ! 289# 6 5 ! 289 7 3 ! ! 235789#@ 3579 2589 ! 2789#@ 1 2789 ! 6 289# 4 ! ! 2789#@ 6 289 ! 234789 2389#@ 24789 ! 1 5 289# ! +----------------------------+----------------------------+----------------------------+ ! 2589#@ 59 6 ! 289# 4 1 ! 3 289# 7 ! ! 12789 179 1289 ! 5 289 3 ! 4 6 289 ! ! 2389 39 4 ! 6 7 289 ! 289 1 5 ! +----------------------------+----------------------------+----------------------------+ EL13c259s-OR4-relation for digits: 2, 8 and 9 in cells (marked #): (r2c7 r2c6 r2c5 r8c5 r9c7 r9c6 r7c8 r7c4 r4c7 r5c8 r6c9 r6c6 r6c5) with 4 guardians (in cells marked @) : n5r2c7 n4r6c6 n7r6c6 n3r6c5 +-------------------------+-------------------------+-------------------------+ ! 169 2 3 ! 14789 5 46789 ! 789 489 189 ! ! 4 159 7 ! 1289 289# 289# ! 2589#@ 3 6 ! ! 1569 8 159 ! 123479 239 24679 ! 2579 249 129 ! +-------------------------+-------------------------+-------------------------+ ! 1289 4 1289 ! 289 6 5 ! 289# 7 3 ! ! 235789 3579 2589 ! 2789 1 2789 ! 6 289# 4 ! ! 2789 6 289 ! 234789 2389#@ 24789#@ ! 1 5 289# ! +-------------------------+-------------------------+-------------------------+ ! 2589 59 6 ! 289# 4 1 ! 3 289# 7 ! ! 12789 179 1289 ! 5 289# 3 ! 4 6 289 ! ! 2389 39 4 ! 6 7 289# ! 289# 1 5 ! +-------------------------+-------------------------+-------------------------+ EL13c259s-OR4-relation for digits: 2, 8 and 9 in cells (marked #): (r2c7 r2c6 r2c4 r7c4 r9c7 r9c6 r8c9 r8c5 r4c7 r6c9 r5c8 r5c6 r5c4) with 4 guardians (in cells marked @) : n5r2c7 n1r2c4 n7r5c6 n7r5c4 +----------------------+----------------------+----------------------+ ! 169 2 3 ! 14789 5 46789 ! 789 489 189 ! ! 4 159 7 ! 1289#@ 289 289# ! 2589#@ 3 6 ! ! 1569 8 159 ! 123479 239 24679 ! 2579 249 129 ! +----------------------+----------------------+----------------------+ ! 1289 4 1289 ! 289 6 5 ! 289# 7 3 ! ! 235789 3579 2589 ! 2789#@ 1 2789#@ ! 6 289# 4 ! ! 2789 6 289 ! 234789 2389 24789 ! 1 5 289# ! +----------------------+----------------------+----------------------+ ! 2589 59 6 ! 289# 4 1 ! 3 289 7 ! ! 12789 179 1289 ! 5 289# 3 ! 4 6 289# ! ! 2389 39 4 ! 6 7 289# ! 289# 1 5 ! +----------------------+----------------------+----------------------+ EL13c259-OR6-relation for digits: 2, 8 and 9 in cells (marked #): (r7c4 r9c7 r9c6 r8c3 r8c9 r8c5 r4c7 r6c3 r6c9 r6c4 r5c3 r5c8 r5c4) with 6 guardians (in cells marked @) : n1r8c3 n3r6c4 n4r6c4 n7r6c4 n5r5c3 n7r5c4 +----------------------------+----------------------------+----------------------------+ ! 169 2 3 ! 14789 5 46789 ! 789 489 189 ! ! 4 159 7 ! 1289 289 289 ! 2589 3 6 ! ! 1569 8 159 ! 123479 239 24679 ! 2579 249 129 ! +----------------------------+----------------------------+----------------------------+ ! 1289 4 1289 ! 289 6 5 ! 289# 7 3 ! ! 235789 3579 2589#@ ! 2789#@ 1 2789 ! 6 289# 4 ! ! 2789 6 289# ! 234789#@ 2389 24789 ! 1 5 289# ! +----------------------------+----------------------------+----------------------------+ ! 2589 59 6 ! 289# 4 1 ! 3 289 7 ! ! 12789 179 1289#@ ! 5 289# 3 ! 4 6 289# ! ! 2389 39 4 ! 6 7 289# ! 289# 1 5 ! +----------------------------+----------------------------+----------------------------+ EL13c259-OR6-relation for digits: 2, 8 and 9 in cells (marked #): (r7c4 r8c9 r8c5 r9c1 r9c7 r9c6 r6c9 r4c1 r4c7 r4c4 r5c1 r5c8 r5c4) with 6 guardians (in cells marked @) : n3r9c1 n1r4c1 n3r5c1 n5r5c1 n7r5c1 n7r5c4 +----------------------------+----------------------------+----------------------------+ ! 169 2 3 ! 14789 5 46789 ! 789 489 189 ! ! 4 159 7 ! 1289 289 289 ! 2589 3 6 ! ! 1569 8 159 ! 123479 239 24679 ! 2579 249 129 ! +----------------------------+----------------------------+----------------------------+ ! 1289#@ 4 1289 ! 289# 6 5 ! 289# 7 3 ! ! 235789#@ 3579 2589 ! 2789#@ 1 2789 ! 6 289# 4 ! ! 2789 6 289 ! 234789 2389 24789 ! 1 5 289# ! +----------------------------+----------------------------+----------------------------+ ! 2589 59 6 ! 289# 4 1 ! 3 289 7 ! ! 12789 179 1289 ! 5 289# 3 ! 4 6 289# ! ! 2389#@ 39 4 ! 6 7 289# ! 289# 1 5 ! +----------------------------+----------------------------+----------------------------+ EL10c8-OR8-relation for digits: 2, 8 and 9 in cells (marked #): (r9c6 r9c1 r9c7 r4c7 r6c6 r6c1 r6c9 r5c6 r5c1 r5c8) with 8 guardians (in cells marked @) : n3r9c1 n4r6c6 n7r6c6 n7r6c1 n7r5c6 n3r5c1 n5r5c1 n7r5c1 +----------------------------+----------------------------+----------------------------+ ! 