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Jan 22, 1996, 3:00:00 AM1/22/96

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I discovered the other day that one can construct a seki involving an arbitrary

number of groups (>= 2), like the following (with 4 groups in the seki):

number of groups (>= 2), like the following (with 4 groups in the seki):

. . . . . . . . . . . . . .

. . . . . . . O O . . . . .

. . . . . . . O . O . . . .

. . . # # # # O O . O . . .

. . # . # O O # O O O . . .

. # . # # O . # # # O . . .

. # # # O O O # . # O . . .

. . . O # . # O O O # # # .

. . . O # # # . O # # . # .

. . . O O O # O O # . # . .

. . . O . O O # # # # . . .

. . . . O . O . . . . . . .

. . . . . O O . . . . . . .

. . . . . . . . . . . . . .

Along the lines of the "how many living groups" thread is the following

question: on a 19x19 board, what is the largest number of groups that

can be in seki at a time? (It's not hard to build a position, using

techniques like in the above, where every stone is part of a group in

seki and there are 48 of them.)

Really, this stuff will probably never happen in a real game of go, but

I got a kick out of realising that a proper definition of seki cannot

rely on the number of groups involved. Four-way seki is not so

unreasonable as it might appear, though. I think maybe there are

sensible invasions that could force such a beast into existance.

-- Ford

Jan 25, 1996, 3:00:00 AM1/25/96

to

Ford Prefect wrote:

> Along the lines of the "how many living groups" thread is the following

> question: on a 19x19 board, what is the largest number of groups that

> can be in seki at a time? (It's not hard to build a position, using

> techniques like in the above, where every stone is part of a group in

> seki and there are 48 of them.)

This is interesting stuff. A great deal of work in recreational

mathematics has concerned "chess tasks", problems based on the board and

rules of chess but unrelated to ordinary game play (e.g., How many queens

can be placed on a chess board such that none attacks the other). I do not

know how much similar work has been done on "go tasks", but I have heard

of very little.

Here's a task suggested by the whole-board ladder problems in _The

Treasure Chest Enigma_: On a board of a given size, what's the maximum

number of moves that can be required to capture a stone in a ladder?

-Rick Rubenstein

Feb 1, 1996, 3:00:00 AM2/1/96

to

Ford Prefect (s...@cse.unl.edu) wrote:

: I discovered the other day that one can construct a seki involving an arbitrary

: number of groups (>= 2), like the following (with 4 groups in the seki):

: I discovered the other day that one can construct a seki involving an arbitrary

: number of groups (>= 2), like the following (with 4 groups in the seki):

: . . . . . . . . . . . . . .

: . . . . . . . O O . . . . .

: . . . . . . . O . O . . . .

: . . . # # # # O O . O . . .

: . . # . # O O # O O O . . .

: . # . # # O . # # # O . . .

: . # # # O O O # . # O . . .

: . . . O # . # O O O # # # .

: . . . O # # # . O # # . # .

: . . . O O O # O O # . # . .

: . . . O . O O # # # # . . .

: . . . . O . O . . . . . . .

: . . . . . O O . . . . . . .

: . . . . . . . . . . . . . .

: Along the lines of the "how many living groups" thread is the following

: question: on a 19x19 board, what is the largest number of groups that

: can be in seki at a time? (It's not hard to build a position, using

: techniques like in the above, where every stone is part of a group in

: seki and there are 48 of them.)

: Really, this stuff will probably never happen in a real game of go, but

: I got a kick out of realising that a proper definition of seki cannot

: rely on the number of groups involved. Four-way seki is not so

: unreasonable as it might appear, though. I think maybe there are

: sensible invasions that could force such a beast into existance.

: -- Ford

Although I have never seen a four-way seki, I have had a game with a three

group seki. The outer two groups had one eye each, and the inner group

shared one liberty with each outer group. My sensei said at the time that

he had never seen one like it. Unfortunatly, I didn't record the game to

see how it developed.

David Carper

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