The New Sudoku Players' Forum

by **ArkieTech** » Thu Jul 10, 2014 11:26 pm

Code: Select all: *-----------* |.47|..2|..5| |53.|...|...| |...|76.|...| |---+---+---| |...|...|5.2| |21.|.3.|.67| |7.9|...|...| |---+---+---| |...|.46|...| |...|...|.13| |8..|5..|74.| *-----------*

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by **SteveG48** » Fri Jul 11, 2014 12:11 am

Code: Select all: *--------------------------------------------------* | 6 4 7 | 3 9-1 2 |g19 8 5 | | 5 3 2 | 149 8 49 | 169 7 f169 | | 1 9 8 | 7 6 5 | 3 2 4 | *----------------+----------------+----------------| | 34 8 34 | 6 7 1 | 5 9 2 | | 2 1 5 | 49 3 489 | 48 6 7 | | 7 6 9 | 2 5 48 | 148 3 18 | *----------------+----------------+----------------| |d39 7 d13 | 189 4 6 | 2 5 e89 | | 49 5 46 | 89 2 7 | 689 1 3 | | 8 2 c16 | 5 a19 3 | 7 4 be69 | *--------------------------------------------------*

(1=9)r9c5 - (9=6)r9*c9 - (6=1)r9c3 - (1=9)r7c13 - (9)r7*9c9 = r1c9 - (9=1)r1c7 => -1 r1c5 ; stte

by **pjb** » Fri Jul 11, 2014 12:29 am

Code: Select all: 6 4 7 | 3 a19 2 | 1-9 8 5 5 3 2 | 14-9 8 4-9 | 169 7 e169 1 9 8 | 7 6 5 | 3 2 4 ---------------------+----------------------+--------------------- 34 8 34 | 6 7 1 | 5 9 2 2 1 5 | 49 3 489 | 48 6 7 7 6 9 | 2 5 48 | 148 3 18 ---------------------+----------------------+--------------------- 39 7 13 |c189 4 6 | 2 5 d89 49 5 46 | 89 2 7 | 689 1 3 8 2 16 | 5 b19 3 | 7 4 69 (9)r1c5 = (9-1)r9c5 = (1-8)r7c4= (8-9)r7c9 = r2c9 => -9 r1c7, r2c46; stte | r9c9

Phil

by **Leren** » Fri Jul 11, 2014 1:00 am

Code: Select all: *--------------------------------------------------------------* | 6 4 7 | 3 19 2 | 19 8 5 | | 5 3 2 |*49+1a 8 *49 | 69-1 7 169 | | 1 9 8 | 7 6 5 | 3 2 4 | |--------------------+--------------------+--------------------| | 34 8 34 | 6 7 1 | 5 9 2 | | 2 1 5 |*49 3 *489 |*48 6 7 | | 7 6 9 | 2 5 *48 |*48+1b 3 18c | |--------------------+--------------------+--------------------| | 39 7 13 | 89-1e 4 6 | 2 5 89d | | 49 5 46 | 89 2 7 | 689 1 3 | | 8 2 16 | 5 19 3 | 7 4 69 | *--------------------------------------------------------------*

7 cell DP (489) r2c46, r5c467, r6c67

(1) r2c4 =DP= 1 r6c7 - (1=8) r6c9 - r7c9 = (8) r7c4 => - 1 r2c7, r7c4; stte

Leren

by **7b53** » Fri Jul 11, 2014 5:51 am

Code: Select all: *--------------------------------------------------------------* | 6 4 7 | 3 1(9) 2 | 19 8 5 | | 5 3 2 | 149 8 49 | 169 7 16(9) | | 1 9 8 | 7 6 5 | 3 2 4 | |--------------------+--------------------+--------------------| | 34 8 34 | 6 7 1 | 5 9 2 | | 2 1 5 | 49 3 489 | 48 6 7 | | 7 6 9 | 2 5 48 | 148 3 18 | |--------------------+--------------------+--------------------| | 39 7 13 |*189 4 6 | 2 5 *89 | | 49 5 46 | 89 2 7 | 689 1 3 | | 8 2 16 | 5 1(9) 3 | 7 4 6(9) | *--------------------------------------------------------------*

(8)r7c4 = (8-9)r7c9 = skyscraper(9)c59 - (9=41)r2c64 => r7c4 <> 1

by **tlanglet** » Fri Jul 11, 2014 1:55 pm

Leren, Great solution. This is a pattern that Danny likes...........

