The New Sudoku Players' Forum

[ronk]

Your alternative is quite possible superior but I'm unlikely to implement it because, as far as I'm concerned, the strategy has been superseded and I'm unlikely to quote its results much longer.

You are going to supersede Conditional Disjoint Subsets? Won't whatever replaces it still be making eliminations based on Almost Locked Sets xz rule?

[ronk]

But I think it's safe to say that just about ALL of these were made possible ONLY by adding almost-locked sets.

I, for one, have spent a little time analyzing the log of Sudoku Assistant ... and find the bottom-to-top sequencing of the solution steps and then the top-to-bottom listing within each step a bit difficult to deal with. For instance, it is most difficult to obtain the proper sequential listing of just the eliminations, the "ISN'T" lines.

If everything read top-to-bottom, then one could just capture the log, and with an editor delete all lines without "ISN'T" in them. Would you consider re-ordering the log? Or do some equivalent to filter, or permit filtering, the eliminations and fills?

[Bob Hanson]

sure. Check now. This may require reloading the page a couple of times
or clearing your cache.

http://www.stolaf.edu/people/hansonr/sudoku

[ronk]

sure. Check now. This may require reloading the page a couple of times or clearing your cache.

Thanks, no cache clearing required.

Do you have a questions and suggestions thread somewhere for Sudoku Assistant?

I should be doing this on such a thread, but I'll start here anyway. With Medusa limited to "strong" chain analysis, I don't think SA is functioning equivalent to simple coloring ... as I recall reading somewhere on your site.

Specifically, for the puzzle of this thread, it won't eliminate r5c1#7 and r5c9#6 ... which Angus Johnson's SS does find. My solver also uses simple coloring for those eliminations.

[Bob Hanson]

could be. In fact, almost certainly. I have to admit I don't understand coloring quite. Can you show the exact configuration where the two operate differently? My guess is that simple coloring is strong+weak 3D Medusa restricted to the single-candidate plain. But it would be nice to have a specific example. If you can help me, that would be great.

[ronk]

But it would be nice to have a specific example. If
you can help me, that would be great.

With candidates ...

Code: Select all

*-----------------------------------------------------------------------------*
 | 56      56      2       | 38      9       348     | 1       348     7       |
 | 179     3       8       | 6       2457    12      | 245     59      259     |
 | 4       179     17      | 123578  2578    1238    | 2568    35689   235689  |
 |-------------------------+-------------------------+-------------------------|
 | 12367   12678   1347    | 39      2678    5       | 2468    16789   12689   |
 | 2567    245678  9       | 278     1       268     | 3       45678   2568    |
 | 123567  125678  1357    | 4       2678    39      | 2568    156789  125689  |
 |-------------------------+-------------------------+-------------------------|
 | 123579  12579   1357    | 12589   2568    12689   | 68      368     4       |
 | 135     15      1345    | 158     4568    7       | 9       2       368     |
 | 8       249     6       | 29      3       249     | 7       15      15      |
 *-----------------------------------------------------------------------------*

Conjugate pairing for 6s is ...

Code: Select all

 A a . | . . . | . . .
 . . . | . . . | . . .
 . . . | . . . | 6 6 6
 - - - + - - - + - - -
 6 6 . | . 6 . | 6 6 6
 6 6 . | . . C | . 6 6
 6 6 . | . 6 . | 6 6 6
 - - - + - - - + - - -
 . . . | . 6 c | 6 6 .
 . . . | . B . | . . b
 . . . | . . . | . . .


Since Bc share a house (box 8), any candidate that "sees" both b and C may be eliminated. Why? Both r7c6=6 and r8c5=6 cannot be true ... therefore either r5c6=6 or r8c9=6 must be true.

Conjugate pairing for 7s is ...

Code: Select all

 . . . | . . . | . . .
 A . . | . a . | . . .
 . 7 7 | B 7 . | . . .
 - - - + - - - + - - -
 7 7 7 | . 7 . | . 7 .
 7 7 . | b . . | . 7 .
 7 7 7 | . 7 . | . 7 .
 - - - + - - - + - - -
 7 7 7 | . . . | . . .
 . . . | . . . | . . .
 . . . | . . . | . . .


Identical situation for r5c1=7.

Hmmm. Could be SA requires "weak links" enabled to chain thru box 8 of the 6s example, box 2 of the 7s.

[Bob Hanson]

Conjugate pairing for 6s is ...

Code: Select all

 A a . | . . . | . . .
 . . . | . . . | . . .
 . . . | . . . | 6 6 6
 - - - + - - - + - - -
 6 6 . | . 6 . | 6 6 6
 6 6 . | . . C | . 6 6
 6 6 . | . 6 . | 6 6 6
 - - - + - - - + - - -
 . . . | . 6 c | 6 6 .
 . . . | . B . | . . b
 . . . | . . . | . . .


Since Bc share a house (box 8), any candidate that "sees" both b and C
may be eliminated. Why? Both r7c6=6 and r8c5=6 cannot be true ...
therefore either r5c6=6 or r8c9=6 must be true.