169 2 3 ! 14789 5 46789 ! 789 489 189 ! ! 4 159 7 ! 1289 289 289 ! 2589 3 6 ! ! 1569 8 159 ! 123479 239 24679 ! 2579 249 129 ! +----------------------------+----------------------------+----------------------------+ ! 1289 4 1289 ! 289 6 5 ! 289# 7 3 ! ! 235789#@ 3579 2589 ! 2789 1 2789#@ ! 6 289# 4 ! ! 2789#@ 6 289 ! 234789 2389 24789#@ ! 1 5 289# ! +----------------------------+----------------------------+----------------------------+ ! 2589 59 6 ! 289 4 1 ! 3 289 7 ! ! 12789 179 1289 ! 5 289 3 ! 4 6 289 ! ! 2389#@ 39 4 ! 6 7 289# ! 289# 1 5 ! +----------------------------+----------------------------+----------------------------+ EL10c8-OR6-relation for digits: 2, 8 and 9 in cells (marked #): (r7c4 r7c1 r7c8 r5c8 r6c4 r6c1 r6c9 r4c4 r4c1 r4c7) with 6 guardians (in cells marked @) : n5r7c1 n3r6c4 n4r6c4 n7r6c4 n7r6c1 n1r4c1 +----------------------------+----------------------------+----------------------------+ ! 169 2 3 ! 14789 5 46789 ! 789 489 189 ! ! 4 159 7 ! 1289 289 289 ! 2589 3 6 ! ! 1569 8 159 ! 123479 239 24679 ! 2579 249 129 ! +----------------------------+----------------------------+----------------------------+ ! 1289#@ 4 1289 ! 289# 6 5 ! 289# 7 3 ! ! 235789 3579 2589 ! 2789 1 2789 ! 6 289# 4 ! ! 2789#@ 6 289 ! 234789#@ 2389 24789 ! 1 5 289# ! +----------------------------+----------------------------+----------------------------+ ! 2589#@ 59 6 ! 289# 4 1 ! 3 289# 7 ! ! 12789 179 1289 ! 5 289 3 ! 4 6 289 ! ! 2389 39 4 ! 6 7 289 ! 289 1 5 ! +----------------------------+----------------------------+----------------------------+ EL13c172-OR8-relation for digits: 2, 8 and 9 in cells (marked #): (r7c1 r7c4 r7c8 r9c1 r9c6 r9c7 r4c4 r4c7 r6c6 r6c9 r5c1 r5c4 r5c8) with 8 guardians (in cells marked @) : n5r7c1 n3r9c1 n4r6c6 n7r6c6 n3r5c1 n5r5c1 n7r5c1 n7r5c4 +----------------------------+----------------------------+----------------------------+ ! 169 2 3 ! 14789 5 46789 ! 789 489 189 ! ! 4 159 7 ! 1289 289 289 ! 2589 3 6 ! ! 1569 8 159 ! 123479 239 24679 ! 2579 249 129 ! +----------------------------+----------------------------+----------------------------+ ! 1289 4 1289 ! 289# 6 5 ! 289# 7 3 ! ! 235789#@ 3579 2589 ! 2789#@ 1 2789 ! 6 289# 4 ! ! 2789 6 289 ! 234789 2389 24789#@ ! 1 5 289# ! +----------------------------+----------------------------+----------------------------+ ! 2589#@ 59 6 ! 289# 4 1 ! 3 289# 7 ! ! 12789 179 1289 ! 5 289 3 ! 4 6 289 ! ! 2389#@ 39 4 ! 6 7 289# ! 289# 1 5 ! +----------------------------+----------------------------+----------------------------+ EL14c19-OR4-relation for digits: 2, 8 and 9 in cells (marked #): (r5c8 r6c3 r6c1 r6c9 r4c4 r4c1 r4c7 r7c4 r7c8 r9c6 r9c7 r8c5 r8c1 r8c9) with 4 guardians (in cells marked @) : n7r6c1 n1r4c1 n1r8c1 n7r8c1 +-------------------------+-------------------------+-------------------------+ ! 169 2 3 ! 14789 5 46789 ! 789 489 189 ! ! 4 159 7 ! 1289 289 289 ! 2589 3 6 ! ! 1569 8 159 ! 123479 239 24679 ! 2579 249 129 ! +-------------------------+-------------------------+-------------------------+ ! 1289#@ 4 1289 ! 289# 6 5 ! 289# 7 3 ! ! 235789 3579 2589 ! 2789 1 2789 ! 6 289# 4 ! ! 2789#@ 6 289# ! 234789 2389 24789 ! 1 5 289# ! +-------------------------+-------------------------+-------------------------+ ! 2589 59 6 ! 289# 4 1 ! 3 289# 7 ! ! 12789#@ 179 1289 ! 5 289# 3 ! 4 6 289# ! ! 2389 39 4 ! 6 7 289# ! 289# 1 5 ! +-------------------------+-------------------------+-------------------------+ EL14c19-OR3-relation for digits: 2, 8 and 9 in cells (marked #): (r5c8 r6c1 r6c3 r6c9 r4c4 r4c3 r4c7 r7c4 r7c8 r9c6 r9c7 r8c5 r8c3 r8c9) with 3 guardians (in cells marked @) : n7r6c1 n1r4c3 n1r8c3 +----------------------+----------------------+----------------------+ ! 169 2 3 ! 14789 5 46789 ! 789 489 189 ! ! 4 159 7 ! 1289 289 289 ! 2589 3 6 ! ! 1569 8 159 ! 123479 239 24679 ! 2579 249 129 ! +----------------------+----------------------+----------------------+ ! 1289 4 1289#@ ! 289# 6 5 ! 289# 7 3 ! ! 235789 3579 2589 ! 2789 1 2789 ! 6 289# 4 ! ! 2789#@ 6 289# ! 234789 2389 24789 ! 1 5 289# ! +----------------------+----------------------+----------------------+ ! 2589 59 6 ! 289# 4 1 ! 3 289# 7 ! ! 12789 179 1289#@ ! 5 289# 3 ! 4 6 289# ! ! 2389 39 4 ! 6 7 289# ! 