The New Sudoku Players' Forum

by **daj95376** » Tue Jul 08, 2008 10:46 pm

???

Code: Select all: +--------------------------------------------------------------+ | 2 7 6 | 148 3 148 | 9 18 5 | | 3 8 1 | 2 5 9 | 6 7 4 | | 9 5 4 | 1678 178 167 | 18 2 3 | |--------------------+--------------------+--------------------| | 5 6 27 | 3 4789 478 | 248 489 1 | | 48 9 38 | 16 2 16 | 348 5 7 | | 478 1 23 | 478 4789 5 | 23 489 6 | |--------------------+--------------------+--------------------| | 6 3 78 | 1478 1478 2 | 5 14 9 | | 178 4 9 | 5 6 78 | 17 3 2 | | 17 2 5 | 9 147 3 | 147 6 8 | +--------------------------------------------------------------+ Templates (A: 1) <> 7 [r3c5]

Code: Select all: +--------------------------------------------------------------+ | 9 137 2 | 4 8 6 | 5 137 137 | | 4 8 6 | 5 37 137 | 39 1379 2 | | 137 5 137 | 9 2 137 | 6 8 4 | |--------------------+--------------------+--------------------| | 5 6 8 | 2 13 9 | 7 4 13 | | 137 1379 4 | 36 136 5 | 2 139 8 | | 2 39 13 | 7 4 8 | 139 5 6 | |--------------------+--------------------+--------------------| | 6 137 9 | 8 5 37 | 4 2 137 | | 37 4 5 | 1 367 2 | 8 367 9 | | 8 2 137 | 36 9 4 | 13 1367 5 | +--------------------------------------------------------------+ Templates (A: 1) <> 3 [r2c8],[r5c5],[r9c38]

by **DanG** » Wed Jul 09, 2008 8:44 pm

Hi daj95376,

Amazing how your solver discovers invalid patterns, sometimes BW/SoPT or just simple empty houses..

Code: Select all: +--------------------------------------------------------------+ | 2 7 6 | 148 3 148 | 9 18 5 | | 3 8 1 | 2 5 9 | 6 7 4 | | 9 5 4 | 1678 178 167 | 18 2 3 | |--------------------+--------------------+--------------------| | 5 6 27 | 3 4789 478 | 248 489 1 | | 48 9 38 | 16 2 16 | 348 5 7 | | 478 1 23 | 478 4789 5 | 23 489 6 | |--------------------+--------------------+--------------------| | 6 3 78 | 1478 1478 2 | 5 14 9 | | 178 4 9 | 5 6 78 | 17 3 2 | | 17 2 5 | 9 147 3 | 147 6 8 | +--------------------------------------------------------------+ Templates (A: 1) <> 7 [r3c5] Filter 7 . . . | . . . | . . . . . . | . . . | . . . . . . | 7 -7 7 | . . . |--------------------+--------------------+--------------------| . . 7T | . 7 7T | . . . . . . | . . . | . . . 7T . . | 7T 7 . | . . . |--------------------+--------------------+--------------------| . . 7T | 7T 7 . | . . . 7T' . . | . . 7T' | 7" . . 7T" . . | . 7 7T" | 7' . . ↑ T - turbot or BW cells ↑ mark the corridor

Whatever parity is true in b9 leaves the other parity in boxes b7,b8 to complete the SoPT (T cells in b5,b5,b7,b8).
Guardians (cells which see the T cells) restricted only to b2 and corridor c5. All Guardians see -7 cell.

