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From: jak@talcott.UUCP (Joe Konstan)
Newsgroups: net.puzzle
Subject: Re: Yet another weighing problem
Message-ID: <419@talcott.UUCP>
Date: Fri, 19-Apr-85 17:08:14 EST
Article-I.D.: talcott.419
Posted: Fri Apr 19 17:08:14 1985
Date-Received: Sun, 21-Apr-85 05:03:25 EST
References: <5755@duke.UUCP>
Organization: Harvard University
Lines: 26

> 	A piece of gold weighing 40 pounds was dropped and broken into 4
> 	pieces. It was broken in such a way that you can, using the 4
> 	pieces, weigh anything weighing from 1 up to 40 pounds. For example
>         something weighing 5 pounds could be weighed using one piece of
> 	gold weighing 15 pounds and another weighing 10 pounds. 
> 
> 	What are the weights of the 4 pieces ?

Easy one:  1, 3, 9, and 27 pounds:

    to way 2, put 1 on the side with the stuff, 3 on other side
    similarly for 5, 6, 7, ...

> 	How about generalizing it, lets assume that the gold originally 
> 	weighed K pounds and was broken into n pieces, what are the weights
> 	of the n pieces given that the above property still holds ? 
> 
>         Note: I do not know (yet) the solution to the second one.

In general, we want to break it into blocks of 3^n for n going from
0 up as high as possible.  I think that leaving the leftover as just one
block will be good enough to weigh everything, by always using that
block for weights above it.

Mithrandir
jak@talcott