289# 1 5 ! +----------------------+----------------------+----------------------+ EL14c19-OR7-relation for digits: 2, 8 and 9 in cells (marked #): (r5c8 r4c3 r4c1 r4c7 r6c4 r6c1 r6c9 r7c4 r7c8 r8c5 r8c9 r9c6 r9c1 r9c7) with 7 guardians (in cells marked @) : n1r4c3 n1r4c1 n3r6c4 n4r6c4 n7r6c4 n7r6c1 n3r9c1 +----------------------------+----------------------------+----------------------------+ ! 169 2 3 ! 14789 5 46789 ! 789 489 189 ! ! 4 159 7 ! 1289 289 289 ! 2589 3 6 ! ! 1569 8 159 ! 123479 239 24679 ! 2579 249 129 ! +----------------------------+----------------------------+----------------------------+ ! 1289#@ 4 1289#@ ! 289 6 5 ! 289# 7 3 ! ! 235789 3579 2589 ! 2789 1 2789 ! 6 289# 4 ! ! 2789#@ 6 289 ! 234789#@ 2389 24789 ! 1 5 289# ! +----------------------------+----------------------------+----------------------------+ ! 2589 59 6 ! 289# 4 1 ! 3 289# 7 ! ! 12789 179 1289 ! 5 289# 3 ! 4 6 289# ! ! 2389#@ 39 4 ! 6 7 289# ! 289# 1 5 ! +----------------------------+----------------------------+----------------------------+ EL14c19-OR7-relation for digits: 2, 8 and 9 in cells (marked #): (r4c7 r6c3 r6c1 r6c9 r5c6 r5c1 r5c8 r9c6 r9c7 r7c4 r7c8 r8c5 r8c1 r8c9) with 7 guardians (in cells marked @) : n7r6c1 n7r5c6 n3r5c1 n5r5c1 n7r5c1 n1r8c1 n7r8c1 +----------------------------+----------------------------+----------------------------+ ! 169 2 3 ! 14789 5 46789 ! 789 489 189 ! ! 4 159 7 ! 1289 289 289 ! 2589 3 6 ! ! 1569 8 159 ! 123479 239 24679 ! 2579 249 129 ! +----------------------------+----------------------------+----------------------------+ ! 1289 4 1289 ! 289 6 5 ! 289# 7 3 ! ! 235789#@ 3579 2589 ! 2789 1 2789#@ ! 6 289# 4 ! ! 2789#@ 6 289# ! 234789 2389 24789 ! 1 5 289# ! +----------------------------+----------------------------+----------------------------+ ! 2589 59 6 ! 289# 4 1 ! 3 289# 7 ! ! 12789#@ 179 1289 ! 5 289# 3 ! 4 6 289# ! ! 2389 39 4 ! 6 7 289# ! 289# 1 5 ! +----------------------------+----------------------------+----------------------------+ EL14c19-OR4-relation for digits: 2, 8 and 9 in cells (marked #): (r4c7 r6c1 r6c3 r6c9 r5c6 r5c3 r5c8 r9c6 r9c7 r7c4 r7c8 r8c5 r8c3 r8c9) with 4 guardians (in cells marked @) : n7r6c1 n7r5c6 n5r5c3 n1r8c3 +----------------------+----------------------+----------------------+ ! 169 2 3 ! 14789 5 46789 ! 789 489 189 ! ! 4 159 7 ! 1289 289 289 ! 2589 3 6 ! ! 1569 8 159 ! 123479 239 24679 ! 2579 249 129 ! +----------------------+----------------------+----------------------+ ! 1289 4 1289 ! 289 6 5 ! 289# 7 3 ! ! 235789 3579 2589#@ ! 2789 1 2789#@ ! 6 289# 4 ! ! 2789#@ 6 289# ! 234789 2389 24789 ! 1 5 289# ! +----------------------+----------------------+----------------------+ ! 2589 59 6 ! 289# 4 1 ! 3 289# 7 ! ! 12789 179 1289#@ ! 5 289# 3 ! 4 6 289# ! ! 2389 39 4 ! 6 7 289# ! 289# 1 5 ! +----------------------+----------------------+----------------------+ EL14c19-OR8-relation for digits: 2, 8 and 9 in cells (marked #): (r4c7 r5c3 r5c1 r5c8 r6c6 r6c1 r6c9 r9c6 r9c7 r8c5 r8c9 r7c4 r7c1 r7c8) with 8 guardians (in cells marked @) : n5r5c3 n3r5c1 n5r5c1 n7r5c1 n4r6c6 n7r6c6 n7r6c1 n5r7c1 +----------------------------+----------------------------+----------------------------+ ! 169 2 3 ! 14789 5 46789 ! 789 489 189 ! ! 4 159 7 ! 1289 289 289 ! 2589 3 6 ! ! 1569 8 159 ! 123479 239 24679 ! 2579 249 129 ! +----------------------------+----------------------------+----------------------------+ ! 1289 4 1289 ! 289 6 5 ! 289# 7 3 ! ! 235789#@ 3579 2589#@ ! 2789 1 2789 ! 6 289# 4 ! ! 2789#@ 6 289 ! 234789 2389 24789#@ ! 1 5 289# ! +----------------------------+----------------------------+----------------------------+ ! 2589#@ 59 6 ! 289# 4 1 ! 3 289# 7 ! ! 12789 179 1289 ! 5 289# 3 ! 4 6 289# ! ! 2389 39 4 ! 6 7 289# ! 289# 1 5 ! +----------------------------+----------------------------+----------------------------+ EL13c168-OR6-relation for digits: 2, 8 and 9 in cells (marked #): (r7c1 r7c4 r7c8 r8c1 r8c5 r8c9 r5c8 r6c1 r6c5 r6c9 r4c3 r4c4 r4c7) with 6 guardians (in cells marked @) : n5r7c1 n1r8c1 n7r8c1 n7r6c1 n3r6c5 n1r4c3 +-------------------------+-------------------------+-------------------------+ ! 169 2 3 ! 14789 5 46789 ! 789 489 189 ! ! 4 159 7 ! 1289 289 289 ! 2589 3 6 ! ! 1569 8 159 ! 123479 239 24679 ! 2579 249 129 ! +-------------------------+-------------------------+-------------------------+ ! 1289 4 1289#@ ! 