Puzzle 4

Tafl puzzles
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crust
Posts: 127
Joined: Sat Mar 21, 2015 9:29 am

Re: Hnefatafl puzzle

Post by crust » Sun Mar 04, 2012 1:13 am

Another puzzle. White to move (fetlar rules).
hnefatafl puzzle - feb 2012.JPG
What will white's next four moves be?
Black's next three moves will be forced, but on the fourth one, there is a choice - what is the best fourth move for black, to prevent disaster?

Hagbard
Posts: 407
Joined: Sat Mar 14, 2015 6:07 pm

Re: Hnefatafl puzzle

Post by Hagbard » Mon Mar 05, 2012 11:40 am

Evans wrote:

Greetings all.
What a way to enter into this forum, with an incredibly difficult and complex puzzle. There are many continuations coming off of every move, and it should also be noted that I use the term Hn before notation to show whether the Hnefi (or King if you want) has been moved. The position is undesirable for Black, and he can only hope for a draw. Of course, if this puzzle was under the Copenhagen rules, it would also be possible for White to win using an edge fort, but that is both not what this puzzle is about, now would it be all that easy. But anyway, this is my idea;

Hn— c1- c4 (threatens to take the b2 piece and win)
d1-c1 (there is another continuation (b1-c1), but this move would actually be disastrous later, after the four moves are made and White goes around the board attacking the corners, meaning that the atual move is surprisingly integral)
Hn— c4-b4 (takes a piece but also threatens to take the Hnefi to the other side of the board where it is an unstoppable win for White)
c5-b5 (blocks this threat, and though c6-b6 was possible as well, this would lead to this piece being captured and is a much weaker option, whereas c5-b5 forms a powerful diagonal)
Hn— b4-b3 (due to the well placed white piece on b2, if the Hnefi moves into a3, he has won)
a4-a3 (this is the only possible move that can block the Hnefi's threat)
Hn— b3-j3 (this move clears away from the corner on which the previous moves were made and forms a powerful threat)
This is my theory for the continuation in which White is to play and plays four moves, the first three being forced but the fourth being a choice.

Now, it becomes interesting. Black has a few options. He could use his j11 piece to defend attack on the other side of the board by bringing it to j8, though now the corner being attacked is going to mean a win for White. He could make other moves that defend other corners, but allow the King to get to the k1 corner by capturing, as capturing with h1-j1 allows the King to threaten coming to j2 with no refutation, which threatens both coming to k2 and winning and moving j1-i1 and winning, which cannot be blocked at the same time. There are now, then, a few possible moves; i8-i1, and those moves that bring a piece to the 2nd Rank. c6-c2 (or c1-c2) is not an option as it can be captured. So the only two, then, that satisfactorily bring a Black piece to the 2nd Rank are e11-e2 or i8-i2. Both of these moves enable a piece to slide into the j2 square after the capture of h1-j1, blocking the Hnefi from going there and claiming victory. Of course, though, once the Black piece moves to j2, then White can move j1-i1 and has achieved essentially the same position with a Black piece gone, and then has won with the continuation: Black: j2-j1, i1-i3, c1-i1, Hn—j3-j2, k3-k2, i3-k3 and White has the win, as again no piece can come to the 2nd Rank after i1-i3. But what about blocking the capture in the first place? The move for Black is... i8-i1. This blocks off the corner, but leaves the other side of the board a little open, so it goes against some preconceptions. But, if Black makes more brilliant moves, then he can stop the threat.
The Hnefi will probably now come to j9 or j10, and right just here we will look at Hn—j3-j10, which is a powerful move but looks a bit drawish, which is what Black is aiming for anyway,as it is impossible to win with the material he already has. j10 forces k7-k10, which not even White's h8-h9 can block due to Black's k3-k9, to which the King cannot quip j10-j3 as this, again, is drawish due to Black's k9-k3, forcing a draw by repetition. After this, though, White could capture with h9-k9, but Black can counter with j11-j9, stopping the Hnefi coming to j9. This is a bit depressing for White, who was playing aggressively but whose position is now, though far from desirable for Black, is drawish.
The other option is Hn—j3-j9, coming to the open 9th rank. The best move here is the one that is not immediate. Black should then play b5-b9, blocking Hn— j9-a9, which is certain defeat for Black (he can delay it for a while but it is absolutely certain a win for White), if Black plays, say, k7-k9. So, now, if Black does play b5-b9, then White probably play Hn— j9-k9, which can be stopped easily enough by b10-k10, and now Black has both corners under reasonable control. Theoretically, White can bring the Hnefi to the opposite corner (a11 area), but Black can respond to all threats, and if the Hnefi then tries to come to c2 to have a go at the original (a1 area) corner, it has to move the b2 piece, meaning that Black can use b1-b2 to block off the corner, and this is why the original d1-c1 was necessary, over b1-c1.

