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From: nader@hound.UUCP (N.MEHRAVARI)
Newsgroups: net.puzzle
Subject: Re: Weighing Problem (solution)
Message-ID: <1062@hound.UUCP>
Date: Thu, 11-Apr-85 08:01:35 EST
Article-I.D.: hound.1062
Posted: Thu Apr 11 08:01:35 1985
Date-Received: Sat, 13-Apr-85 03:02:48 EST
References: <322@tekred.UUCP>
Organization: AT&T Bell Labs, Holmdel NJ
Lines: 40

>Given a pan balance and 12 pool balls of which one may be either too
>light or too heavy, determine with uses of the balance which
>ball, if any, is faulty and whether it is too light or too heavy.

It can be done in three weighings:
Label the coins 1,2,3,.....12, and make the following three weighings:
     1)         1,2,3,4 against 5,6,7,8
     2)         1,2,3,5 against 4,9,10,11
     3)         1,6,9,12 against 2,5,7,10
Let L,S,and H stand for "is lighter than", "is the same as," and
"is heavier than," respectively. The the folling table determines the
false coin, if any, and its nature.

outcome of the three weighings          the false coin
______________________________          ______________
LLL                                       1 is light
LLH                                       2 is light
LLS                                       3 is light
LHS                                       4 is light
HLH                                       5 is light
HSL                                       6 is light
HSH                                       7 is light
HSS                                       8 is light
SHL                                       9 is light
SHH                                       10 is light
SHS                                       11 is light
SSL                                       12 is light
HHH                                       1 is heavy
HHL                                       2 is heavy
HHS                                       3 is heavy
HLS                                       4 is heavy
LHL                                       5 is heavy
LSH                                       6 is heavy
LSL                                       7 is heavy
LSS                                       8 is heavy
SLH                                       9 is heavy
SLL                                       10 is heavy
SLS                                       11 is heavy
SSH                                       12 is heavy
SSS                                       all good