Fluid Drive - tarek's #1

Advanced methods and approaches for solving Sudoku puzzles

Fluid Drive - tarek's #1

Postby gurth » Sat Oct 28, 2006 7:33 am

Fluid Drive (Tarek's #1, SE 9.9)

Code: Select all
  6 . . . . 1 9 . .
  . 8 . . 3 . . . .
  . . 1 7 . . . . 2
  . . 2 . . . . . 7
  . 5 . . . . . 1 .
  4 . . . . . 3 . .
  3 . . . . 9 6 . .
  . . . . 4 . . 8 .
  . . 8 2 . . . . 5   Fluid Drive (tarek)


I've been swopping messages with tarek re above, so what follows is mostly just copying out stuff for you. I don't need to recompose it, it's good as it is. Here's an edited version of our messages.

_______________________
g to t, 19 Oct:

Tarek, it's now a thrilling moment for me, I have just solved the hardest puzzle in my life, your magnificent flagship Tarek's #1 (9.9).

A wonderful opportunity to learn skills in the sublimely fascinating method of Forcing Nets.

I don't know if you are interested to see my efforts, or if there is a thread for solutions to this puzzle. My policy in posting solutions is not to give my final, pruned version, but rather the full manuscript of all my false and true tries. The full history of my journey to the solution.

At the end, SS commented:"FINISHED. 410 hints required & 265 invalid moves."
In this first effort with #1, I ended up with 12 steps, having to throw out 8 tries along the way, of which 3 were repeated attempts to eliminate 2a2. only on the 4th attempt had enough wood been removed to allow successful elimination. Inside my nets, which sometimes contained sub-nets but not sub-sub-nets, I used no techniques outside SSTS. I used GMET once, to create a naked pair.

I've thought of a nice name for it, Fluid Drive. Do you know what a fluid drive is?
________________________________________________________
________________________________________________________

The Manuscript (Tarek's #1):

(1) SSTS

(2) [?3h4 tried and rejected][?3a9 rejected] ?4c2...??, -4c2.

(3) [?9c2 rejected] ?4g3...??, -4g3.

(4) [?4g9 rejected] ?2f6...(?3a8...??, -3a8), (?-3c2... ??, 3c2), ...??, -2f6.

(5) [?2a2 rejected (failed)] ?-27b1...(?6k6...??), 3k6,...(?7k1...??), 1k1...??, 27b1, -59b1. (Note GMET used here, resulting in elimination of 2 candidates).

(6) ?2h2...??, -2h2.

(7) [?2a2 still failing][?-159h1 failed].

(8) ?7h7...(?3a3...??), -3a3, 4a3...??, -7h7.

(9) ?2a2...(?1d1...??), -1d1...??, -2a2, SSTS placing first cells...

(10) ?1d1...??, -1d1.

(11) ?-7e1...??, 7e1, SSTS (several placements).

(12) ?8f4...??, 5f4, SSTS to end.
________________________________________________
________________________________________________
t to g, 19 Oct:

Thanx gurth,

I would be certainly interested to see the full solution.....

Fluid Drive....hmmmmmmm, it has a nice Flow to it. I probably need to look that up ... but it sounds like a hallucinogen to me.......
___________________
g to t, 20 Oct:

Thanks tarek!

The Fluid Drive was in the transmission on Chrysler stable of cars round about 1947 ... two whirling cups on spindles, facing each other, threw the fluid outwards by centrifugal force, impinging on radial fins in the cups. Your #1 looked a lot like it. Rather more prosaic than you imagined, I suppose, but most people won't know what it means anyway.

My "Manuscript" was actually my complete solution! Where you see "..." it simply means steps carried out under SSTS. Just as people solving difficult puzzles just say "singles" instead of listing those singles, so I just say "SSTS" instead of listing the steps under SSTS, as I figure anyone interested in those steps just has to use the SS program to verify those steps. And now I've just gone one further and replaced the repetitive "SSTS" with "..."

I hope you approve of this way of saving effort and space. The essential thing about nets is the order of the candidates chosen for examination. Any steps above SSTS level I would explain - sometimes I do distinguish between "singles", "locked candidates", "naked pairs", "Swordfish" and the like, but usually only to show that a Ruby or Garnet is present, and its size.
__________________
t to g, 20 Oct:

Interesting gurth.... I need to brush up on my mechanics...but a very accurate description it is.

I do agree that SSTS techniques in these ultra hard are sort of trivial but the general public used to do that up to subset level only..... but probably SSTS is another option to save space.....