It is almost comical how the King has gone around the board like a windmill attacking all the corners but being foiled every time. I think I have got the solution, but if something is wrong with my logic please point it out.

crust
Posts: 127
Joined: Sat Mar 21, 2015 9:29 am

Re: Hnefatafl puzzle

Post by crust » Thu Mar 08, 2012 12:09 pm

Thanks Evans for a very carefully considered and detailed response! I hope you enjoyed the puzzle. Your reasoning is very sound. Sorry for my delay in response - your post needed a lot of consideration! Essentially, you've got it, but I got there quicker, and maybe you missed a winning move for white. You brilliantly spotted that I wanted to get the king to go around the board like a windmill, while the hapless black Don Quixotes attempted to block his path. Actually I was aiming to get him right round to the a11 corner after attacking all three of the other corners, but in fact white actually wins at the third (k11) corner.
Evans wrote:Of course, though, once the Black piece moves to j2, then White can move j1-i1 and has achieved essentially the same position with a Black piece gone
- perfect example of the "guillotine" in action - however many pieces black puts on the second rank and feeds into the guillotine on j2, the executioner piece now on h1 will behead them by moving to j1, then return to i1 (equivalent to raising the blade of the guillotine ready for the next victim!).

This is a brilliant winning position for white (usually) but can sometimes be beaten by threatening the king directly and thus forcing him to move, which buys enough tempo to close off the corner or kill off the executioner (or do both in the same move). This puzzle was designed to eliminate that possibility.
Evans wrote:But what about blocking the capture in the first place? The move for Black is... i8-i1. This blocks off the corner, but leaves the other side of the board a little open, so it goes against some preconceptions. But, if Black makes more brilliant moves, then he can stop the threat.
So you're right, the only way the guillotine can be beaten after the king moves to j3 is with i8 - i1, but that itself opens up another can of worms...
Evans wrote:The Hnefi will probably now come to j9 or j10, and right just here we will look at Hn—j3-j10, which is a powerful move but looks a bit drawish, which is what Black is aiming for anyway,as it is impossible to win with the material he already has. j10 forces k7-k10,
...I agree that j3 - j9 looks drawish, but the king's move to j10 looks more winnish than drawish to me, because after j3 - j10, black is forced to move k7 - k10, and white's response h8 - k8 is unstoppable. This move is now possible because black had to move i8 away to prevent the guillotine at the k1 corner.

Here's how I would do it: c1 - c3...d1 - c1
hnefatafl puzzle - feb 2012.solution1.JPG
c3 - j3...i8 - i1
hnefatafl puzzle - feb 2012.solution2.JPG
j3 - j10...k7 - k10
hnefatafl puzzle - feb 2012.solution3.JPG
h8 - k8... !!! (see next post as I'm not allowed more than 3 attachments per post)

crust
Posts: 127
Joined: Sat Mar 21, 2015 9:29 am

Re: Hnefatafl puzzle

Post by crust » Thu Mar 08, 2012 12:15 pm

The coup-de-grace. I was lying - there is no fourth move for black which can prevent disaster - the only choice is whether to resign like a gentleman or go berserk and kick the table over :D

Adam
Posts: 115
Joined: Fri Mar 20, 2015 1:28 pm

Re: Hnefatafl puzzle

Post by Adam » Sat Mar 10, 2012 2:26 pm

Very entertaining, though having made such a fun puzzle, might I ask that the solution not be so quickly revealed next time if someone posts an incomplete or wrong answer? Its fun to try again or see if others can solve it too? Perhaps you could post the puzzle with a deadline at which point the solution is revealed?

crust
Posts: 127
Joined: Sat Mar 21, 2015 9:29 am

Re: Hnefatafl puzzle

Post by crust » Sat Mar 10, 2012 2:45 pm

ok, but I didn't want anyone wasting too much time on it..! (and then complaining that it wasn't worth it). :?

Hagbard
Posts: 407
Joined: Sat Mar 14, 2015 6:07 pm

Re: Hnefatafl puzzle

Post by Hagbard » Sun Aug 04, 2013 4:25 pm

Chuck Ward wrote:

More!!! I want more....Its been far too long Master Crust.

crust
Posts: 127
Joined: Sat Mar 21, 2015 9:29 am

Re: Hnefatafl puzzle

Post by crust » Thu Aug 08, 2013 3:00 pm

Chuck Ward wrote:More!!! I want more
ok, I'll have a rummage round, see what comes out of my brain

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