Edit: Corrected a typo in cell r9c1 (was 7T2")
===============

Code: Select all: +--------------------------------------------------------------+ | 9 137 2 | 4 8 6 | 5 137 137 | | 4 8 6 | 5 37 137 | 39 1379 2 | | 137 5 137 | 9 2 137 | 6 8 4 | |--------------------+--------------------+--------------------| | 5 6 8 | 2 13 9 | 7 4 13 | | 137 1379 4 | 36 136 5 | 2 139 8 | | 2 39 13 | 7 4 8 | 139 5 6 | |--------------------+--------------------+--------------------| | 6 137 9 | 8 5 37 | 4 2 137 | | 37 4 5 | 1 367 2 | 8 367 9 | | 8 2 137 | 36 9 4 | 13 1367 5 | +--------------------------------------------------------------+ Templates (A: 1) <> 3 [r2c8],[r5c5],[r9c38] Filter 3 +--------------------------------------------------------------+ | . 3 . | . . . | . 3 3 | | . . . | . 3 3 | 3 3 . | | 3 . 3 | . . 3 | . . . | |--------------------+--------------------+--------------------| | . . . | . 3 . | . . 3 | | 3 3 . | 3 3 . | . 3 . | | . 3 3 | . . . | 3 . . | |--------------------+--------------------+--------------------| | . 3 . | . . 3 | . . 3 | | 3 . . | . 3 . | . 3 . | | . . 3 | 3 . . | 3 3 . | +--------------------------------------------------------------+

A solution starting with "exclusion cell" is followed by a bunch of singles in different houses till an invalid pattern occurs..
[r2c8]=3, singles in b2, b1, r7, b6, b4, b5, b7 => empty b8!
[r5c5]=3, singles in r4, c4, b9, b3, b7, b2, b4 => empty b1!
[r9c3]=3, singles in b5, b6, b4, b9, b1, b3, b8 => empty b2!
[r9c8]=3, singles in c4, r4, b3, b2, b1, b4, b7/b8=> empty b8/b7!

by **daj95376** » Wed Jul 09, 2008 11:03 pm

DanG wrote:Amazing how your solver discovers invalid patterns, sometimes BW/SoPT or just simple empty houses..

Actually, once I completed my fish search routine, the BW's and other odd patterns just drop out as leftover Templates eliminations.

On the first PM, I finally decided to go with something ronk had said.

Code: Select all: +--------------------------------------------------------------------+ | 2 7 6 | 148 3 148 | 9 18 5 | | 3 8 1 | 2 5 9 | 6 7 4 | | 9 5 4 | 1678 178 167 | 18 2 3 | |----------------------+----------------------+----------------------| | 5 6 27 | 3 4789 478 | 248 489 1 | | 48 9 38 | 16 2 16 | 348 5 7 | | 478 1 23 | 478 4789 5 | 23 489 6 | |----------------------+----------------------+----------------------| | 6 3 78 | 1478 1478 2 | 5 14 9 | | 178 4 9 | 5 6 78 | 17 3 2 | | 17 2 5 | 9 147 3 | 147 6 8 | +--------------------------------------------------------------------+

If [r3c5]=7, then '7' is eliminated from the six (~) cells. There are an odd number of strong links (*) in the resulting bilocation loop: [c3], [b4], [r6], [b5], [c6], [b8], and [r7]. According to ronk, this makes for an invalid pattern. I agree. I think it also makes the (~) cells the guardian cells => [r3c5]<>7. (Technically, [r3c4] isn't a guardian cell for my loop.)

Code: Select all: +-----------------------------------+ | . 7 . | . . . | . . . | | . . . | . . . | . 7 . | | . . . | ~7 7 ~7 | . . . | |-----------+-----------+-----------| | . . *7 | . ~7 *7 | . . . | | . . . | . . . | . . 7 | | *7 . . | *7 ~7 . | . . . | |-----------+-----------+-----------| | . . *7 | *7 ~7 . | . . . | | 7 . . | . . *7 | 7 . . | | 7 . . | . ~7 . | 7 . . | +-----------------------------------+

by **ronk** » Wed Jul 09, 2008 11:12 pm

DanG wrote:
Code: Select all
Filter 7 . . . | . . . | . . . . . . | . . . | . . . . . . | 7 -7 7 | . . . |--------------------+--------------------+--------------------| . . 7T | . 7 7T | . . . . . . | . . . | . . . 7T . . | 7T 7 . | . . . |--------------------+--------------------+--------------------| . . 7T | 7T 7 . | . . . 7T' . . | . . 7T' | 7" . . 7T2" . . | . 7 7T" | 7' . . ↑ T - turbot or BW cells ↑ mark the corridor

Whatever parity is true in b9 leaves the other parity in boxes b7,b8 to complete the SoPT (T cells in b5,b5,b7,b8).
Guardians (cells which see the T cells) restricted only to b2 and corridor c5. All Guardians see -7 cell.

