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        Arimaa >> General Discussion >> Endgame Puzzle 4
        
(Message started by: jdb on Apr 1^st, 2011, 8:43am)

Title: Endgame Puzzle 4
Post by jdb on Apr 1^st, 2011, 8:43am

This puzzle is a hint for yesterday's difficult puzzle.

Gold to play and win

1w Rg2 Hg4
1b ed3 rh5

http://arimaa.com/arimaa/games/planGame.cgi

http://arimaa.com/arimaa/puzzles/show.cgi?p=p62

Title: Re: Endgame Puzzle 4
Post by robinz on Apr 1^st, 2011, 9:08am

This seems even harder than yesterday's (not that I solved yesterday's, at least not to my satisfaction, but I could at least find first moves that didn't instantly lose) - every move I have tried so far has allowed silver to win in quite simple fashion. I will keep trying though :)

Title: Re: Endgame Puzzle 4
Post by robinz on Apr 1^st, 2011, 9:49am

I think I may have it now, although I've not exhausted all of silver's possible defences. EDIT: I'm now fairly convinced it's the right solution, so I've removed a bit of information I gave about the first move.

Whether I'm right or not, this is a really interesting problem (as is the whole series) - I had never realised that positions with such little material could contain so much play. This reminds me of my (long ago) chess-playing days, where the endgame was always my favourite part :) It's just a shame that, unlike in chess, in arimaa there seems to be little practical relevance to knowing how to play in such a position (but I still definitely find arimaa a more interesting game than chess right now).

Title: Re: Endgame Puzzle 4
Post by ginrunner on Apr 1^st, 2011, 11:24am

I got both but I feel like this one is much harder for some reason.

Title: Re: Endgame Puzzle 4
Post by Hippo on Apr 1^st, 2011, 11:31am

Even for this parity :)
OK the same solution pushing rabbit to the corner ... confirming my solution was probably OK. :)

Title: Re: Endgame Puzzle 4
Post by robinz on Apr 1^st, 2011, 11:35am

Incidentally, one thing I really like about this problem is that all 3 different ways of winning come into play. Depending on how silver defends, gold can win either by goal or by elimination, while most of gold's incorrect first moves end up losing by immobilisation. (At least, that happened to most of my first few attempts.)

I also like the fact that, in the initial position, it looks so impossible for silver not to win - a massive material advantage and with a much further advanced rabbit. Amazing that gold can nonetheless win with careful play
:o

Title: Re: Endgame Puzzle 4
Post by robinz on Apr 1^st, 2011, 11:40am

on 04/01/11 at 11:31:50, Hippo wrote:

Even for this parity :)
OK the same solution pushing rabbit to the corner ... confirming my solution was probably OK. :)

Hmm, I haven't had to push the rabbit into a corner in my solution - I simply push it to H6 on the first move (and leave it there). Silver has to move his elephant to F5 or E6 to stop it being captured, but then when silver's elephant is tied up gold wins by moving his rabbit all the way to the a-file and then advancing it. Silver can push or pull the horse away before moving the elephant to the b file to stop the rabbit - thereby preventing gold from capturing silver's rabbit in one move - but gold still ends up capturing silver's rabbit before silver captures gold's. Or have I missed something?

Title: Re: Endgame Puzzle 4
Post by Hippo on Apr 1^st, 2011, 1:28pm

And what about:
1w Ra2 Ca5
1b ra6 ec5

That was position I was thinking about. But even here I am not sure that was needed ... the rabbit has goal in 3 turns and E has not enough steps to prevent both threats.

So what about:
1w Ra1 Ca5
1b ra6 ec5?
There the rabbit cannot goal at h8 on third turn ...

Oops, silver has enough time in both cases and pushing to the corner does not improve things. Actually ... ed7 pulling Cc7 would be at g6 in time and the capture at f3 would be earlier than in c6 so the push to the corner is losing move and rabbit have to start its run immediately.

Title: Re: Endgame Puzzle 4
Post by Fritzlein on Apr 2^nd, 2011, 9:22pm

Man, I am bad at these. I thought I had solved it with

2g Hg4n Hg5s rh5w Rg2n
2s ed3n ed4n ed5e ee5e
3g Rg3e Rh3n Rh4n

But I was wrong. So this is a bonus mini-puzzle: what did Fritz overlook?

Answer: 3s ef5s Hg4s ef4e eg4e.

Title: Re: Endgame Puzzle 4
Post by Hippo on Apr 3^rd, 2011, 2:12am

on 04/02/11 at 21:22:29, Fritzlein wrote:

Yes, it was the only way to stop the h5 rabbit :). (any parity quote #DEE7EF)

Title: Re: Endgame Puzzle 4
Post by mistre on Apr 4^th, 2011, 12:50pm

Got this one in about 15 min. Clever puzzle. Didn't help me with number 3 though. :'(