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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 3, 2004 4:23 AM

&gt; &gt;&gt; poopdeville@gmail.com (Acid Pooh) wrote:
&gt; The post seems to be defining a configuration as standard
&gt; if you can transform it standard configuration. This is a
&gt; circular and meaningless definition.

Ok, let me pose this mini-puzzle:

What is a standard configuration, given that

a) the following is a standard configuration,

&gt; &gt;&gt;&gt; S
&gt; &gt;&gt;&gt; T S
&gt; &gt;&gt;&gt; S E T
&gt; &gt;&gt;&gt; T S T S
&gt; &gt;&gt;&gt; S T S T T

and b)
&gt; &gt;&gt;&gt; A
&gt; &gt;&gt;&gt; configuration is also standard if every S is mapped to a T, or if the
&gt; &gt;&gt;&gt; triangle is reflected across its verticle axis of symmetry.

In other words, we know a member of the set of standard configurations,
and we're told that the set is closed under two operations that are also
given, and it is implied that this definition describes the whole set.

I think this is what Mr Pooh has written, and it is well-defined.

ObPuzzle:
a) This equilateral triangle is in my set. &lt;insert mental image&gt;
b) If a figure is in my set, its likeness rotated by 60 degrees is also
in the set.
c) If two figures are in my set, their superposition is also in my set.
d) These definitions suffice to describe the whole set.
What is in my set?

ObPuzzle^2: Can you pose a more interesting puzzle that folows this
pattern?
(Followup to rec.puzzles if you do this and so desire.)

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