## Dan's Donner December 20,2013

Post puzzles for others to solve here.

### Re: Dan's Donner December 20,2013

SteveG48 wrote:
DonM wrote:There is a major semantics problem going on here and it has to do with the term 'single-stepper'. It would seem to me that a chain that starts off with a single assumption (eg. if not (9)r1c6) and follows a straight inference path to an exclusion or exclusions by continuity or discontinuity that solves the puzzle was the original (and correct) perception of a 'single-stepper'.

Am I correct, then, in assuming that you would not consider something like a swordfish to be a single-stepper?

Years ago, when there were discussions regarding the relative degree of assumptivity we use in solving puzzles, I suggested the concept that what we do when solving puzzles is use Pattern-A and Pattern-B solving. Thus: 'A-patterns' are 'what-is' patterns whereby the mere presence of the pattern directly proves the exclusion (and thus we are using minimal assumptivity). That would include patterns such as x-wings, swordfish etc. So, if an A-pattern (ie. a swordfish) solves a puzzle, it is a single-stepper.

On the other hand, 'B-patterns' are chains which operate more like 'what-may-be' patterns whereby you start off with 'If not x then y etc.' They may or may not be single-steppers (and, either way, we are using greater assumptivity).
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### Re: Dan's Donner December 20,2013

DonM wrote:Years ago, when there were discussions regarding the relative degree of assumptivity we use in solving puzzles, I suggested the concept that what we do when solving puzzles is use Pattern-A and Pattern-B solving. Thus: 'A-patterns' are 'what-is' patterns whereby the mere presence of the pattern directly proves the exclusion (and thus we are using minimal assumptivity). That would include patterns such as x-wings, swordfish etc. So, if an A-pattern (ie. a swordfish) solves a puzzle, it is a single-stepper.

On the other hand, 'B-patterns' are chains which operate more like 'what-may-be' patterns whereby you start off with 'If not x then y etc.' They may or may not be single-steppers (and, either way, we are using greater assumptivity).

Thanks. I've never heard of Pattern-A and Pattern-B before, but I've had similar thoughts. With respect to Pattern-B, I think I prefer "one assumption and all it's exclusions equals one step", but I see where you're coming from.
Steve

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### Re: Dan's Donner December 20,2013

DonM wrote:... what we do when solving puzzles is use Pattern-A and Pattern-B solving. Thus: 'A-patterns' are 'what-is' patterns whereby the mere presence of the pattern directly proves the exclusion (and thus we are using minimal assumptivity). That would include patterns such as x-wings, swordfish etc. So, if an A-pattern (ie. a swordfish) solves a puzzle, it is a single-stepper.

On the other hand, 'B-patterns' are chains which operate more like 'what-may-be' patterns whereby you start off with 'If not x then y etc.' They may or may not be single-steppers (and, either way, we are using greater assumptivity).

Pattern-A and Pattern-B? Why not just call them patterns and chains, respectively?
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### Re: Dan's Donner December 20,2013

Nice to see my post raised some interest!

My view is that using memorised truth conditions, kraken nodes etc can easily trivialise the easier puzzles and take the challenge out of them. They should therefore only be used when there is no other way forward. Furthermore they should be ranked according to how acceptable they are. Both allow branched chains of different lengths to be combined whereas split nodes are only possible when the parallel paths being followed are of the same length. This makes them far more restrictive and is why they're more acceptable to me.

Before split nodes are summarily dismissed, the logic being followed should be compared with that of finned fish, Sue de Coq patterns etc when they are expanded into simple weak and strong links between the individual candidates in the mix. On that basis there are no grounds for disallowing them.

Fundamentally chains are composed of Boolean nodes which are gauged as being true or false depending on how they're specified. Hence the split node (1#2)r2c1,r8c7 is true when these cells both hold 1, but without the '#2' conventionally it would be considered true if either cell held a 1.
Likewise (1)SwordFish:r268c149 is true when the cell set holds 3 1's, and could be written more succinctly as (1#3)r268c149.

For the subject puzzle the split nodes were just used to combine two chains to qualify as a one-stepper, but here's a more serious example taken from < The Ultimate Fish Guide >:
Code: Select all
` +-----------------------------------+ |  7  .  7  |  .  7  7  |  .  .  .  | |  .  7e .  |  .  .  .  |  7d .  7d | |  .  .  7a |  .  7b .  |  7ac.  .  | |-----------+-----------+-----------| |  .  .  7a |  .  .  .  |  7a .  .  | |  7  .  .  |  .  7c .  |  7  7  7  | |  7  7e .  |  .  .  7d |  .  .  .  | |-----------+-----------+-----------| |  .  .  .  |  7  .  .  |  .  .  .  | |  .  .  .  |  .  .  .  |  7  7  .  | |  7  7f 7  |  .  .  .  |  .  .  .  | +-----------------------------------+  a             b             c                d                 e          f   (7#2)r34c37 = (7)Fin:r3c5 - (7#1)r3c7,r5c5 = (7#2)r2c79,r6c6 - (7)r2c26 = (7)r9c2 => r9c3 <> 7 `

Note that r3c7 occurs in both nodes a and c in this chain.

