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Path: utzoo!watmath!clyde!burl!ulysses!mhuxr!mhuxt!houxm!houxa!qts
From: qts@houxa.UUCP (J.RAMMING)
Newsgroups: net.puzzle
Subject: marble puzzle
Message-ID: <952@houxa.UUCP>
Date: Fri, 14-Feb-86 14:53:22 EST
Article-I.D.: houxa.952
Posted: Fri Feb 14 14:53:22 1986
Date-Received: Sat, 15-Feb-86 05:07:53 EST
Organization: AT&T Bell Labs, Holmdel NJ
Lines: 30

keywords:  marbles, hacksaw

*******

Here is a puzzle I ran across several years ago; it hasn't made
the rounds lately, so I thought I would post it.

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.

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

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...)

J. Christopher Ramming

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