The main thing is to show us the implication nets.
__________________
g to t, 25 Oct:

Funny your message of 20th only showed up today.

I do expect to raise some eyebrows with my style of presentation, but I couldn't care TOO much about that "general public" to whom I don't owe this puzzle of yours at all. The thing is this, I want to satisfy YOU in the first place with my solution. But you seem happy with these essentials...
__________________
t to g, 26 Oct:

Gurth, I am happy with any solution that has logic behind it. I am satisfied because it is another proof that the puzzle IS difficult.

I must say that, I myself wouldn't use your method to solve.....

The reason is that I think some players (& myself) would have more techniques to use before contradiction elimination. (which I do use).

The reason why people try to avoid contradiction elimination, is the issue of GUESSING & BRUTE FORCE. (you probably know about this as much as I do)....... Too much talk & too many controversies.

The good thing is that everybody can follow the solution if they have SS ......So go ahead......

tarek
____________________

In a final exchange of messages, tarek indicated he was happy with the name "Fluid Drive" for this puzzle and also commented:

"I'm sure there will be others who wll post their solutions (sometime) & it would be interesting to make comparisons."

Let's hope that "sometime" is sooner rather than later.
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Postby ravel » Sat Oct 28, 2006 2:35 pm

Hi Gurth,

nice to see a solution for this etraordinary puzzle. Please look again at the steps 4, 6 and 11, i could not folllow you there.

I tried to get Explainer ratings for your steps, when possible.

Code: Select all
*--------------------------------------------------------------------------------------*
 | 6        2347     3457     | 458      258      1        | 9        3457     348      |
 | 2579     8        4579     | 4569     3        2456     | 1457     4567     146      |
 | 59       349      1        | 7        5689    @4568     |#458      3456     2        |
 |----------------------------+----------------------------+----------------------------|
 | 189      1369     2        |-1345689 -15689   #34568    |@458      4569     7        |
 | 789      5        3679     |-34689   -6789    #24678    |@248      1        4689     |
 | 4        1679     679      |@15689   @1256789 @#25678   | 3        2569    #689      |
 |----------------------------+----------------------------+----------------------------|
 | 3        1247     457      | 158      1578     9        | 6        247      14       |
 | 12579    12679    5679     | 1356     4        3567     | 127      8        39       |
 | 179      14679    8        | 2        167      367      | 147      39       5        |
 *--------------------------------------------------------------------------------------*
At the beginning there is a nice grouped turbot fish, that eliminates 4 8's (but does not help much).

Now to your steps:
2. r3c2<>4 ER 9.5
3. r7c3<>4 ER 9.4
4. r6c6<>2 No SE chain for that. SS has 3 swordfishes, a quad and coloring, gets stuck again.
I dont understand here how you continue, this is the SS grid.
Code: Select all
*--------------------------------------------------------------------*
 | 6      37     3457   | 58     2      1      | 9      347    348    |
 | 2      8      479    | 469    3      456    | 145    467    146    |
 | 59     39     1      | 7      569    4568   | 458    346    2      |
 |----------------------+----------------------+----------------------|
 | 189    1369   2      | 13469  1569   3456   | 48     469    7      |
 | 78     5      369    | 3469   69     78     | 2      1      469    |
 | 4      1679   679    | 169    78     2      | 3      5      689    |
 |----------------------+----------------------+----------------------|
 | 3      14     57     | 58     78     9      | 6      2      14     |
 | 1579   2      69     | 136    4      3567   | 17     8      39     |
 | 179    469    8      | 2      16     367    | 147    39     5      |
 *--------------------------------------------------------------------*
With r3c2=3 SS gets locked again.
A possibiltity is to eliminate the 3's in box 3, r1c8 (with xy-wing), r1c9 and r3c8.

Anyway, a pretty complicated step, i would give it a rating (comparable to ER) of 40.
5. r2c1<>59 Again no SE chain, with 4 substeps (including xy-wing and coloring) my estimated rating is 46.5.

6. ?2h2: ??? i dont have a 2 in r8c2 ???

8. r8c7<>7 No SE chain, 2 substeps, rate it 39.
SS does not see r4c6<>3 with advanced coloring (3 strong links) here , but it again does not help much.

9. r1c2<>2 No ER chain, 2 substeps, lets say 24.

