The New Sudoku Players' Forum

by **creint** » Wed Oct 16, 2019 4:00 pm

You should not use the APE function from SudokuExplainer because that one does not use ALS larger than 1. I could give more sample puzzles with overlapping ALS, which you can inspect on sudokuwiki.

by **tarek** » Wed Oct 16, 2019 7:03 pm

Too late … I left on for the night and luckily had a response … Here is the counter example:

Code: Select all: +----------------+----------------+----------------+ | 2 1469 7 | 5 1346 49 | 346 36 8 | | 8 5 69 | 36 2346 349 | 2346 7 1 | |*16 146 3 | 7 1246 8 | 9 256 2456 | +----------------+----------------+----------------+ |*69 679 8 | 1 34 34 | 5 269 267 | | 4 179 2 | 8 5 6 | 17 19 3 | | 1356 136 156 | 9 7 2 | 146 8 46 | +----------------+----------------+----------------+ | 3-69 8 4 | 2 369 5 | 1367 136 67 | |#1359 2 1569 | 36 369 7 | 8 4 56 | | 7 *36 *56 | 4 8 1 | 236 2356 9 | +----------------+----------------+----------------+ APE: r7c1<>6

As you can see this can't be explained by an ALS-XZ but it be explained as expected by an ALS-XY

The gist of the SE APE and how it connects to ALS techniques is: There should be a Pilot cell with x candiates. The Pilot cell is connected to x number of bivalue cells each having 1 different candidate (which is in the pilot cell) and a similar candidate. A cell that sees all of these bivalue cells and has that similar cell can be eliminated.

In theory we can have as many bivalue cells reflecting the number of candidates in the pilot cell. In vanilla sudoku if the APE is to have an elimination then it can be explained by an ALS XY using the same cells

I had a look at the link that you provided. All the examples will be solved either with ALS-XZ or ALS-XY

by **creint** » Thu Oct 17, 2019 7:14 pm

Here is one where It can find APE D9 F9 -67r6c9, where no ALS is found using those same cells. Even Xsudo does not find it using the same cells.

Code: Select all: 1...8659.8......2.........1.....7...5.6..4....9..58.....7.45..........6362.1..4..

Code: Select all: +--------------+--------------+------------------+ | 1 3 2 | 47 8 6 | 5 9 47 | | 8 457 459 | 457 39 1 | 367 2 467 | | 479 6 459 | 457 2 39 | 8 347 1 | +--------------+--------------+------------------+ | 24 48 13 | 239 6 7 | 239 1345 24589 | | 5 78 6 | 239 1 4 | 2379 37 2789 | | 247 9 13 | 23 5 8 | 2367 1347 2467 | +--------------+--------------+------------------+ | 3 1 7 | 6 4 5 | 29 8 29 | | 49 45 459 | 8 7 2 | 1 6 3 | | 6 2 8 | 1 39 39 | 4 57 57 | +--------------+--------------+------------------+

Same grid with pencilmarks:

Hidden Text: Show

Here are more with overlapping APE which you can test.

Hidden Text: Show

by **tarek** » Thu Oct 17, 2019 9:15 pm

Hi creint and thanks,

I had a look at the puzzles you posted. and certainly it didn't catch any eliminations with Sukaku Explainer APE/ATE which is SE's APE/ATE.

I went to Andrew Stuart's SudokuWiki page. The elimination is clear as mud as far as I'm concerned and I have to take its word for it. the 3 highlighted ALSs and the 2 Grey cells don't appear to combine forming an ALS-XZ or ALS-XY.

Only 2 puzzles from what you posted had an ATE that SE could catch and these could be replicated with ALS eliminations. There is a possibility that some of these aligned set eliminations outside of what SE can currently do could be explained by a larger set (Aligned quad eliminations, Aligned Set (5) eliminations) but SE hasn't implemented that due to how slow the machine gets.

Does anybody actually use this annoying technique in practice!!

Unless I know what's going on I'm afraid SE's APE/ATE will not be altered and in that sense, it would mean that with the current implementation of SE's APE/ATE there is still no example that can't be solved using an ALS-XY. I may for testing reasons in the future put larger Aligned set exclusion techniques in Sukaku explainer but will be disabled by default.

by **tarek** » Fri Oct 18, 2019 7:01 pm

This is my own counter-example and caught by SE as APE as well :cry:

Code: Select all: +-------------+-------------+-------------+ | 3 8 1 | 4 6 5 | 2 7 9 | | 2 57 567 | 8 9 3 | 1 56 4 | | 56 4 9 | 2 *17 17 | 3 568 68 | +-------------+-------------+-------------+ | 567 1 56 |*57 4 8 | 9 3 2 | | 8 59 3 | 6 25-7 279 | 57 4 1 | | 579 2 4 | 3 1-57 179 | 57 68 68 | +-------------+-------------+-------------+ | 59 3 8 | 1 *25 6 | 4 29 7 | | 1 579 257 | 57 8 4 | 6 29 3 | | 4 6 27 | 9 3 27 | 8 1 5 | +-------------+-------------+-------------+ APE combinations of cells r4c4,r37c5 --> r5c5<>7 r6c5<>5

