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Al Escargot - Hardest Sudoku Ever
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cgordon



Joined: 04 May 2007
Posts: 769
Location: ontario, canada

PostPosted: Thu Aug 23, 2007 9:45 pm    Post subject: Al Escargot - Hardest Sudoku Ever Reply with quote

I came across a 2006 article in USA Today referring to a Finnish mathematician who claimed he had created the hardest Sudoku ever (named Al Escargot - the puzzle not the Finn). I downloaded it from this blog site:
http://photos1.blogger.com/photoInclude/blogger/3235/1499/1600/Al%20escargot.jpg

I started it but it's brutal - after a few moves I got totally stuck - though I will persevere. I hope it's a genuinely solvable and one solution problem.

Try it out. But be afraid !!
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Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA

PostPosted: Thu Aug 23, 2007 10:33 pm    Post subject: Reply with quote

Well Craig, a few moves is more than I could do. I'll be the first to embarrass myself and say that after writing in the pencil marks I couldn't eliminate one candidate. Embarassed
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Asellus



Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA

PostPosted: Fri Aug 24, 2007 4:49 am    Post subject: Reply with quote

There is a finned swordfish on 9 that eliminates four <9>s in B8. After that, I am, so far, stuck.
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cgordon



Joined: 04 May 2007
Posts: 769
Location: ontario, canada

PostPosted: Sat Aug 25, 2007 9:20 pm    Post subject: Reply with quote

I looked at all the popular techniques discussed on this site and couldn't get past a few preliminary steps (though there might be some advanced techniques I've heard mentioned e.g. Sue Coq). Anyway I did finally solve the thing by guesswork - and yes, there is a unique solution.

But I had hoped that all puzzles were solvable by existing techniques, without guesswork. Maybe they still are.
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Ruud



Joined: 18 Jan 2006
Posts: 31

PostPosted: Sat Aug 25, 2007 11:21 pm    Post subject: Reply with quote

There's more info on this puzzle at the Player's Forum.

It is no longer considered the hardest Sudoku ever. Here's a list of the hardest puzzles. Don't try these at home.
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Johan



Joined: 25 Jun 2007
Posts: 206
Location: Bornem Belgium

PostPosted: Sat Aug 25, 2007 11:26 pm    Post subject: Reply with quote

cg,

If this puzzle has a unique solution there must be some logical solving technique,(probably somewhere hidden and yet to be discovered?), for cracking this tough nut(which is an understatement).

In my opinion anyone who can solve this one with only logical solving techniques, has find the ultimate solution path for every SUDOKU, even the hardest one ever designed, like this one.
Chapeau for the one who can solve this without T&E.


Johan
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keith



Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA

PostPosted: Sun Aug 26, 2007 2:59 am    Post subject: Reply with quote

Johan,

You may want to look at the Sudoku Programmer's Forum:

http://www.setbb.com/phpbb/?mforum=sudoku

As I recall, you can determine that a particular puzzle does / does not have a unique solution without "solving" it in human terms.

As I understand it, there are Sudokus which cannot be solved other than by trial-and-error. The nice term for this is "exhaustive search": Try every possibility.

At the risk of irritating the computer scientists who read this: Exhaustive search is how you find the next Mersenne Prime, or prove the four-colour map theorem.

Or, for readers of this forum: The only way to prove a puzzle is valid (has a unique solution) is to solve your puzzle using only methods blessed by Glassman.

Best wishes,

Keith
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Mogulmeister



Joined: 03 May 2007
Posts: 1151

PostPosted: Sun Aug 26, 2007 8:02 pm    Post subject: Reply with quote

Indeed - and most computer solvers make use of this algorithm although you need the brute force capabilities of a computer to do it.
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cgordon



Joined: 04 May 2007
Posts: 769
Location: ontario, canada

PostPosted: Sun Aug 26, 2007 9:12 pm    Post subject: Reply with quote

Quote:
...there must be some logical solving technique,(probably somewhere hidden and yet to be discovered


I'm with you Johan. I have faith that one day someone will come along with an exquisitely simple solution that will not only make all other solutions redundant - it will make Sudokus themselves become too simple to bother with.

