Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
NCTM or The Math Forum.


Math Forum
»
Discussions
»
sci.math.*
»
sci.math
Notice: We are no longer accepting new posts, but the forums will continue to be readable.
Topic:
Billiards Puzzle
Replies:
8
Last Post:
Oct 3, 2004 4:23 AM




Re: Billiards Puzzle
Posted:
Oct 3, 2004 4:23 AM


"Glenn C. Rhoads" schrieb: > >> poopdeville@gmail.com (Acid Pooh) wrote: > The post seems to be defining a configuration as standard > if you can transform it standard configuration. This is a > circular and meaningless definition.
Ok, let me pose this minipuzzle:
What is a standard configuration, given that
a) the following is a standard configuration,
> >>> S > >>> T S > >>> S E T > >>> T S T S > >>> S T S T T
and b) > >>> 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.
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 welldefined.
ObPuzzle: a) This equilateral triangle is in my set. <insert mental image> 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



