5x5 puzzle

Discussion and analysis about certain positions.

5x5 puzzle

Postby Ed Gilbert on Sat Nov 19, 2005 8:00 am

I thought I'd try out the position publisher at the fmjd site by posting this position from the 5x5 database.

Black to move and win.

Image

-- Ed
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Re: 5x5 puzzle

Postby Ed Gilbert on Sun Nov 20, 2005 1:01 pm

I shouldn't really call this a puzzle because the solution is too many moves to visualize. Just take a guess at which move black must make to win. It's not the move I would make :-) I'll post the solution next weekend.

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Re: 5x5 puzzle

Postby matthewkooshad on Sun Nov 20, 2005 2:43 pm

This is not as easy as it looks! I believe 5-9 is a/the way to solve.
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Re: 5x5 puzzle

Postby Alex_Moiseyev on Mon Nov 21, 2005 1:11 am

matthewkooshad wrote:5-9


Agree ! The main idea of this position - bind in sigle corner, where one red King trapped two white Kings. Now, in all many moves ahead red should remain the bind and trade eventually other white Kings.

This position illustrates very well one major ending principle - keep Kings together, and try to separate your opponent Kings !
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Re: 5x5 puzzle

Postby MostFamousDane on Mon Nov 21, 2005 11:05 am

Hmm what about 19-23 to avoid white's 32-27 ?
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Re: 5x5 puzzle

Postby J_D_C_ on Mon Nov 21, 2005 11:08 am

I would most likely move 24-20 here, to keep white from playing 32-27, then I think 19-24 would be forced for red to keep any winning chances. It just appears to me that it would be more difficult to win after that.

I first thought 19-23, but I believe 24-20 will accomplish the same thing without giving white the center of the board. Thats about as far as i can see though :)
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Re: 5x5 puzzle

Postby Alex_Moiseyev on Mon Nov 21, 2005 11:20 am

MostFamousDane wrote:Hmm what about 19-23 to avoid white's 32-27 ?


Hi, Mr. J_D_C ! Welcome to forume :lol: Looking at your photo - I have a strange feelings that we met before on some tournament :idea: Is that correct or wrong assumption ?

19-23 is a good move to prevent 32-27, and I thought seriously about it. However ... after 5-9 32-27 red also can prevent white "join Kings" by playing 19-24. Now you can't play 27-23 because of 1-5, and 27-31 can be met by 24-27. If you returns back 27-32,red plays 9-14 etc

At that point, if both moves, 19-23 and 5-9 prevents 32-27, I prefer 5-9, because red Kings from different flanks are going to join now.

BTW, 19-23 also allows white to play 11-15 and then 3-8-12 etc

20-24 not a bad move, but white can try 3-8-12 and then 32-27. In my opinion 20-24 is wasting time. Red needs one more King at least on another flank. Remember ... "keep Kings together" principle ? Move 5-9 accomplish this mission.
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Re: 5x5 puzzle

Postby Ingo_Zachos on Mon Nov 21, 2005 12:00 pm

I liked 20-24 at first glance best.

Why? Because king 20 is the worst placed black piece.
The pieces on 1 and five control one double corner, so white has to be thrown out of the other double corner.
I still didn't know if the piece on 1 or 5 should attack the white pieces in the single corner, so I keep tham in place to remain maximum flexibility.

19-23 looks suspicious to me as it allows to get more space with 11-15 as Alex pointed out, so my "candidate moves" r:

But these r just heuristical solutuons, so I began to look for tactics.

So I came along the line 1-6, because I liked the position after 1.1-6 32-27, 2. 19-24 27-23, 3. 6-9 with a teribble threat imposed on White! and can't see any way to aviod loss, so 2. ... 27-31 is better, but 3. 24-27 gets a trade with practical chances ( Black activates 20 and controls both double corners!!), as the active white kings can't get to any double corner, and I think advancing down the diagonal 1 to 28 ("the A(ttack) diagonal")is better then advancing along 5- 32,

Do you think that my appoach cpuld work, Alex?
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Re: 5x5 puzzle

Postby Alex_Moiseyev on Mon Nov 21, 2005 12:11 pm

Hi, Ingo !

We all (except Ed Gilbert :lol: ) don't know the answer yet. At this point, if I can't do everything - I do something ! :idea: There is a principle I beleive - "joining King". 5-9 better approcah this mission and help red to join Kings. 5-9 also doesn't allow white to take any control on double corner at all.

Indeed, 20-24 also prevents 32-27, but on my opnion - still wasting time. After 20-24 3-8 5-9 8-12 you have to return back 24-20 to prevent 11-16 ... now, after 24-20 I play 32-27 19-24 27-32 ... and what next ??? I want to go now 12-16, and if you return back 19-24 - we have perpetuum draw.
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Re: 5x5 puzzle

Postby Ingo_Zachos on Mon Nov 21, 2005 12:45 pm

Alex, my main proposal was 1-6,
not 24-20 or 19-23, with the line
1. 1-6 32-27, 2. 19-24 27-23, 3. 6-9! , transposing into your line of 5-9 with the terrible 22-17 thread, and I see no defense...
So I thought 2.- 27-31 is forced, with 3. 24-27 31x24, 4. 20x27 as critical position , which looks better to me then the line with 1. 5-9 32-27, 2. 19-24 27-31, 3. 24-27 31x24, 4. 20x27 , for the advance on the A-Diagonal 1-28 looks more appealing to me then the advance along the 5-32 diagonal, which 1.5-9 achieves.