I see no mention of T' and T" and T2". How are they part of the picture :?:

"Guardians" generally means guard against an illegal pattern. If the illegal pattern is a SoPT, how do candidates in b2 become guardians? :?:

If it's because they see the T cells in c4 and c6 ... then what about the candidate in r8 (or r9) that sees the T' (or T"") cells? :?:

by **DanG** » Thu Jul 10, 2008 4:11 pm

Hi Ronk,
Look what happened if r3c5=7.

Code: Select all: Filter 7 . . . | . . . | . . . . . . | . . . | . . . . . . | - +7 - | . . . |--------------------+--------------------+--------------------| . . 7T | . - 7T | . . . . . . | . . . | . . . 7T . . | 7T - . | . . . |--------------------+--------------------+--------------------| . . 7T | 7T - . | . . . 7T' . . | . . 7T' | 7" . . 7T" . . | . - 7T" | 7' . . if r3c5=7 cancel 7s in cells marked -

The remaining cells makeup an illegal pattern too (no solution can fill the 5 boxes!).
What is going on on r89 is what I called "split cells" here..
Another way to see it is considering two partially overlapping SoPT where the difference is in r8 (' parity true in b9) or r9 (" parity true in b9). Then the pattern became an ordinarily 4 box SoPT.

daj95376,
Your bilocation loop: [c3], [b4], [r6], [b5], [c6], [b8], and [r7] is correct but a little long for me. Why not settle for the simpler ones with 5 links:
[c3], [r7], [c4], [b5], [r4] or..
[c3], [r7], [c4], [r6], [b4]

by **daj95376** » Thu Jul 10, 2008 4:49 pm

DanG wrote:daj95376,
Your bilocation loop: [c3], [b4], [r6], [b5], [c6], [b8], and [r7] is correct but a little long for me. Why not settle for the simpler ones with 5 links: [c3], [r7], [c4], [b5], [r4] or [c3], [r7], [c4], [r6], [b4]

Now you know why I wrote a solver instead of trying to solve puzzles manually. I'm terrible without it :!:

by **ronk** » Thu Jul 10, 2008 5:38 pm

DanG wrote:Hi Ronk,
Look what happened if r3c5=7.
Code: Select all
Filter 7 . . . | . . . | . . . . . . | . . . | . . . . . . | - +7 - | . . . |--------------------+--------------------+--------------------| . . 7T | . - 7T | . . . . . . | . . . | . . . 7T . . | 7T - . | . . . |--------------------+--------------------+--------------------| . . 7T | 7T - . | . . . 7T' . . | . . 7T' | 7" . . 7T" . . | . - 7T" | 7' . . if r3c5=7 cancel 7s in cells marked -

The remaining cells makeup an illegal pattern too (no solution can fill the 5 boxes!).

Thanks for the reply, but there is a much smaller illegal pattern -- an illegal turbotfish in r47c34b5 -- of five cells instead of your ten cells, so I'll just stick with that. At least with this illegal turbotfish, I know at least one guardian must be true in one of the cells shown as empty ('/') below.

Code: Select all: . . / | / . . | . . . . . / | / . . | . . . . . / | / . . | . . . ---------+----------+---------- / / X | / / X | / / / . . / | / / / | . . . . . / | X / / | . . . ---------+----------+---------- / / X | X / / | / / / . . / | / . . | . . . . . / | / . . | . . .