10. r4c1<>1 ER 9.4

11. r6c1<>7 ?? SS gets stuck, need another elimination in step 6 ?
This is my grid:
Code: Select all
 *-----------------------------------------------------------------------------*
 | 6       37      3457    | 458     2       1       | 9       3457    348     |
 | 2       8       4579    | 4569    3       456     | 17      4567    146     |
 | 59      39      1       | 7       5689    4568    | 458     3456    2       |
 |-------------------------+-------------------------+-------------------------|
 | 89      1369    2       | 134689  1689    3468    | 458     4569    7       |
 | 789     5       3679    | 34689   6789    2       | 48      1       4689    |
 | 4       1679    679     | 15689   156789  5678    | 3       2       689     |
 |-------------------------+-------------------------+-------------------------|
 | 3       2       57      | 158     1578    9       | 6       47      14      |
 | 1579    679     5679    | 135     4       357     | 2       8       39      |
 | 179     4       8       | 2       167     367     | 17      39      5       |
 *-----------------------------------------------------------------------------*

12. r6c4<>8 ER 9.2

So i have a sum of about 140.5+ ER step ratings, Thats a lot:)
ravel
 
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Postby ravel » Sat Oct 28, 2006 3:01 pm

This is one of my program's solutions with ER step rating:
r3c2<>4, 9.5
r7c3<>4, 9.4
r9c2<>1, 9.4
r1c9<>4, 9.4
r5c3<>9, 9.3
r5c6<>3, coloring
r6c5<>9, 9.4
r5c3<>7, 9.4
r4c4<>9, 9.4
r2c3<>5, 10.0
r8c1<>9, 10.4
r5c4<>3, 9.5
r3c8<>3, 9.5
r6c8<>6, 10.5
r9c2<>9, 9.4
r8c4<>3, 9.3
r1c8<>7, 9.4
r8c6<>3, 9.4
r1c4<>5, 9.1
r1c2<>2 9.2

Gives a total of 180.9
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re: Fluid Drive

Postby gurth » Mon Oct 30, 2006 9:18 am

re: Fluid Drive

Ravel, thank you for taking the trouble to check my solution.

If you use SS, you can easily verify the details given below, or alternatively, point out where I have gone wrong. Just follow the SS hints in the order given. I have put my presentation in the same order. You will then also be able to spot any typos easily, and get past them.

Let's clear up my step 4 first. Here are the details:
Grid at start of step 4:
Code: Select all
 
 *--------------------------------------------------------------------------------------*
 | 6        2347     3457     | 458      258      1        | 9        3457     348      |
 | 2579     8        4579     | 4569     3        2456     | 1457     4567     146      |
 | 59       39       1        | 7        5689     4568     | 458      3456     2        |
 |----------------------------+----------------------------+----------------------------|
 | 189      1369     2        | 1345689  15689    34568    | 458      4569     7        |
 | 789      5        3679     | 34689    6789     24678    | 248      1        4689     |
 | 4        1679     679      | 15689    1256789  25678    | 3        2569     689      |
 |----------------------------+----------------------------+----------------------------|
 | 3        1247     57       | 158      1578     9        | 6        247      14       |
 | 12579    12679    5679     | 1356     4        3567     | 127      8        39       |
 | 179      14679    8        | 2        167      367      | 147      39       5        |
 *--------------------------------------------------------------------------------------*


(4) ?2f6, 2a5, 2b1, 2e7, 2g8, 2h2, 4gk2, (here I expect the reader to make the consequent removals),(in this case -4a2), 7hk7, 8afg459 (I expect the reader to see that this is a swordfish and make consequent removals), 7ehk167, 3469e3459 (need I say that this means a quad), 1569cdek5, 78e6f5, 5afg348,

-1k2(MC)*, -5d7(MC)**, 5f8, 58ag4, 578g345, (?3a8, 7a2, 9k8, 3h9, 3c2, 7b8, 3e3, 3k6, 3d4, 16h4k5, 9df2, 178dek1, X-Wing 1dk15, XY-Wing 147g2k17: -4g9, 1g9, 4g2, 7h7, 5h6, 8g4, 5a4, 4a3, 8a9, 9b3, 5c1, 4c7, 6b9 and 6c8 ?? ) -3a8,

(?-3c2, 9c2, 5c1, 6c5, 9e5, 1k5, 5d5, 9b4, 5b7, 4b6, 7b3, 3a2, 4a3, 7a8, 8a9, 5a4, 6b8, 1b9, 8c6, 4c7, 3c8, 8d7, 7e6, 8e1, 8f5, 5g3, 8g4, 7g5, 4g9, 6e9, 3e3, 4e4, 9f9, 4d8, 6f3, 1d2 and 1f2 ??) 3c2, 7a2, 4a8, 5a3, 8a4, 3a9, 9c1,

4b3, 6c8, 7b8, 1b9, 5b7, 6b6, 9b4, 5c5, 4c6, 8c7, 4d7, 9d8, 6e9, 9e5, 3e3, 4e4, 8f9, 7f5, 8e6, 7e1, 7g3, 5g4, 8g5, 4g9, 1g2 and 1k1 ?? -2f6.

