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From: john@cisden.UUCP (John Woolley)
Newsgroups: net.puzzle
Subject: Re: marble puzzle
Message-ID: <514@cisden.UUCP>
Date: Tue, 18-Feb-86 13:23:59 EST
Article-I.D.: cisden.514
Posted: Tue Feb 18 13:23:59 1986
Date-Received: Fri, 21-Feb-86 06:46:59 EST
References: <952@houxa.UUCP>
Reply-To: john@cisden.UUCP (John Woolley)
Organization: ConTel Information Systems, Denver
Lines: 40

In article <952@houxa.UUCP> qts@houxa.UUCP (J.RAMMING) writes:
>Given:  an ordinary balance, and twelve marbles.  Of these twelve
>        marbles, 11 of them have exactly the same weight.  The
>        twelfth marble is EITHER lighter OR heavier than the other
>        eleven.  We do not know, at the outset, which marble it
>	is, or whether it is lighter or heavier.
>
>Puzzle 1:  Suppose the balance spontaneously explodes after it has
>	been used three times.  Your task is to determine, in the
>	three weighings available, which is the odd marble out, and
>	whether it is lighter or heavier than its companions.

Yes, this can be done.

>Puzzle 2:  Prove that three weighings is insufficient for the above,
>	when one starts off with 14 marbles.

This also is true.

>Puzzle 3:  (For twisted minds): Find the odd marble out, and figure
>	out whether it is lighter or heavier, starting with 13
>	marbles.  (Might need an extra tool or two...)

This is not possible.  With 13, you can find which one is off-weight in
3 steps, but there's 1 chance in 13 that you won't be able to tell which
way off it is.  (That in itself constitutes a hint.)

And now a miraculously wonderful generalization.  (I'll answer in a couple
of weeks.)

Puzzle 4:  (For very twisted minds.)  Determine how many marbles you can
	solve the puzzle for in n weighings, as a function of n.  This is
	not easy.

Puzzle 5:  (Just take a guess.  Answer follows from 4.)  How many weighings
	would it take with 1000 marbles?
-- 
				Peace and Good!,
				      Fr. John Woolley
"Compared to what I have seen, all that I have written is straw." -- St. Thomas