Sudoku Players' Forum (clone)

Some of this stuff is over my head, and I'm sorry to have tuned some of it out rather than diving whole-hog into everything. On the other hand, I will have the occasion to explain BUG+1, XY wings and W wings to my colleague at work tomorrow, which will oblige me to have learned and understood these myself. Good show and undoubtable progress for me, so thanks again to everyone.

I have a question about the BUG+1 example at Sudopedia, where it says:

As noted above, the same deduction can be made by coloring. Specifically, the chain
r1c3=9 => r7c3=1 => r7c5=3 => r6c5=9
leaves no candidates for digit 9 in box 2.

As noted above where? And while I can see how coloring with the indicated chain can also provide a solution for the puzzle, how is it "the same deduction"? If the 9 can't be at r1c3, is it immediately obvious why it couldn't be at either r1c4 or r1c5? If so, how?

Roy McCoy wrote:I have a question about the BUG+1 example at Sudopedia, where it says:

As noted above, the same deduction can be made by coloring. Specifically, the chain
r1c3=9 => r7c3=1 => r7c5=3 => r6c5=9
leaves no candidates for digit 9 in box 2.

As noted above where? And while I can see how coloring with the indicated chain can also provide a solution for the puzzle, how is it "the same deduction"? If the 9 can't be at r1c3, is it immediately obvious why it couldn't be at either r1c4 or r1c5? If so, how?

You're right, it's not a very good example. It's not the same deduction neither is it immediately clear that r1c4 or r2c5 cannot be 1. But if we really really want to use that chain to make the same deduction, then we can note that the chain works both ways:

r1c3=9 => r7c3=1 => r7c5=3 => r6c5=9
r6c5=9 => r7c5=3 => r7c3=1 => r1c3=9

In other words, neither r1c3 or r6c5 can be 9. From this we can deduce that r1c5 must be 9.

Though I don't think this is what the author of the Sudopedia article had in mind.

RW

Thanks. I don't think it was what he or she had in mind either, but your elaboration seems to correct the problem so I put it in the article. Perhaps you can check to see if I reworded it properly. I saw where the author had mentioned coloring previously, so I left "As noted above".

I was too hesitant last night, however, to make two changes that seemed called for in the Scanning article. I posted in the discussion page, http://www.sudopedia.org/wiki/Talk:Scanning, but nobody's come back on that there. To repeat here, should "filled with another digit" be "filled with other digits"? I finally answered my other question myself: the middle boxrow on the right in the second image with red should not be green, as the digit must be placed in the middle boxrow on the left, which rules out the one I was concerned with; so the complete floor configuration is known, as had just been stated. I guess I find it a little confusing that the color coding of these images doesn't distinguish between available and obligatory boxrows.

I have more fundamental problems with that particular article than these details. There is no way scanning is the most common technique for doing anything. Crosshatching is far more common and does much the same thing. But then I don't contribute there very much and it is way easier to complain than it is to put in the work to fix it.

There is relatively little going on at Sudopedia these days. It isn't common to see replies. There is a slow steady stream of very minor maintenance and occasionally someone goes through and reverts changes that are dead wrong, but not very much is getting added or significantly improved. It would be great if there was some new blood at Sudopedia, as there is always plenty to do.

I'm nevertheless interested in scanning, because I didn't recognize it as anything I'd ever done, didn't immediately understand it, and figured there must be at least something to it for the author to have expressed such appreciation for it. He said it was more methodical but didn't display the complete method - which I would suppose to be completely applied in order to be truly methodical. Maybe it's obvious. Is the idea that you go through all the missing digits on all three floors, for example from top to bottom and left to right?

Also, just to make sure I understand, the reason columns aren't initially involved is because they're relevant only when there's a single available boxrow, right? It would always amount to the same thing to scan the towers and secondarily consider the floors, right?

Scanning is a way to find hidden singles that takes into account the information that locked candidates would reveal but without using pencil marks. It is very similar to cross-hatching, but slightly more powerful and phrased using ideas and terminology from braid analysis.

Many people extend cross-hatching to take locked candidates into account, even though that is not described in the usual cross-hatching tutorials, and reach the same conclusions in a slightly different way. Cross-hatching has an easier learning curve, so it has an advantage there, but the extensions for using locked candidate information are not generally written down, so that is a disadvantage.

Scanning is normally done one digit at a time, looking at each chute in turn. Within a chute, you look at the pattern of available, required, and excluded boxrows/boxcolumns and see if you can pick out a boxrow/boxcolumn that must contain the digit. Once you spot a digit that is limited to a specific boxrow/boxcolumn you look at the intersecting chute to see if you can pin it down to a specific cell.

The section on braid analysis explains the ideas behind scanning in plenty of detail. Typically braid analysis is used on all digits at once, which seems to be beyond the abilities of most people solving puzzles by hand, but the parts of braid analysis that apply to one digit at a time are called scanning and are simple enough to do in your head with just a little practice.