Sure. OK, Ronk, I see what you are talking about. Thanks for that explanation.
That's "weak link" analysis -- any time you are jumping from
Cc to Bb, that would be equivalent to Sudoku Assistant with "+weak"
checked. If you were sticking with CcCcCc---X then that would be just
single "strong chain" analysis.

The difference is that the strong-chain analysis is done as the chains are
identified -- no need to go on if we have an invalid chain -- while the weak
business takes extra effort to identify all the weak connections between
these chains.

It's at that later point where, in this case, the Cc---Bb weak link would be
identified and the C--r5c9#6--b connection would be flagged.

Here's what Sudoku Assistant says:

r5c9 ISN'T 6: weak corner eliminated by both 10(j) and 10(J)--11(K)

Chain 10: r5c6#6(j) r7c6#6(J)
Chain 11: r8c5#6(k) r8c9#6(K)

It's calling r5c9#6 a corner because it is weakly linked to both chains,
but there's a "bend" -- neither chain directly influences the other through
this link.

Of course, a human wouldn't have to wait. A human could just spot this
right away. In principle I could set up the Sudoku Assistant so that it
checks as it goes, but that just seems inefficient, and I thought it would
be better if it separated the stages this way.

I'm glad to see that the coloring letters BbCc etc. map directly onto my
chain lettering JjKk.... You should be able to follow that on the chain table
perfectly. Originally I was using 1s and 0s, but I've switched entirely now
to AaBbCc (though 1/0 is still in the code, of course).

I'm sorry if I somewhere said "strong 3D Medusa" meant coloring. I'm
sure I meant "X cycles".

[Jeff]

I'm sorry if I somewhere said "strong 3D Medusa" meant coloring. I'm sure I meant "X cycles".

Hope this is helpful, Bob. There are 4 types of colouring that have been described by different people in this forum, namely Simple colouring, Multi-colouring, Advanced colouring and Super colouring.

Simple colouring is the 'Solve by colours' as explained here. It is equivalent to 2 of the 4 types of turbot fish or turbot chain.

Multi-colouring is equivalent to 2 of the 4 types types of turbot fish or turbot chain (fishy cycle). It is same as the x-cycle.

Advanced colouring or Super colouring is the same as the 3D-medusa (at least the concept is the same).

Your 3D-medusa should be able to pick up the 2 turbot fish deductions. They are just x-cycles.

I'm not sure what makes this puzzle the "third hardest." Plenty of the top95 puzzles require what I call "Proof++" whcih means you have to go all the way through the next cycle of subset elimination or at least locked candidates to progress. That to me sounds WAY more difficult.

This puzzle (also known as the Nick70's toughest) used to be the toughest in this forum some time ago. It was then overtaken by 2 others. I am sure there are other hard ones as well.

[ronk]

Multi-colouring is equivalent to 2 of the 4 types types of turbot fish or turbot chain (fishy cycle). It is same as the x-cycle.

By your definition then, I assume multi-colouring includes the following example (candidate 4 from #438 of the top870).

Code: Select all

. . -|. * -|. * *
. c .|. * .|. * .
. . a|. . A|. . .
-----+-----+-----
* . *|. . .|. * *
* . *|. . .|. . *
. . .|. . .|. . .
-----+-----+-----
b . .|. . B|. . .
. . .|. . .|. . .
- C .|. b .|. . .

Using the language of exclusions (a!c meaning a excludes c):
 since a!c and C!b, then a!b ... eliminating candidates that "see" A and B
 since B!A and a!c, then B!c ... eliminating candidates that "see" b and C
 since A!B and b!C, then A!C ... eliminating candidates that "see" a and c

For this example, the eliminations ('-') are r1c6, r9c1, and r3c1, respectively. See prior description by Lummox JR.

With Medusa limited to "strong" chain analysis, I don't think SA is functioning equivalent to simple coloring ... as I recall reading somewhere on your site.

I'm sorry if I somewhere said "strong 3D Medusa" meant coloring. I'm sure I meant "X cycles".

My mistake, my recollection was apparently incorrect.

[Jeff]

By your definition then, I assume multi-colouring includes the following example................

Yes, the example shown is a continuous chain in multi-colouring. The name 'complete simple colouring' being used by Lummox JR is seldom mentioned in this forum. In this forum, simple colouring covers chains with all bilocational conjugate links.

[Bob Hanson]

Hope this is helpful, Bob. There are 4 types of colouring that have been
described by different people in this forum, namely Simple colouring,
Multi-colouring, Advanced colouring and Super colouring.

Simple colouring is the 'Solve by colours' as explained here.
It is equivalent to 2 of the 4 types of turbot fish or turbot chain.

Yes, that's helpful. When I read:

"Whenever two cells in a conjugate chain have the same color and also
share the same group, that color must be the 'false' color since each group
can only have one of any value."

I see the building of "strong X-chains"

and

"Also, whenever a candidate outside the chain relates by column, row or
3x3 box to two alternately colored cells in a conjugate chain, that
'non-chain' candidate can be excluded."