In both cases black kings work together and white kings in the single corners get cramped, the difference is where to place the single croner kings on 1 and 5. Either to advance along 5-32 first, keeping back the king on 1 or to advance 1-28, keeping back the king on 5.

So we have four candidates:

1. 5-9
2. 19-23
3. 20-24
4. 1-6.

Like u, I think 19-23 is bad because of 11-15, and 20-24 does not get the trade in the single corner, allowing white to play 32-28 -32 or to force black to "bind" more forces on this sigle corner, so the trade seems desirable, and I think this is why 20-24 must be regarded as inferior, so the choice is between 5-9 and 1-6, do u agree on that?
My preference is 1-6 , but I think we should investigate both 1-6 and 5-9 a little further, which I will do tomorrow.

Greetinx from Dortmund, Germany

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Re: 5x5 puzzle

Postby J_D_C_ on Mon Nov 21, 2005 2:07 pm

Hi Alex! Yes we have meet before at the tennessee tournaments, This is Jonathon Chappell;however, I think you may be confusing my post with MostFamousDane because I did not post a photo.

On 20-24, 8-3, 1-6, 8-12 why not 6-10? 11-16, 19-23, 16-20, 24-19. I don't think white could escape from this postion now. all 3 may be togeather, but are now stuck on the side. Red just needs to wiggle in for a couple trades.
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Re: 5x5 puzzle

Postby Alex_Moiseyev on Mon Nov 21, 2005 3:08 pm

Ingo_Zachos wrote:
So we have four candidates:

1. 5-9
2. 19-23
3. 20-24
4. 1-6.



Very true ! :lol: Finally we collected perhaps all possible moves ! Ed, I think it's a right time now to post first correct red move. If it is the only move to win, it will be also very interesting to see how white draw the game against all other replies posted here.

I also propose to post here not only first correct red move, but portion of 3-4 of them, otherwise it may take few years :evil: for us to find a true !

J_D_C_ wrote:I think you may be confusing my post with MostFamousDane because I did not post a photo.


Opps ! I seriously suspect now that this is Dennik Pawlek photo ! I didn't meet him before (very unfortunately), but saw his photo on Internet somewhere, and this confused me :cry:
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Re: 5x5 puzzle

Postby matthewkooshad on Mon Nov 21, 2005 6:00 pm

My first instinct was 20-24. Then I saw advancement of 11 possible. This is why I say this looks easier than it is! I may be wrong on this.
20-24, 32-28, #
I think is better to leave sq 31 open to white and try to restrict the two pieces in the mobile single corner. The goal of 20-24 is to seemingly place a hold on piece 32, which I don't see possible having the seesaw available in the mobile single corner.
MostFamousDane wrote:Hmm what about 19-23 to avoid white's 32-27 ?
I saw 5-9, 32-27, 19-24. I think the hold on the immobile single corner is just as important as restricting the pieces in the mobile single corner from moving out.
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Re: 5x5 puzzle

Postby Ingo_Zachos on Mon Nov 21, 2005 6:45 pm

Alex, this is NOT Dennis.
This is the Danish Dynymite, Sune Thrane.
U R indeed confused!
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Solution

Postby Ed Gilbert on Mon Nov 21, 2005 8:13 pm

> Ed, I think it's a right time now to post first correct red move.

Ok Alex, I think you are right. The only move that wins here is 1-6, all others allow white to draw. Congratulations to Ingo who correctly picked this move, and to all of you for being brave enough to try this very difficult position. This position is somewhat special, which I will explain in a moment.

About the other choices that looked plausible:
If 5-9, white can draw with either 32-27 or 3-7.
If 19-23, white can draw with either 3-7 or 11-15.
If 20-24, white can draw with 3-8.

This position is the 5th move from the beginning along the path of a very long sequence. The start position in this sequence is the 5x5 all kings position that requires the longest number of moves before a capture move occurs. If white puts up the best defense then black cannot force a capture until 102 moves have been played. Since this is the 5th move along the path, it is 97 moves from a capture. I picked this position to post because the first 4 moves were more obvious. The animated solution to this has been posted at my web page for about a year, but the link is not very prominent and easy to overlook.

Click here to view the animated solution to the win. http://pages.prodigy.net/eyg/Checkers/longest-10pc-allkings.html The intricate maneuvering that occurs in the first 102 moves of this win are really extraordinary.

The numbers in parentheses after each move are the 'moves to conversion', a conversion in this case being a capture move. Black obviously wants to drive the game toward a position with fewer pieces as quickly as possible, so the black moves with the shortest path to conversion are shown with a star. Only black moves that maintain the win are shown. For white, every move is a loss, but some moves lead more quickly to conversions than others. White wants to avoid conversions as long as possible, so the moves with the longest path to conversion are starred for white. The database only has conversion numbers for positions that are at least 10 moves from a conversion, so when you see a move with (?) instead of a number that means there are less than 10 moves to a conversion along that path. When the game gets to within 10 moves of a conversion, kingsrow does a quick search to find the correct moves to continue.

-- Ed
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