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Topic: Billiards Puzzle
Replies: 8   Last Post: Oct 3, 2004 4:23 AM

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Michael Mendelsohn

Posts: 43
Registered: 12/13/04
Re: Billiards Puzzle
Posted: Oct 1, 2004 11:04 AM
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Alan Sagan schrieb:
> poopdeville@gmail.com (Acid Pooh) wrote in message
> > Suppose you're racking up 15 billiard balls in one of the standard
> > configurations (I'm not going to try to typeset these, so just picture
> > an equilateral triangle instead of a right one):
> >
> > S
> > T S
> > S E T
> > T S T S
> > S T S T T
> >
> > where S is a "solid," T is a stripe, and E is the eight ball. A
> > configuration is also standard if every S is mapped to a T, or if the
> > triangle is reflected across its verticle axis of symmetry. Anyway,
> > so you're racking up and you dump 15 balls into the rack randomly.
> > Assuming you don't make any mistakes, what's the maximum number of two
> > ball permuations necessary to get to any of the 4 standard
> > configurations?
>
> I get 4
> E
> SS
> SSS
> STST
> TTTTT

Takes only 3, though:

(E)
S S
S(S)S
S T S T
T T T T T

S
S(S)
S E S
S T S T
T T T T(T)

S
S T
(S)E S
S T S T
T T(T)T S

S
S T
T E S
S T S T
T T S T S

That is a mirror of the setup Pooh gave.

Michael
--
Still an attentive ear he lent Her speech hath caused this pain
But could not fathom what she meant Easier I count it to explain
She was not deep, nor eloquent. The jargon of the howling main
-- from Lewis Carroll: The Three Usenet Trolls




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