With your SoPT -- even the simplest SoPT, I'm still unsure where these are.

by **daj95376** » Wed Jul 16, 2008 12:53 am

From what I can tell, this is not a Broken Wing. It does not appear to be a cascade of singles leading to a contradiction, either. It appears to be complex.

Code: Select all: +-----------------------------------------------------------------------+ | 7 58 2 | 568 3 1 | 9 4 568 | | 589 6 1 | 589 7 4 | 3 258 258 | | 589 4 3 | 2 568 589 | 567 5678 1 | |-----------------------+-----------------------+-----------------------| | 6 57 9 | 3 1 58 | 4 2578 258 | | 1 3 578 | 4 58 2 | 567 56789 5689 | | 4 2 58 | 7 9 6 | 1 58 3 | |-----------------------+-----------------------+-----------------------| | 2 9 57 | 1 56 357 | 8 356 4 | | 3 578 4 | 5689 2 5789 | 56 1 569 | | 58 1 6 | 589 4 3589 | 2 359 7 | +-----------------------------------------------------------------------+ Templates (A: 1) <> 5 [r2c8]

What it does need is the Empty Rectangle in [b9].

Code: Select all: +-----------------------------------+ | . 5 . | 5 . . | . . 5 | | 5 . . | 5 . . | . -5 5 | | 5 . . | . 5 5 | 5 5 . | |-----------+-----------+-----------| | . 5 . | . . 5 | . 5 5 | | . . 5 | . 5 . | 5 5 5 | | . . 5 | . . . | . 5 . | |-----------+-----------+-----------| | . . 5 | . 5 5 | . 5 . | | . 5 . | 5 . 5 | 5 . 5 | | 5 . . | 5 . 5 | . 5 . | +-----------------------------------+

I'll leave it to you to set [r2c8]=5 and reduce the 5-grid to

Code: Select all: X-Wing [r37c56] => [b5]~5

by **Steve K** » Wed Jul 16, 2008 4:21 am

Without using box 5:
AAIC (5): [r79c8=r8c79-r8c4=r2c4]=[r9c4=r1c4-r1c2=r23c1]-r9c1=[r6c8=r6c3-r7c3=r8c2-r8c79=r79c8] => sis[r79c8,r2c4,r6c8] => r2c8<>5

Alternatively:AAIC (5): [r79c8=r8c79-r8c4=r2c4]=[r1c4=r9c4-r9c1=r23c1]-r1c2=[r6c8=r6c3-r4c2=r8c2-r8c79=r79c8] => sis[r79c8,r2c4,r6c8] => r2c8<>5

Also, and more efficiently: hidden grouped xyzt chain using the following sis:
(5): b9, r6, b7, b1, c4 => same sis

also, perhaps more reductively (5): r2c4=[(5)fish using b9(c8=r8), r6c8=c3, b7[c3,r8,r9c1], b1c1=r1, r189c4 ]

by **daj95376** » Wed Jul 16, 2008 6:23 pm

A grouped forcing network.

Code: Select all: [b7] => [r7c3]=5 => [r6 c8]=5 => [r2c8]<>5 || [r8c2]=5 => [r79c8]=5 => [r2c8]<>5 || [r9c1]=5 => [r1 c2]=5 => [r2c4] =5 => [r2c8]<>5 || [r8c4] =5 => [r7c8]=5 => [r2c8]<>5

by **Allan Barker** » Thu Jul 17, 2008 1:48 am

Without using box 9:

1) fish, finned(b3) with 5 sets in 5r3679, 5b5 linked by 5c13568, 5b38 => r2c8<>5 Note, rank 2 with 1 extra weak constraint.
2) fish like with 5 sets 5r679, 5c4, 5b1 linked by 5r12, 5c138, 5b8 => r2c8<>5 Note, sets r9, c4 are link at 5r9c4.
3) Just for beauty, column finned(b3) fish with 7 sets in 5c1245679 linked by 5r1234589 5b238 => r2c8<>5 Note extra boxes 5b28.

by **daj95376** » Thu Jul 17, 2008 2:46 am

My mistake!!! Sorry!!!