289# 6 5 ! 289# 7 3 ! ! 235789 3579 2589 ! 2789 1 2789 ! 6 289# 4 ! ! 2789#@ 6 289 ! 234789 2389#@ 24789 ! 1 5 289# ! +-------------------------+-------------------------+-------------------------+ ! 2589#@ 59 6 ! 289# 4 1 ! 3 289# 7 ! ! 12789#@ 179 1289 ! 5 289# 3 ! 4 6 289# ! ! 2389 39 4 ! 6 7 289 ! 289 1 5 ! +-------------------------+-------------------------+-------------------------+ EL10c1-OR6-relation for digits: 2, 8 and 9 in cells (marked #): (r7c8 r7c4 r7c1 r6c1 r4c4 r4c3 r4c1 r5c8 r5c6 r5c4) with 6 guardians (in cells marked @) : n5r7c1 n7r6c1 n1r4c3 n1r4c1 n7r5c6 n7r5c4 +----------------------+----------------------+----------------------+ ! 169 2 3 ! 14789 5 46789 ! 789 489 189 ! ! 4 159 7 ! 1289 289 289 ! 2589 3 6 ! ! 1569 8 159 ! 123479 239 24679 ! 2579 249 129 ! +----------------------+----------------------+----------------------+ ! 1289#@ 4 1289#@ ! 289# 6 5 ! 289 7 3 ! ! 235789 3579 2589 ! 2789#@ 1 2789#@ ! 6 289# 4 ! ! 2789#@ 6 289 ! 234789 2389 24789 ! 1 5 289 ! +----------------------+----------------------+----------------------+ ! 2589#@ 59 6 ! 289# 4 1 ! 3 289# 7 ! ! 12789 179 1289 ! 5 289 3 ! 4 6 289 ! ! 2389 39 4 ! 6 7 289 ! 289 1 5 ! +----------------------+----------------------+----------------------+ EL12c26-OR7-relation for digits: 2, 8 and 9 in cells (marked #): (r7c1 r7c4 r7c8 r9c1 r9c6 r9c7 r6c1 r6c4 r6c9 r4c3 r4c4 r4c7) with 7 guardians (in cells marked @) : n5r7c1 n3r9c1 n7r6c1 n3r6c4 n4r6c4 n7r6c4 n1r4c3 +----------------------------+----------------------------+----------------------------+ ! 169 2 3 ! 14789 5 46789 ! 789 489 189 ! ! 4 159 7 ! 1289 289 289 ! 2589 3 6 ! ! 1569 8 159 ! 123479 239 24679 ! 2579 249 129 ! +----------------------------+----------------------------+----------------------------+ ! 1289 4 1289#@ ! 289# 6 5 ! 289# 7 3 ! ! 235789 3579 2589 ! 2789 1 2789 ! 6 289 4 ! ! 2789#@ 6 289 ! 234789#@ 2389 24789 ! 1 5 289# ! +----------------------------+----------------------------+----------------------------+ ! 2589#@ 59 6 ! 289# 4 1 ! 3 289# 7 ! ! 12789 179 1289 ! 5 289 3 ! 4 6 289 ! ! 2389#@ 39 4 ! 6 7 289# ! 289# 1 5 ! +----------------------------+----------------------------+----------------------------+ EL12c26-OR7-relation for digits: 2, 8 and 9 in cells (marked #): (r7c1 r7c4 r7c8 r8c1 r8c5 r8c9 r4c1 r4c4 r4c7 r6c3 r6c4 r6c9) with 7 guardians (in cells marked @) : n5r7c1 n1r8c1 n7r8c1 n1r4c1 n3r6c4 n4r6c4 n7r6c4 +----------------------------+----------------------------+----------------------------+ ! 169 2 3 ! 14789 5 46789 ! 789 489 189 ! ! 4 159 7 ! 1289 289 289 ! 2589 3 6 ! ! 1569 8 159 ! 123479 239 24679 ! 2579 249 129 ! +----------------------------+----------------------------+----------------------------+ ! 1289#@ 4 1289 ! 289# 6 5 ! 289# 7 3 ! ! 235789 3579 2589 ! 2789 1 2789 ! 6 289 4 ! ! 2789 6 289# ! 234789#@ 2389 24789 ! 1 5 289# ! +----------------------------+----------------------------+----------------------------+ ! 2589#@ 59 6 ! 289# 4 1 ! 3 289# 7 ! ! 12789#@ 179 1289 ! 5 289# 3 ! 4 6 289# ! ! 2389 39 4 ! 6 7 289 ! 289 1 5 ! +----------------------------+----------------------------+----------------------------+ EL12c25-OR7-relation for digits: 2, 8 and 9 in cells (marked #): (r7c1 r7c4 r7c8 r9c1 r9c6 r9c7 r5c1 r5c4 r5c8 r4c3 r4c4 r4c7) with 7 guardians (in cells marked @) : n5r7c1 n3r9c1 n3r5c1 n5r5c1 n7r5c1 n7r5c4 n1r4c3 +----------------------------+----------------------------+----------------------------+ ! 169 2 3 ! 14789 5 46789 ! 789 489 189 ! ! 4 159 7 ! 1289 289 289 ! 2589 3 6 ! ! 1569 8 159 ! 123479 239 24679 ! 2579 249 129 ! +----------------------------+----------------------------+----------------------------+ ! 1289 4 1289#@ ! 289# 6 5 ! 289# 7 3 ! ! 235789#@ 3579 2589 ! 2789#@ 1 2789 ! 6 289# 4 ! ! 2789 6 289 ! 234789 2389 24789 ! 1 5 289 ! +----------------------------+----------------------------+----------------------------+ ! 2589#@ 59 6 ! 289# 4 1 ! 3 289# 7 ! ! 12789 179 1289 ! 5 289 3 ! 4 6 289 ! ! 2389#@ 39 4 ! 6 7 289# ! 289# 1 5 ! +----------------------------+----------------------------+----------------------------+ EL13c29-OR8-relation for digits: 2, 8 and 9 in cells (marked #): (r9c1 r9c7 r7c4 r7c1 r7c8 r4c1 r4c7 r5c4 r5c3 r5c8 r6c4 r6c3 r6c9) with 8 guardians (in cells marked @) : n3r9c1 n5r7c1 n1r4c1 n7r5c4 n5r5c3 n3r6c4 n4r6c4 n7r6c4 +----------------------------+----------------------------+----------------------------+ ! 