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

 Messages: [ Previous | Next ]
 Michael Mendelsohn Posts: 43 Registered: 12/13/04
Re: Billiards Puzzle
Posted: Oct 1, 2004 11:04 AM

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

Date Subject Author
9/30/04 Acid Pooh
10/1/04 Alan Sagan
10/1/04 Michael Mendelsohn
10/1/04 Michael Mendelsohn