Here we have a set of linear links between well specified Boolean nodes so it's an AIC not a net – or is it?

DPB

 Typo identified by DAJ below corrected
Last edited by David P Bird on Sun Dec 22, 2013 9:23 am, edited 1 time in total.
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### Re: Dan's Donner December 20,2013

ronk wrote:
DonM wrote:... what we do when solving puzzles is use Pattern-A and Pattern-B solving. Thus: 'A-patterns' are 'what-is' patterns whereby the mere presence of the pattern directly proves the exclusion (and thus we are using minimal assumptivity). That would include patterns such as x-wings, swordfish etc. So, if an A-pattern (ie. a swordfish) solves a puzzle, it is a single-stepper.

On the other hand, 'B-patterns' are chains which operate more like 'what-may-be' patterns whereby you start off with 'If not x then y etc.' They may or may not be single-steppers (and, either way, we are using greater assumptivity).

Pattern-A and Pattern-B? Why not just call them patterns and chains, respectively?

Good question! Originally, my premise was simply that we are using 'what-is' pattern-solving when we solve with x-wings, swordfish etc. and that chains are more 'what may be' structures. But Myth Jellies responded that he saw chains also as patterns so I suggested the concept of Pattern-A and Pattern-B (ie. chains) solving.
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### Re: Dan's Donner December 20,2013

David P Bird wrote:For the subject puzzle the split nodes were just used to combine two chains to qualify as a one-stepper, but here's a more serious example taken from < The Ultimate Fish Guide >:
Code: Select all
` +-----------------------------------+ |  7  .  7  |  .  7  7  |  .  .  .  | |  .  7e .  |  .  .  .  |  7d .  7d | |  .  .  7a |  .  7b .  |  7ac.  .  | |-----------+-----------+-----------| |  .  .  7a |  .  .  .  |  7a .  .  | |  7  .  .  |  .  7c .  |  7  7  7  | |  7  7e .  |  .  .  7d |  .  .  .  | |-----------+-----------+-----------| |  .  .  .  |  7  .  .  |  .  .  .  | |  .  .  .  |  .  .  .  |  7  7  .  | |  7  7f 7  |  .  .  .  |  .  .  .  | +-----------------------------------+  a             b             c                d                 e          f   (7#2)r34c37 = (7)Fin:r3c5 - (7#1)r3c7,r5c5 = (7#2)r2c79,r6c6 - (7)r2c26 = (7)r9c2 => r9c3 <> 7 `

Note that r3c7 occurs in both nodes a and c in this chain.

Here we have a set of linear links between well specified Boolean nodes so it's an AIC not a net – or is it?

First, I corrected a typo for the labels for r2c2 and r6c2. Next, it appears that you chose an alternate way to represent the Kraken X-Wing that I presented in TUFG thread.

Start of Quote:

I see a Kraken X-Wing where the fin cell needs a network to perform the elimination.

Code: Select all
`X-Wing r34\c37 or r3c5=7(7): r3c5 - r1c6 = r6c6  - r6c2             ||                 = r9c2 - r9c3            r3c7 = r2c79 - r2c2 +-----------------------------------+ |  7  .  7  |  .  7  7  |  .  .  .  | |  .  7  .  |  .  .  .  |  7  .  7  | |  .  . *7  |  . @7  .  | *7  .  .  | |-----------+-----------+-----------| |  .  . *7  |  .  .  .  | *7  .  .  | |  7  .  .  |  .  7  .  |  7  7  7  | |  7  7  .  |  .  .  7  |  .  .  .  | |-----------+-----------+-----------| |  .  .  .  |  7  .  .  |  .  .  .  | |  .  .  .  |  .  .  .  |  7  7  .  | |  7  7 -7  |  .  .  .  |  .  .  .  | +-----------------------------------+`

End of Quote:

Given my exposure to JC's fishy chains since the above post, I would probably now present a Kraken Column [c2] for the elimination:

Code: Select all
` (7)r2c2 - r1c13 = t1c56 - r3c5 = X-Wing[r34c37] - (7)r9c3 (7)r6c2 - r6c6  = r5c5  - r3c5 = X-Wing[r34c37] - (7)r9c3 (7)r9c2                                         - (7)r9c3`

Few would argue that a Kraken Unit can't constitute a single-stepper. I'm not sure if all of them would also accept a Kraken X-Wing with a remote fin cell that needs to be networked to the elimination cell. Hmmm!

