Path: utzoo!utgpu!jarvis.csri.toronto.edu!mailrus!bbn!gateway!dsys.icst.nbs.GOV!rbj
From: rbj@dsys.icst.nbs.GOV (Root Boy Jim)
Newsgroups: comp.emacs
Subject: Blackbox
Message-ID: <8905022249.AA02054@dsys.icst.nbs.gov>
Date: 2 May 89 22:49:31 GMT
Sender: news@bbn.COM
Organization: National Institute of Standards and Technology
	formerly National Bureau of Standards
Lines: 42

? Regarding best scores, I believe the minimum score possible in
? order to secure a sure match is equal to the number of balls in
? the box.  However, as this is an extreme case, most scores will
? be at least twice the number of balls.

My lowest score has been 10. I don't see how you could score 4.

? By the way, blackbox reminds me of some mechanical puzzle boxes
? that Martin Garder wrote up in one of his books on mathematical
? puzzles.  The puzzles were solid boxes constructed of wood that
? contained a hole into which you were to place a ball bearing.
? The object was retrieve the ball out of a second opening, while
? manipulating the box in any manner possible EXCEPT OPENING up
? the box or damaging it.  The boxes were especially devious,
? however, and often contained magnets that trapped the balls, or
? trap doors that required manipulation of doodads on the outside
? of the box.  In fact, one of these boxes proved so hard that one
? solver had to have the box X-RAYED before he could solve it!
? Fortunately, the game blackbox is nowhere near as hard.

Isn't X-raying opening? :-)

? Ps. Is there some inherent reason why the game is limited to an
? 8 x 8 box?  It might be more interesting if the size were
? adjustable as well as the number of balls.

It is possible that 8x8 may be the smallest size that can uniquely
determine the four balls. Four balls is the maximum that may be placed
in a box arbitrarily and be uniquely determined. Consider the pattern

			0 - 0
			x x x
			0 - 0

A fifth ball placed on any of the x squares could no be distinguished.

? julian@uhccux.uhcc.hawaii.edu
? uunet!ucsd!nosc!uhccux!julian
? julian@uhccux.bitnet

	Root Boy Jim is what I am
	Are you what you are or what?