169 2 3 ! 14789 5 46789 ! 789 489 189 ! ! 4 159 7 ! 1289 289 289 ! 2589 3 6 ! ! 1569 8 159 ! 123479 239 24679 ! 2579 249 129 ! +----------------------------+----------------------------+----------------------------+ ! 1289#@ 4 1289 ! 289 6 5 ! 289# 7 3 ! ! 235789 3579 2589#@ ! 2789#@ 1 2789 ! 6 289# 4 ! ! 2789 6 289# ! 234789#@ 2389 24789 ! 1 5 289# ! +----------------------------+----------------------------+----------------------------+ ! 2589#@ 59 6 ! 289# 4 1 ! 3 289# 7 ! ! 12789 179 1289 ! 5 289 3 ! 4 6 289 ! ! 2389#@ 39 4 ! 6 7 289 ! 289# 1 5 ! +----------------------------+----------------------------+----------------------------+ EL13c29-OR7-relation for digits: 2, 8 and 9 in cells (marked #): (r8c1 r8c9 r7c4 r7c1 r7c8 r6c1 r6c9 r5c4 r5c3 r5c8 r4c4 r4c3 r4c7) with 7 guardians (in cells marked @) : n1r8c1 n7r8c1 n5r7c1 n7r6c1 n7r5c4 n5r5c3 n1r4c3 +-------------------------+-------------------------+-------------------------+ ! 169 2 3 ! 14789 5 46789 ! 789 489 189 ! ! 4 159 7 ! 1289 289 289 ! 2589 3 6 ! ! 1569 8 159 ! 123479 239 24679 ! 2579 249 129 ! +-------------------------+-------------------------+-------------------------+ ! 1289 4 1289#@ ! 289# 6 5 ! 289# 7 3 ! ! 235789 3579 2589#@ ! 2789#@ 1 2789 ! 6 289# 4 ! ! 2789#@ 6 289 ! 234789 2389 24789 ! 1 5 289# ! +-------------------------+-------------------------+-------------------------+ ! 2589#@ 59 6 ! 289# 4 1 ! 3 289# 7 ! ! 12789#@ 179 1289 ! 5 289 3 ! 4 6 289# ! ! 2389 39 4 ! 6 7 289 ! 289 1 5 ! +-------------------------+-------------------------+-------------------------+ EL14c152-OR8-relation for digits: 2, 8 and 9 in cells (marked #): (r5c6 r5c8 r4c4 r4c7 r6c1 r6c6 r6c9 r9c6 r9c7 r7c1 r7c8 r8c3 r8c1 r8c9) with 8 guardians (in cells marked @) : n7r5c6 n7r6c1 n4r6c6 n7r6c6 n5r7c1 n1r8c3 n1r8c1 n7r8c1 +-------------------------+-------------------------+-------------------------+ ! 169 2 3 ! 14789 5 46789 ! 789 489 189 ! ! 4 159 7 ! 1289 289 289 ! 2589 3 6 ! ! 1569 8 159 ! 123479 239 24679 ! 2579 249 129 ! +-------------------------+-------------------------+-------------------------+ ! 1289 4 1289 ! 289# 6 5 ! 289# 7 3 ! ! 235789 3579 2589 ! 2789 1 2789#@ ! 6 289# 4 ! ! 2789#@ 6 289 ! 234789 2389 24789#@ ! 1 5 289# ! +-------------------------+-------------------------+-------------------------+ ! 2589#@ 59 6 ! 289 4 1 ! 3 289# 7 ! ! 12789#@ 179 1289#@ ! 5 289 3 ! 4 6 289# ! ! 2389 39 4 ! 6 7 289# ! 289# 1 5 ! +-------------------------+-------------------------+-------------------------+ EL14c17-OR8-relation for digits: 2, 8 and 9 in cells (marked #): (r7c8 r8c3 r8c1 r8c9 r9c6 r9c1 r9c7 r5c6 r5c8 r6c6 r6c1 r6c9 r4c4 r4c7) with 8 guardians (in cells marked @) : n1r8c3 n1r8c1 n7r8c1 n3r9c1 n7r5c6 n4r6c6 n7r6c6 n7r6c1 +-------------------------+-------------------------+-------------------------+ ! 169 2 3 ! 14789 5 46789 ! 789 489 189 ! ! 4 159 7 ! 1289 289 289 ! 2589 3 6 ! ! 1569 8 159 ! 123479 239 24679 ! 2579 249 129 ! +-------------------------+-------------------------+-------------------------+ ! 1289 4 1289 ! 289# 6 5 ! 289# 7 3 ! ! 235789 3579 2589 ! 2789 1 2789#@ ! 6 289# 4 ! ! 2789#@ 6 289 ! 234789 2389 24789#@ ! 1 5 289# ! +-------------------------+-------------------------+-------------------------+ ! 2589 59 6 ! 289 4 1 ! 3 289# 7 ! ! 12789#@ 179 1289#@ ! 5 289 3 ! 4 6 289# ! ! 2389#@ 39 4 ! 6 7 289# ! 289# 1 5 ! +-------------------------+-------------------------+-------------------------+ EL14c14-OR7-relation for digits: 2, 8 and 9 in cells (marked #): (r4c7 r5c6 r5c4 r5c8 r6c1 r6c4 r6c9 r7c4 r7c8 r8c5 r8c9 r9c1 r9c6 r9c7) with 7 guardians (in cells marked @) : n7r5c6 n7r5c4 n7r6c1 n3r6c4 n4r6c4 n7r6c4 n3r9c1 +----------------------------+----------------------------+----------------------------+ ! 169 2 3 ! 14789 5 46789 ! 789 489 189 ! ! 4 159 7 ! 1289 289 289 ! 2589 3 6 ! ! 1569 8 159 ! 123479 239 24679 ! 2579 249 129 ! +----------------------------+----------------------------+----------------------------+ ! 1289 4 1289 ! 289 6 5 ! 289# 7 3 ! ! 235789 3579 2589 ! 2789#@ 1 2789#@ ! 6 289# 4 ! ! 2789#@ 6 289 ! 234789#@ 2389 24789 ! 1 5 289# ! +----------------------------+----------------------------+----------------------------+ ! 2589 59 6 ! 289# 4 1 ! 