Same thing there. This is exactly what Sudoku Assistant finds
when the "strong" and the "X cycles only" options are selected.
So then "simple coloring" is "strong Medusa, X cycles only"

Multi-colouring is equivalent to 2 of the 4 types types of turbot fish or turbot chain (fishy cycle). It is same as the x-cycle.

OK, I was pretty sure that was what that was, where you stick with
a single candidate, right? Anyway, I'm betting this is the same as the
"strong+weak Medusa, X cycles only" option.

Advanced colouring or Super colouring is the same as the
3D-medusa (at least the concept is the same). Your 3D-medusa should be
able to pick up the 2 turbot fish deductions. They are just x-cycles.

If they only involve one candidate, then they are still "strong+weak
Medusa, X cycles only." If they cross over to more candidates, the way
I think these techniques do, then they are full 3D Medusa.

In any case, the configuration you introduced is arrived at by
"strong+weak Medusa, X cycles only," I think.

[Bob Hanson]

OK, sorry about diverting this thread from the intended direction. Here's how
far Sudoku Assistant gets without trial and error:

starting with

Code: Select all

 *-----------------------------------------------------------------------------*
 | 56      56      2       | 38      9       348     | 1       348     7       |
 | 179     3       8       | 6       2457    12      | 245     59      259     |
 | 4       179     17      | 123578  2578    1238    | 2568    35689   235689  |
 |-------------------------+-------------------------+-------------------------|
 | 12367   12678   1347    | 39      2678    5       | 2468    16789   12689   |
 | 2567    245678  9       | 278     1       268     | 3       45678   2568    |
 | 123567  125678  1357    | 4       2678    39      | 2568    156789  125689  |
 |-------------------------+-------------------------+-------------------------|
 | 123579  12579   1357    | 12589   2568    12689   | 68      368     4       |
 | 135     15      1345    | 158     4568    7       | 9       2       368     |
 | 8       249     6       | 29      3       249     | 7       15      15      |
 *-----------------------------------------------------------------------------*


...without almost-locked sets (includes multicoloring, I think!):

Code: Select all

   |---c1---|---c2---|---c3--||---c4--|---c5--|---c6--||---c7--|---c8---|---c9---
---------------------------------------------------------------------------------
r1 |     56 |     56 |     2 ||    38 |     9 |    34 ||     1 |     48 |      7
---+--------+--------+-------||-------+-------+-------||-------+--------+--------
r2 |    179 |      3 |     8 ||     6 |  2457 |    12 ||   245 |     59 |    259
---+--------+--------+-------||-------+-------+-------||-------+--------+--------
r3 |      4 |    179 |    17 || 12578 |  2578 |   128 ||  2568 |  35689 |  23568
=============================||=======================||=========================
r4 |   1236 |  12678 |    47 ||    39 |  2678 |     5 ||   246 |  16789 |  12689
---+--------+--------+-------||-------+-------+-------||-------+--------+--------
r5 |    256 | 245678 |     9 ||   278 |     1 |   268 ||     3 |  45678 |    258
---+--------+--------+-------||-------+-------+-------||-------+--------+--------
r6 | 123567 | 125678 |  1357 ||     4 |  2678 |    39 ||  2568 | 156789 | 125689
=============================||=======================||=========================
r7 |  12579 |  12579 |  1357 ||   125 |  2568 |  1268 ||    68 |    368 |      4
---+--------+--------+-------||-------+-------+-------||-------+--------+--------
r8 |    135 |     15 |  1345 ||   158 |  4568 |     7 ||     9 |      2 |    368
---+--------+--------+-------||-------+-------+-------||-------+--------+--------
r9 |      8 |     24 |     6 ||    29 |     3 |    49 ||     7 |     15 |     15
---------------------------------------------------------------------------------


...and with almost-locked set analysis:

Code: Select all


562|893|147
738|641|592
491|752|683
---+---+---
287|365|419
649|218|375
153|479|268
---+---+---
975|126|834
314|587|926
826|934|751



[Jeff]

Advanced colouring or Super colouring is the same as the
3D-medusa (at least the concept is the same). Your 3D-medusa should be
able to pick up the 2 turbot fish deductions. They are just x-cycles.

If they only involve one candidate, then they are still "strong+weak
Medusa, X cycles only." If they cross over to more candidates, the way
I think these techniques do, then they are full 3D Medusa.

In any case, the configuration you introduced is arrived at by
"strong+weak Medusa, X cycles only," I think.

Advanced colouring involves all 9 digits. Refer this example by Lummox JR. Do I understand you correctly?

[Jeff]

...without almost-locked sets (includes multicoloring, I think!)......:

You sound unsure about the 2 turbot fish eliminations. I think your 3D-medusa would have picked them up. My understanding is that the deductions from 3D-medusa are same as those from advanced colouring and simple nice loops of bilocation/bivalue plot. These deductions are double implication chains including turbot fish or x-cycle.

[Jeff]

at least two logical solutions have been found

There is only one solution, so I guess you mean at last two ways to get there.

Two? There must be at least 20 along these lines:

Thanks for pointing this out, Mac. I should have written 'logical-solution' as a hyphenated word.