I'm working on it .. and when I find it - I'll miss you guys.
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Mogulmeister



Joined: 03 May 2007
Posts: 1151

PostPosted: Mon Aug 27, 2007 8:52 am    Post subject: Reply with quote

If you look in the Sudoku programmer's forums you will see some conversation with Arto Inkala himself the creator of AI Escargot.
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Swampy



Joined: 27 Mar 2008
Posts: 1

PostPosted: Thu Mar 27, 2008 3:10 pm    Post subject: Completed puzzle Reply with quote

I found this puzzle about 15min's ago

Have finished it and can confirm a logical solution
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ravel



Joined: 21 Apr 2006
Posts: 536

PostPosted: Thu Mar 27, 2008 5:12 pm    Post subject: Reply with quote

The solutions i have seen so far for puzzles of this difficulty took me more than an hour to read and verify them (and it was more work than fun).

So what did you do in these 15 minutes ?
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nataraj



Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria

PostPosted: Fri Mar 28, 2008 9:44 pm    Post subject: Re: Completed puzzle Reply with quote

Swampy wrote:
I found this puzzle about 15min's ago

Have finished it and can confirm a logical solution


There is always a "logical solution":

"It is logical that this must be the solution, because otherwise the sudoku rules would have been violated".

Hm. Can't dispute the logic. Doesn't feel right, though.

Can you do better than that?
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waleeed12



Joined: 26 Mar 2016
Posts: 2

PostPosted: Sat Mar 26, 2016 8:49 am    Post subject: Reply with quote

this site and couldn't get past a few preliminary steps (though there might be some advanced techniques I've heard mentioned e.g. Sue Coq). Anyway I did finally solve the thing by guesswork - and yes, there is a unique solution.




waleeed
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dongrave



Joined: 06 Mar 2014
Posts: 563

PostPosted: Sun Mar 27, 2016 3:38 am    Post subject: Reply with quote

The link to the hardest Sudoku puzzle ever seems to be broken for me but luckily Gordon mentioned it by name so I was able to find it. I'm guessing that this is the puzzle that everyone is referring to here.
Code:

 +-------+-------+-------+
 | 1 . . | . . 7 | . 9 . |
 | . 3 . | . 2 . | . . 8 |
 | . . 9 | 6 . . | 5 . . |
 +-------+-------+-------+
 | . . 5 | 3 . . | 9 . . |
 | . 1 . | . 8 . | . . 2 |
 | 6 . . | . . 4 | . . . |
 +-------+-------+-------+
 | 3 . . | . . . | . 1 . |
 | . 4 . | . . . | . . 7 |
 | . . 7 | . . . | 3 . . |
 +-------+-------+-------+

If this is the right puzzle, here's the grid that I had after basics.
Code:

 +-----------------+---------------------+-----------------+
 | 1    2568  2468 | 458    345   7      | 246  9     346  |
 | 457  3     46   | 1459   2     159    | 1467 467   8    |
 | 2478 278   9    | 6      134   138    | 5    2347  134  |
 +-----------------+---------------------+-----------------+
 | 2478 278   5    | 3      167   126    | 9    4678  146  |
 | 479  1     34   | 579    8     569    | 467  34567 2    |
 | 6    2789  238  | 12579  1579  4      | 178  3578  135  |
 +-----------------+---------------------+-----------------+
 | 3    25689 268  | 245789 45679 25689  | 2468 1     4569 |
 | 2589 4     1    | 2589   3569  235689 | 268  2568  7    |
 | 2589 25689 7    | 124589 14569 125689 | 3    24568 4569 |
 +-----------------+---------------------+-----------------+

That's it? I thought they said it was 'hard'? This is the toughest they've got? (snicker.) I'm not going to even bother listing my solution here. Come on, they can't come up with anything tougher than this? (snort.)
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dongrave



Joined: 06 Mar 2014
Posts: 563

PostPosted: Sun Mar 27, 2016 2:36 pm    Post subject: Reply with quote

Of course I was being sarcastic in my last post. I wasn't able to make ANY progress at all after the basics so even though I hate to, I'm going to have to use a computer to tell me if this thing can be solved using only moves that are commonly used on this site (i.e. basics, wings, fish moves, chains, etc.). And while I'm at it, Keith has inspired me to find the 50th Mersenne prime! (I expect it to only contain somewhere around 30 million digits.)
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dongrave



Joined: 06 Mar 2014
Posts: 563

PostPosted: Sun Mar 27, 2016 8:36 pm    Post subject: Reply with quote

Well, apparently according to the computer it's possible to begin solving this puzzle by showing that r2c6=9. Now I'm not saying that it's easy - but at least it appears to be possible! I didn't check it for correctness (since that would take me the rest of my life) but it was able to show after a couple dozen advanced chains that r2c6 could not be 1 or 5 so it must be 9.