I also spotted the (489) pattern, so I looked for an alternate and found an almost skyscraper.

Code: Select all: *--------------------------------------------------* | 6 4 7 | 3 *19 2 | 1-9 8 5 | | 5 3 2 | 14-9 8 4-9 | 169 7 *169 | | 1 9 8 | 7 6 5 | 3 2 4 | |----------------+----------------+----------------| | 34 8 34 | 6 7 1 | 5 9 2 | | 2 1 5 | 49 3 489 | 48 6 7 | | 7 6 9 | 2 5 48 | 148 3 18 | |----------------+----------------+----------------| | 39 7 13 | 189 4 6 | 2 5 f89 | | 49 5 46 | 89 2 7 | 689 1 3 | | 8 2 16 | 5 *19 3 | 7 4 *69 | *--------------------------------------------------*

Skyscraper (9) in r19c5, r29c9 with 9r7c9
shyscraper(9) => r1c7,r2c46<>9
||
(9-8)r7c9=(8-1)r7c4=1r2c4-(1=9)r1c5 => r1c7,r2c46<>9

Ted

by **blue** » Fri Jul 11, 2014 5:19 pm

Code: Select all: +-----------+-----------------+----------------+ | 6 4 7 | 3 1(9) 2 | 1(9) 8 5 | | 5 3 2 | 149 8 49 | 169 7 169 | | 1 9 8 | 7 6 5 | 3 2 4 | +-----------+-----------------+----------------+ | 34 8 34 | 6 7 1 | 5 9 2 | | 2 1 5 | 49 3 489 | 48 6 7 | | 7 6 9 | 2 5 48 | 148 3 18 | +-----------+-----------------+----------------+ | 39 7 13 | 189 4 6 | 2 5 89 | | 49 5 46 | (89) 2 7 | (689) 1 3 | | 8 2 16 | 5 1-9 3 | 7 4 (69) | +-----------+-----------------+----------------+

Almost XY-Wing:

9r1c5 = r1c7 - 9r8c7 =* [ XY-Wing: (9=8)r8c4 - (8*=6)r8c7 - (6=9)r9c9 ] => r9c5<>9; stte

by **tlanglet** » Sat Jul 12, 2014 2:26 pm

blue wrote:
Code: Select all
+-----------+-----------------+----------------+ | 6 4 7 | 3 1(9) 2 | 1(9) 8 5 | | 5 3 2 | 149 8 49 | 169 7 169 | | 1 9 8 | 7 6 5 | 3 2 4 | +-----------+-----------------+----------------+ | 34 8 34 | 6 7 1 | 5 9 2 | | 2 1 5 | 49 3 489 | 48 6 7 | | 7 6 9 | 2 5 48 | 148 3 18 | +-----------+-----------------+----------------+ | 39 7 13 | 189 4 6 | 2 5 89 | | 49 5 46 | (89) 2 7 | (689) 1 3 | | 8 2 16 | 5 1-9 3 | 7 4 (69) | +-----------+-----------------+----------------+

Almost XY-Wing:

9r1c5 = r1c7 - 9r8c7 =* [ XY-Wing: (9=8)r8c4 - (8*=6)r8c7 - (6=9)r9c9 ] => r9c5<>9; stte

Very nice solution Blue.

I also have occasional difficulties notating "almost" solutions especially if the almost condition interrupts the natural flow of the logic.

A possible notational technique to address this issue is to separate the basic logic/pattern from the almost term and then notate both paths. For example, your solution would then look like:

Almost xy-wing(68-9) with (68=9)r8c7
xy-wing(68-9) => r9c5<>9
||
9r8c7-9r1c7=9r1c5 = r9c5<>9

This alternate approach does not require the use of "*" or other funny gimmicks which can be hard for others to understand.

