The New Sudoku Players' Forum

by **tarek** » Wed Oct 09, 2019 5:51 pm

Code: Select all: .2....89.1..6..4.5.......27....3......42.8...7..59..6.23..7......9.....65.63...1. .2....89. 1..6..4.5 .......27 ....3.... ..42.8... 7..59..6. 23..7.... ..9.....6 5.63...1.

by **ArkieTech** » Wed Oct 09, 2019 8:02 pm

Code: Select all: *-----------------------------------------------------------* | 6 2 357 | 47 45 3457 | 8 9 1 | | 1 89 78 | 6 28 279 | 4 3 5 | | 348 4589 358 | 89 1 359 | 6 2 7 | *-------------------+-------------------+-------------------| | 89 6 1258 | 47 3 147 | 1259 458 2489 | | 39 15 4 | 2 6 8 | 157 57 39 | | 7 18 1238 | 5 9 14 | 12 6 2348 | *-------------------+-------------------+-------------------| | 2 3 18 | 189 7 6 | 59 458 489 | | 48 1478 9 | 18 25 25 | 3 78 6 | | 5 78 6 | 3 48 49 | 279 1 289 | *-----------------------------------------------------------* [83r45c1-(83=1)r6c237]-1r6c6; ste

Nice! what is it?

by **SpAce** » Wed Oct 09, 2019 8:44 pm

ArkieTech wrote:[83r45c1-(83=1)r6c237]-1r6c6; ste

Nice! what is it?

Hi Dan! I don't quite understand your expression, but there's a Sue de Coq / Doubly-Linked ALS-XZ in those cells. I'd write it:

(8=9'3)r45c1 - (3=12'8)r4c723 - loop => -1 r6c6, -2 r6c9, -8 r4c3

Or as a Rank 0 pattern:

Alien 5-Fish (Rank 0): {45N1 6N237} \ {12r6 389b4} => -1 r6c6, -2 r6c9, -8 r4c3

--

Something less nice:

Code: Select all: .--------------------.------------------.-----------------. | 6 2 357 | 47 c45 3457 | 8 9 1 | | 1 89 78 | 6 28 279 | 4 3 5 | | 48-3 4589 358 | 89 1 d(3)59 | 6 2 7 | :--------------------+------------------+-----------------: | a89 6 1258 | 47 3 147 | 1259 458 2489 | | a[3]9 15 4 | 2 6 8 | 157 57 39 | | 7 a81 1238 | 5 9 b14 | 12 6 2348 | :--------------------+------------------+-----------------: | 2 3 18 | 189 7 6 | 59 458 489 | | 48 1478 9 | 18 25 25 | 3 78 6 | | 5 78 6 | 3 c48 bc49 | 279 1 289 | '--------------------'------------------'-----------------'

(3=981)b4p418 - (14)r69c6 = (459)r91c5,r9c6 - (5|9=3)r3c6 => -3 r3c1; stte

by **tarek** » Wed Oct 09, 2019 8:53 pm

ArkieTech wrote:[83r45c1-(83=1)r6c237]-1r6c6

I'm trying to follow … you chose 1 as the restricted common which is correct, but 2 is also restricted and therefore gives you the loop that you need so that you eliminate more candidates along the weak links too

[Edit: corrected spelling mistake]

by **eleven** » Wed Oct 09, 2019 9:09 pm

ArkieTech wrote:[83r45c1-(83=1)r6c237]-1r6c6; ste

Strange notation, but i like the view, that one of r45c1 must be 3 or 8, and therefore the ALS 1238r6c237 must contain 1 and 2 (eliminating also 2r6c9).
or
5 digits in 5 cells, all must be there, because none can be twice (eliminating also the 8 r4c4).

by **SpAce** » Wed Oct 09, 2019 10:24 pm

eleven wrote:
ArkieTech wrote:[83r45c1-(83=1)r6c237]-1r6c6; ste

Strange notation, but i like the view, that one of r45c1 must be 3 or 8, and therefore the ALS 1238r6c237 must contain 1 and 2 (eliminating also 2r6c9).