3 289# 7 ! ! 12789 179 1289 ! 5 289# 3 ! 4 6 289# ! ! 2389#@ 39 4 ! 6 7 289# ! 289# 1 5 ! +----------------------------+----------------------------+----------------------------+ EL14c7-OR4-relation for digits: 2, 8 and 9 in cells (marked #): (r5c8 r6c1 r6c3 r6c9 r4c4 r4c3 r4c7 r8c9 r7c4 r7c1 r7c8 r9c6 r9c1 r9c7) with 4 guardians (in cells marked @) : n7r6c1 n1r4c3 n5r7c1 n3r9c1 +----------------------+----------------------+----------------------+ ! 169 2 3 ! 14789 5 46789 ! 789 489 189 ! ! 4 159 7 ! 1289 289 289 ! 2589 3 6 ! ! 1569 8 159 ! 123479 239 24679 ! 2579 249 129 ! +----------------------+----------------------+----------------------+ ! 1289 4 1289#@ ! 289# 6 5 ! 289# 7 3 ! ! 235789 3579 2589 ! 2789 1 2789 ! 6 289# 4 ! ! 2789#@ 6 289# ! 234789 2389 24789 ! 1 5 289# ! +----------------------+----------------------+----------------------+ ! 2589#@ 59 6 ! 289# 4 1 ! 3 289# 7 ! ! 12789 179 1289 ! 5 289 3 ! 4 6 289# ! ! 2389#@ 39 4 ! 6 7 289# ! 289# 1 5 ! +----------------------+----------------------+----------------------+ EL14c3-OR7-relation for digits: 2, 8 and 9 in cells (marked #): (r8c5 r9c7 r9c6 r7c1 r7c8 r7c4 r5c1 r5c8 r6c1 r6c9 r6c5 r4c3 r4c7 r4c4) with 7 guardians (in cells marked @) : n5r7c1 n3r5c1 n5r5c1 n7r5c1 n7r6c1 n3r6c5 n1r4c3 +----------------------------+----------------------------+----------------------------+ ! 169 2 3 ! 14789 5 46789 ! 789 489 189 ! ! 4 159 7 ! 1289 289 289 ! 2589 3 6 ! ! 1569 8 159 ! 123479 239 24679 ! 2579 249 129 ! +----------------------------+----------------------------+----------------------------+ ! 1289 4 1289#@ ! 289# 6 5 ! 289# 7 3 ! ! 235789#@ 3579 2589 ! 2789 1 2789 ! 6 289# 4 ! ! 2789#@ 6 289 ! 234789 2389#@ 24789 ! 1 5 289# ! +----------------------------+----------------------------+----------------------------+ ! 2589#@ 59 6 ! 289# 4 1 ! 3 289# 7 ! ! 12789 179 1289 ! 5 289# 3 ! 4 6 289 ! ! 2389 39 4 ! 6 7 289# ! 289# 1 5 ! +----------------------------+----------------------------+----------------------------+ EL14c2-OR5-relation for digits: 2, 8 and 9 in cells (marked #): (r8c9 r9c6 r9c7 r7c1 r7c4 r7c8 r6c1 r6c9 r4c1 r4c4 r4c7 r5c3 r5c6 r5c8) with 5 guardians (in cells marked @) : n5r7c1 n7r6c1 n1r4c1 n5r5c3 n7r5c6 +----------------------+----------------------+----------------------+ ! 169 2 3 ! 14789 5 46789 ! 789 489 189 ! ! 4 159 7 ! 1289 289 289 ! 2589 3 6 ! ! 1569 8 159 ! 123479 239 24679 ! 2579 249 129 ! +----------------------+----------------------+----------------------+ ! 1289#@ 4 1289 ! 289# 6 5 ! 289# 7 3 ! ! 235789 3579 2589#@ ! 2789 1 2789#@ ! 6 289# 4 ! ! 2789#@ 6 289 ! 234789 2389 24789 ! 1 5 289# ! +----------------------+----------------------+----------------------+ ! 2589#@ 59 6 ! 289# 4 1 ! 3 289# 7 ! ! 12789 179 1289 ! 5 289 3 ! 4 6 289# ! ! 2389 39 4 ! 6 7 289# ! 289# 1 5 ! +----------------------+----------------------+----------------------+ EL14c2-OR7-relation for digits: 2, 8 and 9 in cells (marked #): (r8c9 r7c4 r7c8 r9c1 r9c6 r9c7 r6c1 r6c9 r5c1 r5c6 r5c8 r4c3 r4c4 r4c7) with 7 guardians (in cells marked @) : n3r9c1 n7r6c1 n3r5c1 n5r5c1 n7r5c1 n7r5c6 n1r4c3 +----------------------------+----------------------------+----------------------------+ ! 169 2 3 ! 14789 5 46789 ! 789 489 189 ! ! 4 159 7 ! 1289 289 289 ! 2589 3 6 ! ! 1569 8 159 ! 123479 239 24679 ! 2579 249 129 ! +----------------------------+----------------------------+----------------------------+ ! 1289 4 1289#@ ! 289# 6 5 ! 289# 7 3 ! ! 235789#@ 3579 2589 ! 2789 1 2789#@ ! 6 289# 4 ! ! 2789#@ 6 289 ! 234789 2389 24789 ! 1 5 289# ! +----------------------------+----------------------------+----------------------------+ ! 2589 59 6 ! 289# 4 1 ! 3 289# 7 ! ! 12789 179 1289 ! 5 289 3 ! 4 6 289# ! ! 2389#@ 39 4 ! 6 7 289# ! 289# 1 5 ! +----------------------------+----------------------------+----------------------------+ EL15c89-OR6-relation for digits: 2, 8 and 9 in cells (marked #): (r7c4 r7c8 r8c5 r8c9 r9c1 r9c6 r9c7 r5c1 r5c8 r4c1 r4c4 r4c7 r6c3 r6c5 r6c9) with 6 guardians (in cells marked @) : n3r9c1 n3r5c1 n5r5c1 n7r5c1 n1r4c1 n3r6c5 +----------------------------+----------------------------+----------------------------+ ! 169 2 3 ! 14789 5 46789 ! 789 489 189 ! ! 4 159 7 ! 1289 289 289 ! 2589 3 6 ! ! 1569 8 159 ! 123479 239 24679 ! 