Comments ...............

Ted

by **ArkieTech** » Sat Jul 12, 2014 3:36 pm

tlanglet wrote:Almost xy-wing(68-9) with (68=9)r8c7
xy-wing(68-9) => r9c5<>9
||
9r8c7-9r1c7=9r1c5 = r9c5<>9

The * confuses me also. I would note it:

Code: Select all: (68r8c7)xyw:689r8c47,r9c9 => -9r9c5 9r8c7-r1c7=r1c5-------------

by **daj95376** » Sat Jul 12, 2014 4:40 pm

_

I try to break the notation when a pattern is involved: (very similar to blue's notation)

Code: Select all: 9r1c5 = r1c7 - 9r8c7 ; XY-Wing[(9=8)r8c4 - (8=6)r8c7 - (6=9)r9c9] => -9 r9c5

_

by **blue** » Sat Jul 12, 2014 8:40 pm

tlanglet wrote:I also have occasional difficulties notating "almost" solutions especially if the almost condition interrupts the natural flow of the logic.

(...)

This alternate approach does not require the use of "*" or other funny gimmicks which can be hard for others to understand.

ArkieTech wrote:The * confuses me also.

I don't really like them myself. Ted's "funny gimmicks" characterization, seems apt.
I wrote a "chain" for a network puzzle the other day, that had a '*', '#' and '@' in it.
The last strong link looked like a cartoonist's depiction of someone swearing.

I don't really like notation like "XYWing(68-9)", either -- not without the full cell list being mentioned, at least.
Dan's suggestion is interesting -- "(68r8c7)xyw:689r8c47,r9c9".

daj95376 wrote:I try to break the notation when a pattern is involved: (very similar to blue's notation)

(...)

I like seeing the small familiar patterns broken out too -- especially when it can be one small pattern at the end of a chain.
It makes things less abstract and more grounded in the easy and familiar.
It also hints at a way to think, when you're trying to spot something small and useful.
This one could have been written as a Kraken cell elimination, of course.

For (hopefully) perfect clarity, I would have written it in one of these forms:

Code: Select all: +---------------------+ | XY-Wing | | | | 8r8c7 - (8=9)r8c4 ---- | || | \ | 6r8c7 - (6=9)r9c9 ------ 9r9c5 | || | +---------------------+ || 9r9c5 - 9r1c5 = r1c7 - 9r8c7

Code: Select all: +---------------------+ | XY-Wing | | pivot: r8c7 | | pincers: r8c4,r9c9 | | | | 8r8c7 - (8=9)r8c4 ---- | || | \ | 6r8c7 - (6=9)r9c9 ------ 9r9c5 | || | +---------------------+ || 9r9c5 - 9r1c5 = r1c7 - 9r8c7

The 2nd one is full of details, but it looks messy and somewhat intimidating.
I would probably grit my teeth, go with the first one, and hope for the best.
For single digit patterns, it's easier to specify details -- e.g. "Kite: (6)r2c3\b1", labeling a "boxed patern".

I also don't like the fact that the "chain" doesn't start with a strong link.
With the far end being what it is, though, including the "9r9c5's" seems necessary.

by **David P Bird** » Sat Jul 12, 2014 11:40 pm

Code: Select all: +-----------+-----------------+----------------+ | 6 4 7 | 3 1(9) 2 | 1(9) 8 5 | | 5 3 2 | 149 8 49 | 169 7 169 | | 1 9 8 | 7 6 5 | 3 2 4 | +-----------+-----------------+----------------+ | 34 8 34 | 6 7 1 | 5 9 2 | | 2 1 5 | 49 3 489 | 48 6 7 | | 7 6 9 | 2 5 48 | 148 3 18 | +-----------+-----------------+----------------+ | 39 7 13 | 189 4 6 | 2 5 89 | | 49 5 46 | (89) 2 7 | (689) 1 3 | | 8 2 16 | 5 1-9 3 | 7 4 (69) | +-----------+-----------------+----------------+

The XY-Wing can be considered a Boolean that is true when (9)r8c7 is false.
There is therefore a strong link (9)r8c7 = XYWing
Similarly there is a weak link between the XYWing and (9)r9c5 so the full AIC has the form:

(9)r9c5 - (9)r1c5 = (9)r1c7 - (9)r8c7 = (689)XYWing:r8c47,r9c9 - (9)r9c5 => r9c5 <> 9

Every term is a Boolean and the link types alternate properly.
The weak links at either end aren't strictly necessary but act as a bit of a crutch.