That's how I read it too (though 83r45c1 implies 8 AND 3; should have been (8|3)). It's possibly the simplest way to see those eliminations, but it's actually a compacted forcing chain and not an AIC. Basically the same as this (which is an AIC if stretched out):

(8)r45c1 - (83=12)r6c237
||
(3)r45c1 - (38=12)r6c237

=> +12 r6c237

One kludgy way to write it as a compact AIC is to start with a DP (contradiction) node [!]:

([!]=8|3)r45c1 - (83=12)r6c237 => +12 r6c237

That way the chain has two strongly-linked end-points like a normal AIC. One of them just happens to be a known false, which makes the other one true.

by **tarek** » Wed Oct 09, 2019 10:49 pm

So as you all noticed this indeed a double linked ALS-XZ, VWXYZ-Wing or a Sue-De-Coq … It is now caught by Sukaku Explainer VWXYZ-Wing technique

Code: Select all: +----------------+----------------+----------------+ | 6 2 357 | 47 45 3457 | 8 9 1 | | 1 89 78 | 6 28 279 | 4 3 5 | | 348 4589 358 | 89 1 359 | 6 2 7 | +----------------+----------------+----------------+ |%89 6 125-8| 47 3 147 | 1259 458 2489 | |%39 15 4 | 2 6 8 | 157 57 39 | | 7 %18 %1238 | 5 9 -14 |*12 6 -2348 | +----------------+----------------+----------------+ | 2 3 18 | 189 7 6 | 59 458 489 | | 48 1478 9 | 18 25 25 | 3 78 6 | | 5 78 6 | 3 48 49 | 279 1 289 | +----------------+----------------+----------------+ Double-linked VWXYZ-wing *:r6c7 %:r45c1 r6c23 => r4c3<>8 r6c6<>1 r6c9<>2

The following is what I thought is best to be presented as an explanation with SE:

Hidden Text: Show

Here are 2 bonus gifts for people who enjoy these types of eliminations (I also enjoy watching you struggle with your AIC notation :lol:

)

Code: Select all: +-------------------+-------------------+-------------------+ | 137 579 8 | 2356 1367 257 | 134 12579 2347 | | 137 79 2 | 8 4 57 | 136 15679 137 | | 6 4 135 | 23 137 9 | 13 1257 8 | +-------------------+-------------------+-------------------+ | 8 3 9 | 4 5 6 | 2 17 17 | | 2 1 4 | 7 9 8 | 5 3 6 | | 5 6 7 | 1 2 3 | 8 4 9 | +-------------------+-------------------+-------------------+ | 134 2 136 | 9 367 47 | 1346 8 5 | | 347 57 356 | 2356 8 1 | 9 26 234 | | 9 8 1356 | 2356 36 245 | 7 126 1234 | +-------------------+-------------------+-------------------+ +-------------------+-------------------+-------------------+ | 679 56 179 | 156 367 8 | 4 37 2 | | 678 68 127 | 126 367 4 | 379 5 19 | | 3 245 24 | 25 9 17 | 6 17 8 | +-------------------+-------------------+-------------------+ | 2 7 8 | 4 5 3 | 1 9 6 | | 5 9 34 | 7 1 6 | 2 8 34 | | 1 34 6 | 8 2 9 | 5 347 347 | +-------------------+-------------------+-------------------+ | 467 1 237 | 9 8 5 | 37 23467 347 | | 678 368 5 | 16 4 2 | 379 367 19 | | 469 26 29 | 3 67 17 | 8 1246 5 | +-------------------+-------------------+-------------------+

by **ArkieTech** » Wed Oct 09, 2019 11:23 pm

SpAce wrote:
eleven wrote:
ArkieTech wrote:[83r45c1-(83=1)r6c237]-1r6c6; ste

Strange notation, but i like the view, that one of r45c1 must be 3 or 8, and therefore the ALS 1238r6c237 must contain 1 and 2 (eliminating also 2r6c9).