2579 249 129 ! +----------------------------+----------------------------+----------------------------+ ! 1289#@ 4 1289 ! 289# 6 5 ! 289# 7 3 ! ! 235789#@ 3579 2589 ! 2789 1 2789 ! 6 289# 4 ! ! 2789 6 289# ! 234789 2389#@ 24789 ! 1 5 289# ! +----------------------------+----------------------------+----------------------------+ ! 2589 59 6 ! 289# 4 1 ! 3 289# 7 ! ! 12789 179 1289 ! 5 289# 3 ! 4 6 289# ! ! 2389#@ 39 4 ! 6 7 289# ! 289# 1 5 ! +----------------------------+----------------------------+----------------------------+ EL15c64-OR8-relation for digits: 2, 8 and 9 in cells (marked #): (r4c7 r5c1 r5c4 r5c8 r6c3 r6c6 r6c9 r7c4 r7c8 r9c1 r9c6 r9c7 r8c3 r8c5 r8c9) with 8 guardians (in cells marked @) : n3r5c1 n5r5c1 n7r5c1 n7r5c4 n4r6c6 n7r6c6 n3r9c1 n1r8c3 +----------------------------+----------------------------+----------------------------+ ! 169 2 3 ! 14789 5 46789 ! 789 489 189 ! ! 4 159 7 ! 1289 289 289 ! 2589 3 6 ! ! 1569 8 159 ! 123479 239 24679 ! 2579 249 129 ! +----------------------------+----------------------------+----------------------------+ ! 1289 4 1289 ! 289 6 5 ! 289# 7 3 ! ! 235789#@ 3579 2589 ! 2789#@ 1 2789 ! 6 289# 4 ! ! 2789 6 289# ! 234789 2389 24789#@ ! 1 5 289# ! +----------------------------+----------------------------+----------------------------+ ! 2589 59 6 ! 289# 4 1 ! 3 289# 7 ! ! 12789 179 1289#@ ! 5 289# 3 ! 4 6 289# ! ! 2389#@ 39 4 ! 6 7 289# ! 289# 1 5 ! +----------------------------+----------------------------+----------------------------+ EL15c62-OR7-relation for digits: 2, 8 and 9 in cells (marked #): (r7c4 r9c1 r9c7 r9c6 r8c3 r8c9 r8c5 r4c7 r4c4 r5c1 r5c8 r5c4 r6c3 r6c9 r6c5) with 7 guardians (in cells marked @) : n3r9c1 n1r8c3 n3r5c1 n5r5c1 n7r5c1 n7r5c4 n3r6c5 +----------------------------+----------------------------+----------------------------+ ! 169 2 3 ! 14789 5 46789 ! 789 489 189 ! ! 4 159 7 ! 1289 289 289 ! 2589 3 6 ! ! 1569 8 159 ! 123479 239 24679 ! 2579 249 129 ! +----------------------------+----------------------------+----------------------------+ ! 1289 4 1289 ! 289# 6 5 ! 289# 7 3 ! ! 235789#@ 3579 2589 ! 2789#@ 1 2789 ! 6 289# 4 ! ! 2789 6 289# ! 234789 2389#@ 24789 ! 1 5 289# ! +----------------------------+----------------------------+----------------------------+ ! 2589 59 6 ! 289# 4 1 ! 3 289 7 ! ! 12789 179 1289#@ ! 5 289# 3 ! 4 6 289# ! ! 2389#@ 39 4 ! 6 7 289# ! 289# 1 5 ! +----------------------------+----------------------------+----------------------------+ EL15c60-OR5-relation for digits: 2, 8 and 9 in cells (marked #): (r5c8 r4c1 r4c4 r4c7 r6c3 r6c5 r6c9 r7c4 r7c8 r8c1 r8c5 r8c9 r9c1 r9c6 r9c7) with 5 guardians (in cells marked @) : n1r4c1 n3r6c5 n1r8c1 n7r8c1 n3r9c1 +-------------------------+-------------------------+-------------------------+ ! 169 2 3 ! 14789 5 46789 ! 789 489 189 ! ! 4 159 7 ! 1289 289 289 ! 2589 3 6 ! ! 1569 8 159 ! 123479 239 24679 ! 2579 249 129 ! +-------------------------+-------------------------+-------------------------+ ! 1289#@ 4 1289 ! 289# 6 5 ! 289# 7 3 ! ! 235789 3579 2589 ! 2789 1 2789 ! 6 289# 4 ! ! 2789 6 289# ! 234789 2389#@ 24789 ! 1 5 289# ! +-------------------------+-------------------------+-------------------------+ ! 2589 59 6 ! 289# 4 1 ! 3 289# 7 ! ! 12789#@ 179 1289 ! 5 289# 3 ! 4 6 289# ! ! 2389#@ 39 4 ! 6 7 289# ! 289# 1 5 ! +-------------------------+-------------------------+-------------------------+ EL15c59-OR7-relation for digits: 2, 8 and 9 in cells (marked #): (r5c1 r6c9 r6c5 r6c3 r4c7 r4c4 r4c3 r8c9 r8c5 r9c7 r9c6 r9c1 r7c8 r7c4 r7c1) with 7 guardians (in cells marked @) : n3r5c1 n5r5c1 n7r5c1 n3r6c5 n1r4c3 n3r9c1 n5r7c1 +----------------------------+----------------------------+----------------------------+ ! 169 2 3 ! 14789 5 46789 ! 789 489 189 ! ! 4 159 7 ! 1289 289 289 ! 2589 3 6 ! ! 1569 8 159 ! 123479 239 24679 ! 2579 249 129 ! +----------------------------+----------------------------+----------------------------+ ! 1289 4 1289#@ ! 289# 6 5 ! 289# 7 3 ! ! 235789#@ 3579 2589 ! 2789 1 2789 ! 6 289 4 ! ! 2789 6 289# ! 234789 2389#@ 24789 ! 1 5 289# ! +----------------------------+----------------------------+----------------------------+ ! 2589#@ 59 6 ! 289# 4 1 ! 3 289# 7 ! ! 12789 179 1289 ! 5 289# 3 ! 4 6 289# ! ! 2389#@ 39 4 ! 6 7 289# ! 289# 1 5 ! +----------------------------+----------------------------+----------------------------+