SE hint explanation: Show

This confirms that my understanding of how APE is related to ALS eliminations was incorrect. Therefore even the SE APE and ATE will remain. Another technique comes to mind "subset counting" which looks at the target eliminations and their relationship with a group of cells to establish if they can be eliminated or not.

by **creint** » Fri Oct 18, 2019 8:01 pm

Yes but it would be more powerfull to allow for ALS in APE, which is not implemented in SE.
I would place it after ALS and before complex/dynamic chaining because it can progress where chains cannot. Check the pencilmarkgrid, a placement in 6r2c9 after the removal of the 7r6c9 could be very powerful.
It's very limited brute force with only ALS check for contradiction.

About subset counting:
http://sudopedia.enjoysudoku.com/Subset_Counting.html
http://sudopedia.enjoysudoku.com/Subset_Exclusion.html

I could not find an example where an ALS would not find exclusions, it is just another name of a Sue de Coq like structure, 2 ALS with overlap. Only if it cannot fit into 2 constraint. Xsudo can probably do more with those cells. With APE Xsudo could not find the exclusions.

by **tarek** » Sat Oct 19, 2019 9:38 am

My example above can't be explained by ALS straight away as the 3 cells in question do not link by anything outside the elimination cells. Subset counting also is not straight forward as each individual elimination multiplicities reduction doesn't reduce them to below the cell number. But when you take each of those individual elimination cells, you can then see the other elimination happening if you add the cell into the other 3 cells to make them 4 cells and the ALS elimination is clear. overlapping ALSs as you called them.

This awfully sounds familiar as cannibalistic fish do eliminate base candidates. My feeling is that I'm missing a 1 step AHS type eliminations here with all of the cells involved here!

by **creint** » Sat Oct 19, 2019 11:22 am

In you example here with 2 ALS/XYZ-wing gives same result:
r4c4,r36c5 -> r5c5<>7
r4c4,r57c5 -> r6c5<>5

Is it that 1-57 means -5 and -7, and if you only want to mention one should it be 17-5 in your pencilmarks?

APE combinations of cells r4c4,r37c5 --> r5c5<>7 r6c5<>5

because the r6c5<>7 is not mentioned.

While my pencilmark example has no other possible explanation for -6r6c9.

by **tarek** » Sat Oct 19, 2019 12:32 pm

I can see how it can be confusing but others use it same way. If I wanted to eliminate 7 as well it would have appeared as 1-5-7 or 1-(57)

I think until we see an ALS implemented in SE we will keep on like this

by **SpAce** » Sat Oct 19, 2019 4:55 pm

tarek wrote:This awfully sounds familiar as cannibalistic fish do eliminate base candidates. My feeling is that I'm missing a 1 step AHS type eliminations here with all of the cells involved here!

I think your feeling is right. Would this overlapping AHS-cannibal work for you:

Code: Select all: .---------------.--------------------.-------------. | 3 8 1 | 4 6 5 | 2 7 9 | | 2 57 567 | 8 9 3 | 1 56 4 | | 56 4 9 | 2 a[17] 17 | 3 568 68 | :---------------+--------------------+-------------: | 567 1 56 | c57 4 8 | 9 3 2 | | 8 59 3 | 6 be(25)-7 279 | 57 4 1 | | 579 2 4 | 3 ad[17]-5 179 | 57 68 68 | :---------------+--------------------+-------------: | 59 3 8 | 1 e(25) 6 | 4 29 7 | | 1 579 257 | 57 8 4 | 6 29 3 | | 4 6 27 | 9 3 27 | 8 1 5 | '---------------'--------------------'-------------'

(17)r36c5 = (7)r5c5 - (7=5)r4c4 - (5)r6c5 = (52)r75c5 => -7 r5c5, -5 r6c5

...or either one of these shorter versions:

(17)r3c36 = (75)b5p51 - (5=17)r36c5 => -7 r5c5, -5 r6c5

(25)r57c5 = (57)b5p81 - (7=25)r57c5 => -7 r5c5, -5 r6c5

?

As a side note from a human solver: I've never ever used APE (much less ATE) and probably never will. As such it's in a very rare company, among the likes of POM (not much else even comes to mind). Except in very simple and obvious cases (where other techniques are just as obvious), I consider it a complicated form of T&E, and I don't think it should be counted among pattern-based techniques.

The concept of such case-by-case analysis has value in much more complicated situations such as JExocets or multi-cell T&E, but I think anyone using it for simple ALS situations is missing something. That said, some human solvers (most notably gfick) have reported using it, so this is just one opinion.

by **tarek** » Sat Oct 19, 2019 7:25 pm

Thanks Space,

The original idea was to find replacements to APE/ATE and drop them off :cry:

by **SpAce** » Sat Oct 19, 2019 9:39 pm

tarek wrote:The original idea was to find replacements to APE/ATE and drop them off

Well, I would definitely support that goal, for aforementioned reasons. All of the "normal" patterns prove verities, and can be described and found in terms of AICs (or rarely krakens, such as Death Blossom). On the other hand, APE/ATE is a contradiction-based technique. It's a totally different paradigm, and that's one reason why it doesn't belong in the same family at all.