Scanning [...] is very similar to cross-hatching, but slightly more powerful

That adds to its provisional attraction, if it provides any kind of edge.

and phrased using ideas and terminology from braid analysis.

I'm not sure if this adds to or subtracts from said attraction, but... okay, I've read the article - and was nervy enough to make a couple of edits even without understanding it generally. Braid analysis isn't attractive but scanning is, so I'll try to make a point of finally getting sure on that.

Within a chute, you look at the pattern of available, required, and excluded boxrows/boxcolumns and see if you can pick out a boxrow/boxcolumn that must contain the digit.

I suppose this is what I'll have to get comfortable doing.

RW wrote:

Roy McCoy wrote:I have a question about the BUG+1 example at Sudopedia, where it says:

As noted above, the same deduction can be made by coloring. Specifically, the chain
r1c3=9 => r7c3=1 => r7c5=3 => r6c5=9
leaves no candidates for digit 9 in box 2.

As noted above where? And while I can see how coloring with the indicated chain can also provide a solution for the puzzle, how is it "the same deduction"? If the 9 can't be at r1c3, is it immediately obvious why it couldn't be at either r1c4 or r1c5? If so, how?

You're right, it's not a very good example. It's not the same deduction neither is it immediately clear that r1c4 or r2c5 cannot be 1. But if we really really want to use that chain to make the same deduction, then we can note that the chain works both ways:

r1c3=9 => r7c3=1 => r7c5=3 => r6c5=9
r6c5=9 => r7c5=3 => r7c3=1 => r1c3=9

In other words, neither r1c3 or r6c5 can be 9. From this we can deduce that r1c5 must be 9.

Though I don't think this is what the author of the Sudopedia article had in mind.

RW

If we express that chain in full we find every inference is conjugate (one of the two arguments must be true and the other false).

(9'~1"r1c3 ~ (1')r7c3 ~ (1"~3')r7c5 ~ (3"~9')r6c5

Either all the candidates tagged 0' are true or all those tagged 0" are, and so (9)r1c3 and (9)r6c5 are equivalent. If they are assumed to be true a contradiction is produced so they must be false.

So Roy what you describe as a 'ambidirectional chain' in Sudopedia is a conjugate chain expressed in forcing chain notation. As such it's a bit of a dog's dinner in my eyes.

Purists would consider this deduction to be assumptive because it shows a contradiction if the end nodes are assumed to be true. To satisfy them there are two AICs to make the same eliminations individually:

(5=9)r1c4 - (9=1)r1c3 - (1)r7c3 = (1)r7c5 - (1=5)r8c5 => r1c3 <> 5, r8c4 <> 5
(7=1)r1c9 - (1)r1c3 = (1)r7c3 - (1=3)r7c5 - (3=9)r6c5 - (9=7)r2c5 => r1c5 <> 7

These eliminations aren't considered assumptive because the end arguments can't both be false and no truth state has to be assumed.

The first of these AICs also solves the BUG+1 pattern as it reduces r8c4 to a singleton.

RW I agree that what the author of the article had in mind when he said that colouring could be used is obscure, and probably not that chain.

So Roy what you describe as a 'ambidirectional chain' in Sudopedia is a conjugate chain expressed in forcing chain notation. As such it's a bit of a dog's dinner in my eyes.

Well, they can't all be hit sudoku guesses. Could you please revise the page with an acceptable formulation, then?

I still have my book in Dutch about sudokus that I want to read before taking it back to the library, but other than that I'm feeling pretty comfortable about the newspaper sudokus that my colleague could solve without pencilmarks and that I couldn't. I was just staying within the "chutes" and not paying enough attention to row-column interactions. Even if I haven't picked up this university-level symbolic-logic stuff (or what looks like it, anyway), I think my bit of dabbling with it has gotten me into fairly good shape for the ordinary non-fiendish puzzles they have in the papers here, which is enough for me. This isn't to say I won't ask here again if I get stuck sometime.

Roy, I don't want to dissuade you completely but just from jumping in too quickly while you are still on the learning slopes.

The Sudopedia entry wasn't particularly good in the first place and needed tidying. But sadly although there is still much to do, there are only a minority here that are prepared to contribute there, and I'm not inclined to be the only one in the boat that's rowing. However with some reluctance I've spent time editing the page as you'll see.

Roy, I don't want to dissuade you completely but just from jumping in too quickly while you are still on the learning slopes.

Thanks. Trying to read a book in Dutch on sudokus, including computer solution and generation, might be interpreted as jumping in too quickly, but on the other hand it's good for me to read at least some things in Dutch since I've lived here forever and still haven't acquired full fluency.

The Sudopedia entry wasn't particularly good in the first place and needed tidying. But sadly although there is still much to do, there are only a minority here that are prepared to contribute there, and I'm not inclined to be the only one in the boat that's rowing. However with some reluctance I've spent time editing the page as you'll see.

Yay! Thanks again.