A Math Forum Project

ESCOT Problem of the Week: Archive of Problems, Submissions, & Commentary

Pirates and Diamonds: Part III - posted October 15, 1999

(Be sure to try Pirates and Diamonds - Part I and Pirates and Diamonds - Part II before you do this problem.)

You now have a choice of five pairs of containers to use for measuring. For each pair of containers, can you make the purchase of 8 lbs. of diamonds? For those pairs that work, how can you make the purchase?

Use these pages for further information:

• Diamond Activity Directions
• Student Ideas
• Teacher Ideas

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Comments

There was only one completely correct answer submitted for Part III.

Because the Pirate Diamond Problem was the first ESCOT Problem of the Week and there were some technical problems as we started, few students who were participating got to the point of trying Part III or Part IV. The other students who submitted a solution to Part III did not completely answer the question.

Highlighted solutions:

Page Part 3
For the 6 lb. and 10 lb. containers:

First Fill A to get 6 lbs. in the 6 lb. container.
Then Pour A to B to get 6 lbs. in the 10 lb. container.
Next Fill A again and pour A to B also.  This leaves you with 2 lbs. in the 6
lb. container and 10 lbs. in the 10 lb. container.
Then Empty B and pour A to B so you have 2 lbs in the 10 lb. container.
After Filling A again pour A to B for the last time.  This leaves you with 8
lbs. in the 10 lb. container.

I can't get 8 lbs. of diamonds with only a 4 lb. and 3 lb. containers because
the most they could hold is 7 lbs.

With the 3 lb. and 7 lb. containers:

First Fill B and Pour B to A to get 3 lbs. in the 3 lb. container and 4 lbs.
in the 7 lb. container.
Then Empty A and Pour B to A to get 3 lbs. in the 3 lb. container and 1 lb. in
the 7 lb. container.
Again Empty A and pour B to A to get 1 lb. in the 3 lb. container.
After filling B you are left with 1 lb. in the 3 lb. container and 7 lbs. in
the 7 lb. container which is 8 lbs.

For the 10 lb. and 12 lb. containers:

Fill B and Pour B to A to get 10 lbs. in the 10 lb. container and 2 lbs. in
the 12 lb. container.  Then Empty A and Pour B to A to get 2 lbs. in the 10
lb. container.  Repeat this 3 times and you are left with 8 lbs. in the 10 lb.
container.

First Fill A and Pour A to B to get 6 ponds in B.  Then Fill A and Pour A to B
to get 1 pound in A and 11 lbs. in B.  Then Empty B.
Again Pour A to B, Fill A, Pour A to B, Fill A, and Pour A to B to get 2
pounds in A and 11 pounds in B.  Next empty B and Pour A to B.  Finally, Fill
A and Pour A to B to get 8 lbs. in B.

(When I first revised it and tried to save it froze on me and I had to type
everything over again.  PLEASE save me the trouble and time by fixing this
error.  Thank you)

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1 students received credit this week.

Atena A., age 13 - Lionville Middle School, Exton, PA

View most of the solutions submitted by the students above