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ESCOT Problem of the Week: Archive of Problems, Submissions, & Commentary |
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ESCOT Problem of the Week: Archive of Problems, Submissions, & Commentary |
(Be sure to try Pirates and Diamonds - Part I before you do this problem.)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?
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Very few students submitted responses to this problem. Perhaps when they first read it it seemed impossible to attempt! As you can read in the two highlighted solutions, it wasn't as bad as it seemed.
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Page Part 2 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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Page Part 2 To get two pounds we first filled A and then poured it to B. Then we had six pounds in B. Then we filled A again and poured it to B. That left two pounds in A because B will only fit ten pounds. It is impossible to get one because you can never get an odd number by adding, subtracting, multiplying, or dividing two even numbers. In conclusion you can only measure even pounds of diamonds using a six and ten pound containers. ------------------------------------
Atena A., age 13 - Lionville Middle School, Exton, PA
Honora D., age 13 - School of the Arts, San Francisco, CA
Chelsea H., age 13 - School of the Arts, San Francisco, CA