Note: JC's fish solution in that thread appears incorrect to me. Cell r9c3 appears only in base sector [r9] and cover sector [c3]. It does not qualify as a PE !!! ___ I don't believe anyone caught this in TUFG.

JC wrote:Locally Finned Whale : (7)r49c6b134/r126c137 with XF(7)r9c2 NF(7)r4c3 :=> r9c3<>7 (autocannibalism).
daj95376
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### Re: Dan's Donner December 20,2013

DAJ thanks for picking up on my typo which I've now corrected.

You seem to miss my underlying theme: when we compare our different solutions it's disheartening to find that a hard won path found using one rule set is considered inferior to someone else's who used a more relaxed one. We would all prefer to compete on a level playing field, and the tighter the rules are, the easier that will be.

Allowing kraken nodes and memory chains is a step too far for me particularly for the simpler puzzles. Once those doors are opened a crack there is nothing to stop them being flung wide open to allow all sorts of tactics. In comparison I hope I've demonstrated that split nodes can be considered to comply with all the basic rule requirements, and don't allow the doors to be swung so wide. Only a minority of kraken/memorised node deductions can be expressed as split nodes.

My thinking is also influenced by wanting to discourage methods based on single-sided assumptions (guessing) but I've already made my opinions clear on that, and plainly they don't accord with yours.

DPB
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### Re: Dan's Donner December 20,2013

daj95376 wrote:(9*)r1c6=r1c8-(9=165)r2c715-(*95=2)r1c6-(2=5)r8c6-(5=1)r8c7-(1=9)r2c7-r1c8=(9)r1c6
[/code]

I like

(abc)rncn

(a*)rncn=...-(*b=c)rncn-....
dan

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### Re: Dan's Donner December 20,2013

David wrote:Allowing kraken nodes and memory chains is a step too far for me particularly for the simpler puzzles.

My thinking is also influenced by wanting to discourage methods based on single-sided assumptions (guessing)....

Very reasonable, I agree. The kraken cell that started all this is the product of not just a guess, but three guesses, IMO. Still, an excellent find, and quite coincidentally the same "kraken net" that the HoDoKu solver returns .

Some of the greatest manual players in the short history of this game would use kraken units to solve the toughest puzzles. However, even those guys would much more often use pattern based nets before the more assumptive ones , esp patterns like fish, uniqueness, aals, and aaals and so on.

I think there's a reason that kraken unit logic lies at the bottom of most program solvers' hierarchies, usually shortly before "brute force."

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### Re: Dan's Donner December 20,2013

Code: Select all
`(9*)r1c6=r1c8-(9=165)r2c715-(*95=2)r1c6-(2=5)r8c6-(5=1)r8c7-(1=9)r2c7-r1c8=(9)r1c6`

It occurs to me that RonK might see the above as a chain and a discontinuous loop. Making it a two-stepper solution. _ _

Code: Select all
`(9)r1c6=r1c8-(9=165)r2c715  =>  r1c6<>5(9=2)r1c6-(2=5)r8c6-(5=1)r8c7-(1=9)r2c7-r1c8=(9)r1c6`

I have given up on the issues of "manual solving", "guessing", "T&E", and all the other rhetoric floating around. All I care about is if a sequence of interactions clearly explains an elimination in a PM. The less complex the sequence ... the better!

Luke wrote:I think there's a reason that kraken unit logic lies at the bottom of most program solvers' hierarchies, usually shortly before "brute force."

Any time that I need to find a step manually qualifies as "guessing"/"brute force" to me by the time I'm done.
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### Re: Dan's Donner December 20,2013

daj95376 wrote:I have given up on the issues of "manual solving", "guessing", "T&E", and all the other rhetoric floating around.

One can call it the rather pejorative 'rhetoric' or one can call it the core of lively discussion which has been the life-blood of manual-solving sudoku threads since the hobby's inception. Take a look at the view-count of this thread. This is one of the last forum sections that is keeping sudoku-solving alive and IMO it will benefit from anything that raises interest.
DonM
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### Re: Dan's Donner December 20,2013

daj95376 wrote:Any time that I need to find a step manually qualifies as "guessing"/"brute force" to me by the time I'm done.