Website · by **denis_berthier** » Sat Nov 09, 2024 4:48 am

... continued
We get the first elimination not due to the tridagon:

EL14c19-OR3-whip[3]: OR3{{n1r8c3 n1r4c3 | n7r6c1}} - r8n7{c1 c2} - c2n1{r8 .} ==> r3c3≠1
Entering_level_L4_with_<Fact-10849>
Trid-OR2-ctr-whip[4]: c4n3{r3 r6} - c4n4{r6 r1} - c4n7{r1 r5} - OR2{{n3r6c5 n7r5c6 | .}} ==> r3c4≠9
Trid-OR2-ctr-whip[4]: c4n3{r3 r6} - c4n4{r6 r1} - c4n7{r1 r5} - OR2{{n3r6c5 n7r5c6 | .}} ==> r3c4≠2
Trid-OR2-ctr-whip[4]: c4n3{r3 r6} - c4n4{r6 r1} - c4n7{r1 r5} - OR2{{n3r6c5 n7r5c6 | .}} ==> r3c4≠1
EL13c290-OR4-whip[4]: c2n7{r8 r5} - r5n3{c2 c1} - OR4{{n3r9c1 n7r5c6 n7r6c1 | n5r7c1}} - r7c2{n5 .} ==> r8c2≠9
EL14c19-OR4-whip[4]: c2n1{r2 r8} - c2n7{r8 r5} - OR4{{n7r5c6 n1r8c3 n7r6c1 | n5r5c3}} - r3c3{n5 .} ==> r2c2≠9
biv-chain[3]: r3n1{c9 c1} - r2c2{n1 n5} - r3c3{n5 n9} ==> r3c9≠9
z-chain[3]: r2n9{c6 c7} - c7n5{r2 r3} - r3c3{n5 .} ==> r3c6≠9, r3c5≠9
biv-chain[4]: c7n7{r1 r3} - b3n5{r3c7 r2c7} - r2c2{n5 n1} - b2n1{r2c4 r1c4} ==> r1c4≠7
z-chain[3]: c4n7{r6 r3} - c4n3{r3 r6} - r6n4{c4 .} ==> r6c6≠7
Trid-OR2-ctr-whip[3]: c4n3{r3 r6} - c4n7{r6 r5} - OR2{{n7r5c6 n3r6c5 | .}} ==> r3c4≠4
biv-chain[4]: r3c5{n2 n3} - c4n3{r3 r6} - c4n4{r6 r1} - b2n1{r1c4 r2c4} ==> r2c4≠2
biv-chain[4]: r3c5{n2 n3} - c4n3{r3 r6} - c4n4{r6 r1} - b3n4{r1c8 r3c8} ==> r3c8≠2
finned-x-wing-in-columns: n2{c8 c4}{r7 r5} ==> r5c6≠2
z-chain[4]: r3c4{n7 n3} - r3c5{n3 n2} - b3n2{r3c9 r2c7} - c7n5{r2 .} ==> r3c7≠7
hidden-single-in-a-block ==> r1c7=7
biv-chain[3]: b2n7{r3c6 r3c4} - c4n3{r3 r6} - c4n4{r6 r1} ==> r3c6≠4
hidden-single-in-a-row ==> r3c8=4
biv-chain[4]: c2n1{r2 r8} - c2n7{r8 r5} - c6n7{r5 r3} - r3n6{c6 c1} ==> r3c1≠1
hidden-single-in-a-row ==> r3c9=1
whip[1]: b3n2{r3c7 .} ==> r4c7≠2, r9c7≠2
naked-pairs-in-a-column: c7{r4 r9}{n8 n9} ==> r3c7≠9, r2c7≠9, r2c7≠8
whip[1]: r2n8{c6 .} ==> r1c4≠8, r1c6≠8
whip[1]: r2n9{c6 .} ==> r1c4≠9, r1c6≠9
whip[1]: b3n9{r1c9 .} ==> r1c1≠9
finned-x-wing-in-columns: n2{c9 c3}{r8 r6} ==> r6c1≠2
biv-chain[4]: r1c6{n6 n4} - b5n4{r6c6 r6c4} - c4n3{r6 r3} - r3n7{c4 c6} ==> r3c6≠6
stte

The use of two Imp630 patterns has allowed to reduce the maximum length of chains from 6 to 4.

Remark: if my purpose was to publish the resolution path, I would now restart all the computations with only tridagons, EL14c19 and EL13c290 activated in order to eliminate all the useless patterns. (*)
But my purpose here was to show that many instances of some impossible pattern can appear. It doesn't happen for the tridagon in this puzzle but the same happens for the tridagon in other puzzles.

(*) Indeed, I would first observe that EL13c290 belongs to the Select1 subset of Imp630 and EL14c19 to the Select3 subset. So I would first try with Select1 alone. I would then observe that chains of length 5 are needed and only then would I try with Select3 activated.

Additional remark: In [UMNR] (https://www.researchgate.net/publication/372364607_User_Manual_and_Research_Notebooks_for_CSP-Rules), I've studied the 630 impossible patterns only wrt T&E(3) puzzles. But they can obviously also appear and be useful in T&E(2) or T&E(1) puzzles.
.

by **coloin** » Sat Nov 09, 2024 12:21 pm

Thats great Denis !!
I think you can only use "[hidden][code] with 150 or so lines

I will post the [morphed] puzzle in the puzzle section ...
Morphed as it is so much easier [for a reader] to understand the patterns ....

Website · by **denis_berthier** » Sat Nov 09, 2024 12:25 pm

coloin wrote:I will post the [morphed] puzzle in the puzzle section ...
Morphed as it is so much easier [for a reader] to understand the patterns ....

You can always morph it further to 3 diags and 1 antidiag (or the converse).

by **coloin** » Sat Nov 09, 2024 12:41 pm

denis_berthier wrote: You can always morph it further to 3 diags and 1 antidiag (or the converse).

You are right ...now morphed as per your tridagon thread ....

Code: Select all: +-------------------------------+-------------------------------+ ! 123456789 . . ! 123 . . ! ! . 123 . ! . 123 . ! ! . . 123 ! . . 123 ! +-------------------------------+-------------------------------+ ! 123 . . ! * * * ! ! . 123 . ! * * * ! ! . . 123 ! * * * ! +-------------------------------+-------------------------------+

and the 3 impossible patterns in box 5 for me to relearn ! are ....

Hidden Text: Show

by **DEFISE** » Sat Nov 09, 2024 2:27 pm

Hi Denis and coloin,
This puzzle is in S3 + W6 + Trid-OR2-W4 (with few chains and without using any eleven's impossible pattern).
Far from a "mission impossible" I think.

Website · by **denis_berthier** » Sat Nov 09, 2024 3:50 pm

Yes, it's a morph of a previous puzzle.

by **coloin** » Sat Nov 09, 2024 5:46 pm

DEFISE wrote:Hi Denis and coloin,
This puzzle is in S3 + W6 + Trid-OR2-W4 (with few chains and without using any eleven's impossible pattern).
Far from a "mission impossible" I think.

Well... as we know none of our valid puzzles are "impossible"

Denis.. it would be great if you could repeat your above "impossible " patterns anaysis on the morphed puzzle ?
It would perhaps be clearer ?

Code: Select all: +---+---+---+ |.79|.48|.6.| |6.4|5.9|...| |85.|67.|.4.| +---+---+---+ |.46|.8.|...| |5.8|...|..6| |79.|.65|..4| +---+---+---+ |96.|...|47.| |...|...|..2| |...|.5.|.91| +---+---+---+ Mission Impossible

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