That's how I read it too (though 83r45c1 implies 8 AND 3; should have been (8|3)).

Thanks SpAce My mistake; should be [8|3r45c1-(83=1)r6c237]-1r6c6; ste

My eagerness for simplicity sometimes goes awry.

by **ArkieTech** » Wed Oct 09, 2019 11:45 pm

Code: Select all: *--------------------------------------------------------------------* | 137 579 8 | 2356 1367 257 | 134 12579 2347 | | 137 79 2 | 8 4 57 | 136 15679 137 | | 6 4 135 | 23 137 9 | 13 1257 8 | *----------------------+----------------------+----------------------| | 8 3 9 | 4 5 6 | 2 17 17 | | 2 1 4 | 7 9 8 | 5 3 6 | | 5 6 7 | 1 2 3 | 8 4 9 | *----------------------+----------------------+----------------------| | 134 2 136 | 9 367 47 | 1346 8 5 | | 347 57 356 | 2356 8 1 | 9 26 234 | | 9 8 1356 | 2356 36 245 | 7 126 1234 | *--------------------------------------------------------------------* [7|2r12c6-(72=13)r3c457]-13r3c3; ste

by **ArkieTech** » Thu Oct 10, 2019 12:12 am

Code: Select all: *--------------------------------------------------------------------* | 679 56 179 | 156 367 8 | 4 37 2 | | 678 68 127 | 126 367 4 | 379 5 19 | | 3 245 24 | 25 9 17 | 6 17 8 | *----------------------+----------------------+----------------------| | 2 7 8 | 4 5 3 | 1 9 6 | | 5 9 34 | 7 1 6 | 2 8 34 | | 1 34 6 | 8 2 9 | 5 347 347 | *----------------------+----------------------+----------------------| | 467 1 237 | 9 8 5 | 37 23467 347 | | 678 368 5 | 16 4 2 | 379 367 19 | | 469 26 29 | 3 67 17 | 8 1246 5 | *--------------------------------------------------------------------* [3|7r7c7=37r8c4789]-37r7c89; singles to bug

by **SpAce** » Thu Oct 10, 2019 9:39 am

ArkieTech wrote:[3|7r7c7=37r8c4789]-37r7c89; singles to bug

Hi Dan! I don't see how that's supposed to work. Can you elaborate on how it should be interpreted? Even if the strong link (3|7=37) were valid (which I don't see either) it wouldn't give us the eliminations (you'd need 37=37).

With that starting cell, your original way doesn't produce those eliminations either:

(3|7)r7c7 - (37=196)r8c4789 => -6 r8c12

But this does:

(1|6)r8c4 - (16=937)b9p1456 => -37 r7c89

Any of the Rank-0 approaches {SDC, DL-VWXYZ-Wing, DL-ALS-XZ, Alien Fish} gives both at the same time:

(3=7)r7c7 - (7=169'3)r8c4789 - loop => -6 r8c12, -37 r7c89

{7N7 8N4789} \ {169r8 37b9} => -6 r8c12, -37 r7c89

by **ArkieTech** » Thu Oct 10, 2019 11:06 am

SpAce wrote:
ArkieTech wrote:[3|7r7c7=37r8c4789]-37r7c89; singles to bug

Hi Dan! I don't see how that's supposed to work. Can you elaborate on how it should be interpreted? Even if the strong link (3|7=37) were valid (which I don't see either) it wouldn't give us the eliminations (you'd need 37=37).