We now have to consider how the XYWing Boolean is notated. I belong to the camp that defines a pattern as a recognisable arrangement of required elements that has been pre-analysed and is known to produce certain standard eliminations. In other words it doesn't need proving again in the chain. Note that this in in accord with how we treat DPs and Fish. Therefore all that is theoretically necessary to notate any pattern is its name and the list of cells and digits that meet its criteria.
(689)XYWing:r8c47,r9c9 does just that but it rather indigestible.
XYWing:(89)r8c4,(68)r8c7,(69)r9c9 is longer but is somewhat easier, particularly as it shows r8c7 without the (9).
XYWing:(98)r8c4,(86)r8c7,(69)r9c9 orders the digits to make it simpler yet.

Now, if the previous line of argument is accepted, any pattern that needs its internal links to be notated ceases to be a pattern!

Although I don't like entering a chainable pattern at a cell other than at either end, I can't argue against it if the pattern can be recognised without needing to track the logic. Unfortunately that depends on players' individual talents so defies tight definition. All I can say is that I would rank these almost forms of the pattern higher and would try to avoid them when trying to develop the simplest solution possible.

[Edit] typos in notation (189)XYWing: corrected to (689)XYWing etc

by **ArkieTech** » Sun Jul 13, 2014 12:20 am

David P Bird wrote:(9)r9c5 - (9)r1c5 = (9)r1c7 - (9)r8c7 = (189)XYWing:r8c47,r9c9 - (9)r9c5 => r9c5 <> 9

I like!

starting and ending strong:

(9)r1c5 = (9)r1c7 - (9)r8c7 = (189)XYWing:r8c47,r9c9 => r9c5 <> 9

by **blue** » Sun Jul 13, 2014 2:53 pm

David P Bird wrote:(9)r9c5 - (9)r1c5 = (9)r1c7 - (9)r8c7 = (689)XYWing:r8c47,r9c9 - (9)r9c5 => r9c5 <> 9

Yes, very nice !

XYWing:(89)r8c4,(68)r8c7,(69)r9c9 is longer but is somewhat easier, particularly as it shows r8c7 without the (9).

I like that sentiment as well.
Minor point: I'ld rather see the the pivot cell listed first.

(9)r9c5 - (9)r1c5 = (9)r1c7 - (9)r8c7 = XYWing:(68)r8c7,(89)r8c4,(69)r9c9 => r9c5 <> 9

Now, if the previous line of argument is accepted, any pattern that needs its internal links to be notated ceases to be a pattern!

Quite true.

I'm not sure what "line of argument" was referring to, though.
For my part, I wasn't arguing for any particular notation.
I just liked the idea of highlighting the small pattern in the first place (when the alternative was a Kraken cell presentation).

by **David P Bird** » Sun Jul 13, 2014 7:05 pm

blue wrote:I'm not sure what "line of argument" was referring to, though.

The issue is what defines a pattern.

Before I wrote: I belong to the camp that defines a pattern as a recognisable arrangement of required elements that has been pre-analysed and is known to produce certain standard eliminations.

I also added the proviso that the pattern had to be recognisable without needing to track the logic. But that is in direct contradiction with Champagne's view. Effectively he allows patterns to be identified, (by whatever means) on the fly. That in turn means they must be proved in the notation before the inferences they derive can be used. There obviously is a vast difference between these two views.

Regarding notation of an XYWing, I just showed three alternatives without suggesting which was best or any others that could be used. In the expanded version I simply chose the cell order that showed the 2 cells that would contain the either/or (9)s that would produce the elimination first and last. If the pure AIC view is generally accepted, then I guess one or other notation will eventually emerge as a favourite. (From past experience for me to voice my preference would be to give it the kiss of death.)

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