-that's it. Agree?

Footnotes: If you are using SS, you will follow the (MCs) * and **. If not, these "MCs" are too cryptic and need to be replaced as follows:
(1) Replace -1k2(MC) with (?1k2, 1d1, 1f4, no 1 box 7 ??)-1k2
(2) Replace -5d7 with (?5d7, 5a8, 5c1, 5g3, 5h6, no 5 box 2 ??)-5d7
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Postby ravel » Mon Oct 30, 2006 11:17 am

Thanks Gurth, for the elaborate answer to this point. Since i am not used to your notation i missed the '-' before 3c2 (thought you wanted to show that r3c2 cannot be 3 either in this situation).

The short the notation is, the easy it is to make some mistake following it (and only people having SS really can - under linux here i cannot do it at all). But this of course is also a problem with all other notations for very complex deductions.
So my wish for Christmas is still a good tool for parsing, writing and verifying sophisticated solutions:)
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Fluid Drive

Postby gurth » Tue Oct 31, 2006 10:36 am

Further Report to ravel on Fluid Drive:

In step 4, it occurs to me that you might have tested (?3c2.. instead of (?-3c2.. ( ravel, I have since seen your reply verifying this suspicion.)

Step 6: I should have used SSTS after establishing -2f6 in step 4. That would have eliminated the 2h2 and also 4a2. That is why I still had the 2 in my grid at step 6. It did not affect the subsequent course of the solution. The solution may be improved by adding ".." to the end of my step 4, and omitting step 6.

Step 11: Your grid agrees exactly with mine at the start of this step.
You wrote "11. r6c1<>7.." but I wrote "11. ?-7e1.." (different row). It looks like a typo on your part, since we have given 4f1. You just have to put
?-7e1 (which you did not do, as your grid still shows 789e1) and you reach ?? via SSTS including 4xColouring and 1xXY-Wing.

Any further queries will be gladly received.
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Postby tarek » Tue Oct 31, 2006 11:01 am

impressive gurth...... 11 steps.........

I'm wondering what would you do about FLUID DRIVE #2:D

tarek
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Fluid Drive #2

Postby gurth » Tue Oct 31, 2006 12:24 pm

Hi tarek: I'd definitely like to try it. Where is it, please?
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Postby RW » Tue Oct 31, 2006 1:37 pm

I suppose he was refering to this puzzle. Good luck!:D

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Postby tarek » Tue Oct 31, 2006 4:06 pm

what ArtoI has posted seems to beat all that has been posted before.........

I'll be posting some new Fluid Drives in the hardest thread[following the pattern above] to commemorate the nice name which gurth gave to it:D

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Fluid Drives

Postby gurth » Wed Nov 01, 2006 9:42 am

ArtoI's astounding creation I will keep for the future, meanwhile will await Fluid Drives or will respond to any requests for solutions to 9.9ers.
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Postby Finlip » Wed Nov 01, 2006 2:09 pm

I started reading this thread and thought I couldn't continue until I understand what SSTS and GMET mean.
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Postby ronk » Wed Nov 01, 2006 2:26 pm

Finlip wrote:I started reading this thread and thought I couldn't continue until I understand what SSTS and GMET mean.

With links to initial definitions:

SSTS <=> Simple Sudoku Technique Set
GMET <=> Gurth's Multiple Elimination Technique
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Postby Finlip » Wed Nov 01, 2006 2:35 pm

I guessed SSTS had to do with that program. Thanks.
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Postby daj95376 » Wed Nov 01, 2006 6:15 pm

Finlip, Below is the order in which Simple Sudoku applies its techniques. When someone refers to SSTS, they're referring to these techniques. When fish are being discussed, it's very likely that the minus (-) techniques are excluded. Note: Jellyfish is missing from this list!

Code: Select all
===== ===== ===== ===== Simple Sudoku

  Naked  Singles
  Hidden Singles
  Naked  Pairs
  Locked Candidates
  Naked  Triples
  Naked  Quads
  Hidden Pairs
- X-Wing
- Swordfish
- Colors
- Multi-Colors
  Hidden Triples
  XY-Wing
  Hidden Quads

From a personal standpoint, I wish that Naked Triples were before Locked Candidates and Hidden Triples/Quads were before X-Wing. That way, SSTS would more closely match my ordering.:D
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