🚀 go-pugleaf

In article <Bu26KK.DEB@ireq.hydro.qc.ca> bouchard@ireq.hydro.qc.ca (Marco Bouchard ETUDIANT sept-dec 92) writes:
>  [reformatted to fit 80 char lines]
>You have 10 vending machines to fill out with chocolate bars. In fact,
>after finishing to put the chocolate, you remember that you had 9 boxes
>of chocolate bars of 100g. and one box of bars of 90g and you gotta know
>in which machine you put those of 90g. You cannot tell just by looking on
>the paper on the bar if it has 90 or 100 g. But, beside the 10 vending
>machine, you have an electronic weighing machine. When you put a quarter
>in it, it tells you the weight (it makes only one measure). The problem
>is that you have only a quarter (only one try) and you gotta know, just
>by one try, in which machine you put the chocolate bars of 90g. You don't
>have access to the money of the vending machines.  You can weigh as much
>bars as you want, but you can take one measure.    
>How can you do this (it's mathematic)?

Take 1 bar from machine #1, 2 bars from machine #2, ... and 10 bars from
machine #10.  Weight the whole set of bars.  The expected weight is 5500g.
But some of the bars weight only 90g, so the actual weight will be some
number of 10g increments less then 5500g, that number is the number of the 
machine with the 90g bars.

--
Mark Biggar
mab@wdl1.wdl.loral.com

bouchard@ireq.hydro.qc.ca (Marco Bouchard ETUDIANT sept-dec 92) writes:
>You have 10 vending machines to fill out with chocolate bars. In fact,
>after finishing to put the chocolate, you remember that you had 9 boxes
>of chocolate bars of 100g. and one box of bars of 90g and you gotta know
>in which machine you put those of 90g....
>You can weigh as [many]
>bars as you want, but you can take one measure.    

mab@wdl39.wdl.loral.com (Mark A Biggar) replies:
>Take 1 bar from machine #1, 2 bars from machine #2, ... and 10 bars from
>machine #10.  Weight the whole set of bars.  The expected weight is 5500g.
>But some of the bars weight only 90g, so the actual weight will be some
>number of 10g increments less then 5500g, that number is the number of the 
>machine with the 90g bars.

Of course, this approach can be generalized to handle the case in
which you're not sure how many of the boxes were underweight: take 1
bar from machine #1, 2 from #2, 4 from #3, 8 from #4, etc.  Only
problem is, one of the vending machines has to be capable of holding
1024 chocolate bars, and your scale has to be able to handle over 200 kg
of chocolate.  And then there's the question of what to DO with over
200 kg of chocolate... :-)

-- 
					Stephen Bloch
				sbloch@silver.cs.umanitoba.ca