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Weighing Bolts

Date: 2/14/96 at 8:43:58
From: Anonymous
Subject: math puzzle

My math teacher gave me this problem to solve:

Jim works in a hardware plant and makes rivets 6 inches long and 
6 ounces in weight. One day Jim didn't come to work, and Harry, 
his replacement, made a drum of rivets 6 inches long, but which only 
weighed 5 ounces each. Harry's drum was stored along with 9 
other proper drums. 

When Harry returned, he was given an ultimatum: Find the rivets 
or lose your job. Harry could only use a scale one time, and could 
take only one reading from that scale. So if he is guessing, it had 
better be a good guess. How could poor Harry be sure of picking 
the right drum out of the ten?

I really don't know how to approach this problem. I have solved 
it in three weighings, but how can I do it in just one?

Date: 2/14/96 at 9:33:19
From: Doctor Byron
Subject: Re: math puzzle

As with a lot of problems like this, there's a bit of a trick to this 
one that you have to catch on to - namely, that you don't have to 
weigh the full contents of each drum.  Consider the possibilities if 
you can take individual bolts or groups of bolts from the drums....

Want to give it another shot?  Now would be a good time, because if
you read on, I'm going to give away the solution...

Okay, here's the idea:  You take a different number of bolts from 
each of the ten drums, one from the first, two from the second, etc.
This will give you a total of 55 bolts.  If each weighs 6 oz., the
total weight should be 330 oz.  When you weigh this group of bolts, 
however, the weight will be off by a number equal to the number 
of bolts taken from the 5 oz. batch.  For example, if the fifth drum 
(from which 5 bolts were taken) is the odd batch, the weight will 
read 325 oz or 5 less than would be expected otherwise.  

Pretty sneaky, huh?

-Doctor Byron,  The Math Forum

Associated Topics:
Middle School Puzzles

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