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Sample submitted
solution:
From:
Atena, age 13
School: Lionville Middle School, Exton,
Pennsylvania
Can you measure 1 lb. of
diamonds using only one 10-lb. and one 6-lb.
measuring container? How about 2 lbs.? Consider
the amounts between 1 lb. and 16 lbs. What
conclusion can you make about the amounts
of diamonds that can be purchased using
only one 10-lb. and one 6-lb. measuring
container?
When I first saw this problem
I thought,"This is too hard. Which of these
problems do I have to solve. There are too
many in one question" Then I started to
solve them. Can you measure 1 lb. of diamonds
using only one 10-lb. and one 6-lb. measuring
container? I don't think so. How about 2
lbs.? I think so. First I filled A and got
6 lbs in A. Then I poured A to B so I had
6 lbs in B. Next I filled A again and again
poured it into B. This left me with 2 lbs.
in A and 10 lbs. in B. Then I emptied B.
I'm not sure if this is correct, b/c I was
kind of confused with the instructions of
using only one 10-lb and one 6-lb. Didn't
I do that in the last problem. Consider
the amouts between 1 lb. and 16 lbs. What
conclusion can you make about the amounts
of diamonds that can be purchased using
only one 10-lb. and one 6-lb. measuring
container? I conclude that with one 6-lb.
and one 10-lb. measuring container it is
only possible to measure out even amounts,
such as 2 lbs., 4 lbs., 6 lbs., 8 lbs.,
etc. upto 16 lbs. Since the total number
of diamonds you could take with a 6 lb.
and a 10 lb. container is 16 lbs., the greatest
amount would be 16 lbs. of diamonds. I reached
this conclusion by trying to get 5 lbs.,
7 lbs., 4 lbs., 15 lbs., and 8 lbs. I was
only able to get 2 lbs., 4 lbs., 6 lbs.,
8 lbs., 10 lbs., and 16 lbs. I am sure if
I tried to get 14 or 12 lbs, I could. So
that is how I reached my conclusion. Now
that I look at it, it's not that confusing.
I now know what you were looking for, I
think. :)
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