Furthermore, I haven't seen a single example of APE/ATE that couldn't be replaced with a short AIC (if you have such examples, I'll be happy to take a look). Even if that AIC is not quite as simple as ALS-XZ or ALS-XY-Wing, it's still usually simpler to understand and to find than the APE/ATE alternative, imho. Then again, I'm biased because I'm the most comfortable with AICs.

Btw, about marking eliminations in the grid:

creint wrote:Is it that 1-57 means -5 and -7, and if you only want to mention one should it be 17-5 in your pencilmarks?

Yes! That's how it should be.

tarek wrote:I can see how it can be confusing but others use it same way. If I wanted to eliminate 7 as well it would have appeared as 1-5-7 or 1-(57)

That style is EXTREMELY confusing!

I don't know anyone else on the forum who marks eliminations that way. I've only seen that style in some VERY old posts. If anyone marks 1-57 on the grid it obviously means that both 5 and 7 are eliminated. I thought it was just a typo, but apparently not. Please reconsider!

by **tarek** » Sat Oct 19, 2019 10:11 pm

SpAce wrote: I've only seen that style in some VERY old posts.

SpAce wrote: Please reconsider!

Fine

by **SpAce** » Sat Oct 19, 2019 11:57 pm

tarek wrote:
SpAce wrote: Please reconsider!
Fine

Thanks!

Btw, have you guys considered seeing some of those APE eliminations as AALS moves? I think it's a pretty neat way to see them, when applicable. For example:

tarek wrote:Too late … I left on for the night and luckily had a response … Here is the counter example:

Code: Select all
+----------------+----------------+----------------+ | 2 1469 7 | 5 1346 49 | 346 36 8 | | 8 5 69 | 36 2346 349 | 2346 7 1 | |*16 146 3 | 7 1246 8 | 9 256 2456 | +----------------+----------------+----------------+ |*69 679 8 | 1 34 34 | 5 269 267 | | 4 179 2 | 8 5 6 | 17 19 3 | | 1356 136 156 | 9 7 2 | 146 8 46 | +----------------+----------------+----------------+ | 39-6 8 4 | 2 369 5 | 1367 136 67 | |#1359 2 1569 | 36 369 7 | 8 4 56 | | 7 *36 *56 | 4 8 1 | 236 2356 9 | +----------------+----------------+----------------+ APE: r7c1<>6

As you can see this can't be explained by an ALS-XZ but it be explained as expected by an ALS-XY

It could also be written as an AALS-XY-Z (or whatever the AALS-equivalent to ALS-XZ is called):

(6=35)r9c23 - (3|5=196)r834c1 => -6 r7c1

or:

(6=19)r34c1 - (1|9=356)b7p489 => -6 r7c1

For me that would be preferable to a cannibalistic ALS-XY-Wing (though the latter gets one more elimination):

(6=1)r3c1 - (1=3569)b7p1478 - (9=6)r4c1 => -6 r67c1

by **SpAce** » Sun Oct 20, 2019 1:01 am

creint wrote:Here is one where It can find APE D9 F9 -67r6c9, where no ALS is found using those same cells. Even Xsudo does not find it using the same cells.

Could one reason be that the APE cells presented by SudokuWiki don't make any sense in the first place?

: ape.png (84.59 KiB) Viewed 1102 times

Or can you explain to me how the APE is supposed to work with those colored cells? Me, I think the brownish r7c9 is irrelevant, while r6c7 should be added to the green ALS. Then I can see how it works, though not with a simple ALS move. Like the previous example, it's easy to present as an AALS move instead:

(67=45)r129c9 - (4|5=2389'67)b6p134567 => -67 r6c9, -6 r2c7

In any case, my take on these few APE examples so far is that I haven't yet seen anything that wouldn't be doable and usually easier with more normal patterns or chaining techniques. No, not all of them can be presented as simple ALS moves (at least when multi-digit eliminations are wanted in a single step with the same exact cells), but I'm pretty sure I can write a relatively simple AIC for any of them (and also find such AICs much more easily in a live puzzle). At least with these examples there are also simpler and more powerful alternatives around if using other cells is allowed. I'm happy to be proven wrong, though. If someone finds an APE example that isn't easily seen as something else, then I think it has some actual value.

So, at least this manual solver's point of view is that APE is neither necessary nor human-friendly a technique. I very much doubt that many human solvers actually use it, so it should probably have a pretty low priority in a human-style software solver too. That said, I can only speak for myself, of course.

Edit. Added the elimination -6 r2c7, thanks to creint (and his XSudo).

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