From: landman@hal.COM (Howard Landman)
Newsgroups: rec.games.go
Subject: Re: Funny problem
Date: 28 Dec 92 22:13:12 GMT
Organization: HaL Computer Systems, Inc.
NNTP-Posting-Host: bang.hal.com

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|. . . . . . . . . m . . . . . . . . .|
|. . . . . . . . . O j k l . . . . . .|
|. . . . . . # . . O h i # . . . . . .|
|. . . . . . # O . e f O # g . . . . .|
|. . . . . O O # # # # # O O d . . . .|
|. . . . . . # O O O O O # c . . . . .|
|. . . . . . # . . # a b # . . . . . .|
|. . . . . . # # # . # # # . . . . . .|
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I'm surprised no one has pointed out yet that this seems to be a variation
on the famous problem called "Iwami Jutaro's Prison Break", which appears
in one of the old English language Go books (Go Proverbs Illustrated?).

Since the problem is symmetric, we can restrict ourselves to only
considering moves on one side.  I have labelled these 'a' through 'm'
above.  To any other move, White simply answers at 'e' or 'f'.

The problem is symmetric.  Therefore, if there is a unique solution,
it must be on the center line.  The only move which has a prayer of
working *and* being unique is therefore 'm'.  But before looking at
that move, let's refute all the others.

a or b: W fills a liberty at e or f and wins the race.

c or g: W plays d

d: W turns at g.  If B nets, W has 3 libs and simply wins by playing f.
   If B tries to ladder, the ladder doesn't work, and eventually W gets
   at least 3 liberties.  (see below for further analysis)

e: W f

f: Gets complicated.  Almost works, but not quite.

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	|. . . . . . . . . . a . . . . . . . .|
	|. . . . . . . . . 9 6 7 . . . . . . .|
	|. . . . . . . . . O 5 4 8 . . . . . .|
	|. . . . . . # . . O 3 2 # . . . . . .|
	|. . . . . . # O . . 1 O # . . . . . .|
	|. . . . . O O # # # # # O O . . . . .|
	|. . . . . . # O O O O O # . . . . . .|
	|. . . . . . # . . # . . # . . . . . .|
	|. . . . . . # # # . # # # . . . . . .|
	|. . . . . . . . . . . . . . . . . . .|
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	 -------------------------------------

	|. . . . . . . . . . . . . . . . . . .|
	|. . . . . . . . . . O . . . . . . . .|
	|. . . . . . . . 6 # O # . . . . . . .|
	|. . . . . . . 4 5 O # O O . . . . . .|
	|. . . . . . # 2 3 O # O # . . . . . .|
	|. . . . . . # O 1 7 # O # . . . . . .|
	|. . . . . O O # # # # # O O . . . . .|
	|. . . . . . # O O O O O # . . . . . .|
	|. . . . . . # . . # . . # . . . . . .|
	|. . . . . . # # # . # # # . . . . . .|
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	 -------------------------------------

	|. . . . . . . . . . . . . . . . . . .|
	|. . . . . . . . . . O . . . . . . . .|
	|. . . . . . . . O # O # . . . . . . .|
	|. . . . . . . O # 8 # O O . . . . . .|
	|. . . . . . # O # . # O # . . . . . .|
	|. . . . . . # O # # # O # . . . . . .|
	|. . . . . O O # # # # # O O . . . . .|
	|. . . . . . # O O O O O # . . . . . .|
	|. . . . . . # . . # . . # . . . . . .|
	|. . . . . . # # # . # # # . . . . . .|
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	 -------------------------------------

	B is caught in a snap-back, and doesn't have time to double-atari.

h or i or j or k or l: W f

So, how can m possibly work?  Well, it doesn't!

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	|. . . . . . . . . . . . . . . . . . .|
	|. . . . . . . . 8 1 . . . . . . . . .|
	|. . . . . . . 6 7 O . . . . . . . . .|
	|. . . . . . # 4 5 O . . # . . . . . .|
	|. . . . . . # O 3 . 2 O # . . . . . .|
	|. . . . . O O # # # # # O O . . . . .|
	|. . . . . . # O O O O O # . . . . . .|
	|. . . . . . # . . # . . # . . . . . .|
	|. . . . . . # # # . # # # . . . . . .|
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	 -------------------------------------

This leads us to the conclusion that there is no solution!  But wait!
What about that failing ladder that I so casually dismissed?  Can B
gain by forcing, then escape?

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	|. . . . . . . . . O . . . . . . . . .|
	|. . . . . . # . . O . . # 3 5 . . . .|
	|. . . . . . # O . . . O # 2 4 6 . . .|
	|. . . . . O O # # # # # O O 1 . . . .|
	|. . . . . . # O O O O O # . . . . . .|
	|. . . . . . # . . # . . # . . . . . .|
	|. . . . . . # # # . # # # . . . . . .|
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	 -------------------------------------

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

Yes!  Perhaps we are getting close to the truth now.  Still, W has other
things to try, so this isn't the whole answer.

It is worth noting that even if W captures the 5 stones, he only has 1 eye.
But it seems difficult for B to completely surround the entire W group and
suffocate it. :-)
	Howard