The generic fish module in my solver only checks for fish up to N=6 because this is the largest fish that I'd encountered previously during normal operations. My GFF program goes higher, and found these fish:

Code: Select all: 7-Fish r67c2479b5 \r1458c3b8+r2|c8|b3 <> 5 [r2c8] 7-Fish r67c24 b569\r1458c3b8+r2|c8 <> 5 [r2c8]

I'll update my solver so this oversight doesn't happen again.

by **Allan Barker** » Thu Jul 17, 2008 3:40 am

My mistake!!!

No, maybe my mistake! Although the first 2 are only N=5, all 3 use uncommon constraints to make eliminations, I'm sure #2 is not a fish, just fish-like meaning it uses 2 sets of constraints.

by **ronk** » Thu Jul 17, 2008 7:34 am

daj95376 wrote:My GFF program goes higher, and found these fish:

Code: Select all
7-Fish r67c2479b5 \r1458c3b8+r2|c8|b3 <> 5 [r2c8] 7-Fish r67c24 b569\r1458c3b8+r2|c8 <> 5 [r2c8]

Nice find! I much prefer the first, as it has two normal fins -- meaning there is no endofin.

by **daj95376** » Mon Jun 28, 2010 1:55 am

A lot of information was lost about solving NoFish puzzles. I decided to take another look at NoFish1.

Previously, I had mentioned a "Dual Kraken X-Wing" configuration and Mike Barker applied it to NoFish1.

I now realize that a (remotely) finned Jellyfish contains both X-Wing patterns.

Code: Select all: +-----------------------+ | . . . | . . . | . . 2 | | 9 . 2 | . . . | . . 4 | | . 6 . | 3 . . | 9 8 . | |-------+-------+-------| | . 1 . | . . 8 | . 6 . | | . . . | 1 3 . | . . . | | . 3 . | . . 7 | 4 . . | |-------+-------+-------| | . . 8 | . . . | . . . | | 6 . . | 2 4 . | 3 1 . | | . . . | . 7 . | . . 5 | +-----------------------+ # NoFish1 reduced to: +--------------------------------------------------------------+ | 137 78 1347 | 4679 689 149 | 16 5 2 | | 9 578 2 | 567 568 15 | 16 3 4 | | 145 6 145 | 3 25 1245 | 9 8 7 | |--------------------+--------------------+--------------------| | 247 1 479 | 49 29 8 | 5 6 3 | | 245 245 6 | 1 3 245 | 8 7 9 | | 8 3 59 | 569 569 7 | 4 2 1 | |--------------------+--------------------+--------------------| | 245 25 8 | 59 1 3 | 7 49 6 | | 6 579 57 | 2 4 59 | 3 1 8 | | 13 49 13 | 8 7 6 | 2 49 5 | +--------------------------------------------------------------+

Code: Select all: finned Jellyfish c1346\r2378 w/remote fins r5c16,r6c34 => r3c5<>5 +-----------------------------------+ | . . . | . . . | . 5 . | | . 5 . | *5 5 *5 | . . . | | *5 . *5 | . -5 *5 | . . . | |-----------+-----------+-----------| | . . . | . . . | 5 . . | | #5 5 . | . . #5 | . . . | | . . #5 | #5 5 . | . . . | |-----------+-----------+-----------| | *5 5 . | *5 . . | . . . | | . 5 *5 | . . *5 | . . . | | . . . | . . . | . . 5 | +-----------------------------------+

If unfinned Jellyfish is true, then r3c5<>5.

If either r5c1|r6c4 is true, then the Jellyfish reduces to finned X-Wing c36\r38 => r3c5<>5.

If either r5c6|r6c3 is true, then the Jellyfish reduces to Sashimi X-Wing c14\r37 => r3c5<>5.

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