Could you expound a bit more on this? You seem to be saying that if a computer can't solve it, i.e., you need to find a step manually (?), then it's guessing/brute force. But computers can solve all puzzles by brute force, so your meaning is unclear to me.
Steve

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### Re: Dan's Donner December 20,2013

SteveG48 wrote:
daj95376 wrote:Any time that I need to find a step manually qualifies as "guessing"/"brute force" to me by the time I'm done.

Could you expound a bit more on this? You seem to be saying that if a computer can't solve it, i.e., you need to find a step manually (?), then it's guessing/brute force. But computers can solve all puzzles by brute force, so your meaning is unclear to me.

My point is that I'm a terrible manual solver; and, if I decide to look for something that my solver doesn't handle, then it's never easy for me to find an elimination manually through other techniques. I'm always "guessing" at which technique might be present, and it's always a "brute force" effort to search for a pattern present for a technique. I'd much rather review/analyze how my solver was able to resolve a puzzle/PM. I also like to review interesting (non-convoluted) solutions found by others.

Unlike DonM, I've accepted that a majority of hard-line purist on form and technique have "left the building". What's left is adjusting to solutions as they are presented.
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### Re: Dan's Donner December 20,2013

daj95376 wrote:My point is that I'm a terrible manual solver; and, if I decide to look for something that my solver doesn't handle, then it's never easy for me to find an elimination manually through other techniques. I'm always "guessing" at which technique might be present, and it's always a "brute force" effort to search for a pattern present for a technique. I'd much rather review/analyze how my solver was able to resolve a puzzle/PM. I also like to review interesting (non-convoluted) solutions found by others.

Got it. Thanks. Out of curiosity, is your solver something that you've written yourself, or a product started by someone else that you build on?

Unlike DonM, I've accepted that a majority of hard-line purist on form and technique have "left the building". What's left is adjusting to solutions as they are presented.

Maybe that's a good thing (?). Purity is nice, but it doesn't give us innovation.
Steve

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### Re: Dan's Donner December 20,2013

SteveG48 wrote:
daj95376 wrote:My point is that I'm a terrible manual solver; and, if I decide to look for something that my solver doesn't handle, then it's never easy for me to find an elimination manually through other techniques. I'm always "guessing" at which technique might be present, and it's always a "brute force" effort to search for a pattern present for a technique. I'd much rather review/analyze how my solver was able to resolve a puzzle/PM. I also like to review interesting (non-convoluted) solutions found by others.

Got it. Thanks. Out of curiosity, is your solver something that you've written yourself, or a product started by someone else that you build on?

Unlike DonM, I've accepted that a majority of hard-line purist on form and technique have "left the building". What's left is adjusting to solutions as they are presented.

Maybe that's a good thing (?). Purity is nice, but it doesn't give us innovation.

Don't be misled by the premise that 'hard-line purists on form and technique' somehow limited innovation or that those who strived for good form and technique were 'hard-line' purists in the first place. I'm not sure how long you have been following Sudoku on the forum(s), but in case it is only recently, here are some facts:

This forum, the Players', in its original form provided perhaps the greatest contribution to the foundation for many of the basic and some advanced solving technique still used today. But it was over at the UK Eureka forum that some of the most active and innovative manual-solving occurred between 2007 and 2010. Some of the best manual solvers, Steve K, TTT, Myth Jellies and our still-present David P Bird were often found there.

Around 2010, a major hacking of the Eureka forum wiped out almost all the precious information that solvers were formerly able to refer to so as not to be re-inventing the wheel as has to some extent been going on in this forum. Partly due to that loss of threads started by Steve K, TTT and others and probably also due to other reasons, these major contributors left for good around that time.

However, some remnants of the forum were resurrected and a reliable number of excellent solvers remained in the Eureka forum where puzzles called The Extremes were solved weekly. These puzzles were more difficult than those usually found in this forum and some very useful and interesting manual-solving innovation continued. However, another major hacking occurred and wiped out the entire Eurkea forum and it was gone for good including every last one of threads that had helped solvers learn more advanced techniques.

Now to my main point: Rather than this being a case of 'hard-line' purists squelching innovation by insisting on good form and technique, it was the very fact that those/we solvers co-operated in using good form and technique and in using reasonably consistent notation that innovation could occur. (No, we didn't agree on every little thing, but we did agree on the most important things.)

One other unrelated factotum, but something I might as well get off my chest: Nothing will squelch one's incentive to manually solve sudoku puzzles more than the use of a computer solver. If one makes the mistake of using a solver such as HoDoKu to solve puzzles in these threads, one will never evolve as a manual solver. Some related good news is that if one challenges oneself with more advanced puzzles, most if not all computer solvers still can't match the elegance of a humanly-derived solution.
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