Then after it determined that r2c6=9, it's apparently possible (after another dozen chains) to eliminate the 4 from r5c3 so it must be 3. And then another dozen chains later it showed that r2c1=5. THEN another dozen chains later it showed that r6c3=8 and after that, it ONLY required a few chains to prove that r7c3=2. It was only at this point that it was finally able to solve it - but NOT by using just basics; it STILL required more advanced chains! This puzzle is absolutely insane!!!

Strangely enough, this was the ONLY solution that it found (with my help) using the common moves used on this site - and there were a number of times that it could have used an advanced move other than a chain (like the swordfish that Asellus mentioned and several wings) but I had it focus on chains. If anyone finds anything else (either with or without the use of a computer), I'd love to hear about it! Thanks, Don.
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keith



Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA

PostPosted: Sat Apr 02, 2016 7:56 am    Post subject: Reply with quote

Zombie thread!

I believe there are puzzles much more difficult for a human solver than this one.

I may still have the poster from Cray Research in my attic that has the 29th Mersenne Prime. That filled a 2x4 foot poster with digits in a fairly small font.

Keith
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dongrave



Joined: 06 Mar 2014
Posts: 563

PostPosted: Sat Apr 02, 2016 6:34 pm    Post subject: Reply with quote

What's it doing in your attic? Why isn't it on your wall? You know Keith - it'll probably take you close to 1000 posters that size to print out the next one when they find it!

Hey! By the way, when I searched the internet looking for 'Al Escargot', I saw that the guy that created it followed it up with a new one that he says is much more difficult - so now apparently they're referring to this one as the 'hardest Sudoku in the world'. Here it is:
Code:

 +-------+-------+-------+
 | 8 . . | . . . | . . . |
 | . . 3 | 6 . . | . . . |
 | . 7 . | . 9 . | 2 . . |
 +-------+-------+-------+
 | . 5 . | . . 7 | . . . |
 | . . . | . 4 5 | 7 . . |
 | . . . | 1 . . | . 3 . |
 +-------+-------+-------+
 | . . 1 | . . . | . 6 8 |
 | . . 8 | 5 . . | . 1 . |
 | . 9 . | . . . | 4 . . |
 +-------+-------+-------+

Of course I'd have NO chance of making ANY progress whatsoever so I used my computer tell me if it could be solved using 'human methods' and surprisingly enough, it can! If anyone wants to see how it's possible, let me know. I'd be glad to post it (but only in general terms of course; the entire solution would take forever). Someone said on another site that he didn't believe that this puzzle could be solved by using human methods so I might post it there.

Another interesting thing that I noticed about this puzzle is that it's possible to solve by using chains if you assume the right first value for either of 2 different cells - but since that's not a 'human method', I disredarded them.
It's perfectly okay to assume a wrong value and then use chains to arrive at a contradiction in order to eliminate it - but assuming a right value and then solving the puzzle is not (at least in my mind).

I guess the 'hardest' possible Sudoku in the world would have to be one that could not be solved by using ANY methods used by humans and could ONLY be solved by pure trial and error - and would include so many branches that only a computer could solve it. I'm sure eventually someone (probably this same Finnish mathematician) will create a puzzle where you'll only be able to proceed by assuming a candidate of any given cell and then it would branch out to a number of possibilities which would then branch out again - and then again, etc. until you finally arrive at all of the bottom branches (except one) leading to contradictions.

Anyway, I've rambled on long enough.
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waleeed12



Joined: 26 Mar 2016
Posts: 2

PostPosted: Wed Apr 06, 2016 9:36 am    Post subject: Nice Reply with quote

There is a finned swordfish on 9 that eliminates four <9>s in B8. After that, I am, so far, stuck.





== Solitaire ==
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