With that starting cell, your original way doesn't produce those eliminations either:

(3|7)r7c7 - (37=196)r8c4789 => -6 r8c12

But this does:

(1|6)r8c4 - (16=937)b9p1456 => -37 r7c89

Any of the Rank-0 approaches {SDC, DL-VWXYZ-Wing, DL-ALS-XZ, Alien Fish} gives both at the same time:

(3=7)r7c7 - (7=169'3)r8c4789 - loop => -6 r8c12, -37 r7c89

{7N7 8N4789} \ {169r8 37b9} => -6 r8c12, -37 r7c89

Code: Select all: *--------------------------------------------------------------------* | 679 56 179 | 156 367 8 | 4 37 2 | | 678 68 127 | 126 367 4 | 379 5 19 | | 3 245 24 | 25 9 17 | 6 17 8 | *----------------------+----------------------+----------------------| | 2 7 8 | 4 5 3 | 1 9 6 | | 5 9 34 | 7 1 6 | 2 8 34 | | 1 34 6 | 8 2 9 | 5 347 347 | *----------------------+----------------------+----------------------| | 467 1 237 | 9 8 5 | 37 23467 347 | | 678 368 5 | 16 4 2 | 379 367 19 | | 469 26 29 | 3 67 17 | 8 1246 5 | *--------------------------------------------------------------------* [3|7r7c7=37r8c4789]-37r7c89 r7c7 is going to be a 3 or 7 if it is a 3 then set r8c4789 must contain a 7 if it is a 7 then set r8c4789 must contain a 3 3 and 7 must be in r7c7,r8c4789 therefore cannot be in r7c89 [37r7c7,r8c4789]-37r7c89 might be better

by **SpAce** » Thu Oct 10, 2019 11:38 am

ArkieTech wrote:[3|7r7c7=37r8c4789]-37r7c89

r7c7 is going to be a 3 or 7
if it is a 3 then set r8c4789 must contain a 7
if it is a 7 then set r8c4789 must contain a 3
3 and 7 must be in r7c7,r8c4789 therefore cannot be in r7c89

While that's true, the chain does not depict it in any way. Remember that '=' means OR in Eureka. I think something like this might work instead (using your ubercompact style):

[3|7r7c7->37r7c7,r8c4789]-37r7c89

Even then it doesn't do a great job explaining why the implication is true.

[37r7c7,r8c4789]-37r7c89

might be better

Well, at least it's a valid statement, but it's basically starting with the conclusion. It would be nice to display a piece of logic that explains why 37 must be locked in those cells. Otherwise I could just as well say: (6)r1c4,r8c8,r9c5 => -6 r8c4; stte. Isn't it obvious why 6 must be in (at least) one of those cells?

Added. I think something like this would suffice:

{Rank 0 pattern name}: (13679)r7c7,r8c4789 => -37 r7c89, -6 r8c12

I do think it needs to be accompanied with a pattern name (SDC, DDS, ...) or a textual explanation in eleven's style, to provide an explicit reason why all of the digits are locked in those cells. Without that extra piece of information it's asking a lot of the reader. (On the other hand, a loop or an alien fish make the Rank 0 logic explicit, so they work just as well without any pattern names. That's why I'd generally prefer them.)

"Everything should be made as simple as possible, but no simpler."

by **SpAce** » Thu Oct 10, 2019 12:04 pm

In case it wasn't obvious...

Code: Select all: .--------------------.------------------.----------------------. | d679 d56 d179 | c15(6) 367 8 | 4 k{37} 2 | | df678 d68 e127 | 126 B367 4 | f379 5 19 | | 3 245 24 | 25 9 17 | 6 17 8 | :--------------------+------------------+----------------------: | 2 7 8 | 4 5 3 | 1 9 6 | | 5 9 j34 | 7 1 6 | 2 8 j34 | | 1 34 6 | 8 2 9 | 5 k{37}4 347 | :--------------------+------------------+----------------------: | g467 1 hi237 | 9 8 5 | gh37 23467 347 | | g678 368 5 | 1-6 4 2 | 379 k{376} 19 | | 469 26 29 | 3 A[6]7 17 | 8 1246 5 | '--------------------'------------------'----------------------'

(6=7)r9c5 - r2c5 = [(6=1|5)r1c4 - (15=9867)b1p12345 - (7)r2c3 = r2c17 - r78c1&r7c7 = (7)r7c3|(3)r7c7 - (3)r7c3 = (3,4)r5c39 - (4=376)r618c8] => -6 r8c4; stte

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