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

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### Pirates and Diamonds: Part I - posted October 1, 1999

The pirate ship has just landed, loaded with diamonds. You've been sent to buy 8 lbs. of diamonds but you only have one 10-lb. and one 6-lb. measuring container.

How can you make the purchase?

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Students used two basic methods to solve the problem. One method begins with container A, and the other starts with container B. Since we hadn't specified that we wanted the method using the least number of steps, we counted both methods as correct.

Most students' solutions provided only the steps involved in finding 8 lbs. of diamonds, without including the amounts that were poured. Since we thought that the amounts would help people understand the solution, we only gave credit if students included them. Because so many students left out the amounts, it's possible that the wording of the problem didn't clearly ask for what we wanted.

### Highlighted solutions:

 From: Anna G., age 13Kai N., age 13 School: School of the Arts, San Francisco, CA

```Page Part 1
Fill A and pour it to B. You should have 6 lbs in the 10 lbs container. Fill A
again and pour again into B. Giving you a full ten pound container but leaving
you with only two in the six lbs container. Now empty the 10 lbs
container.Pour the 2lbs inside A into B. Giving you 2 lbs in the 10 lbs
container.Now fill A again, and pour it into B giving you 8 lbs in the 10 lb
container.
------------------------------------
```

 From: Wil D., age 13Jeanette G., age 13 School: School of the Arts, San Francisco, CA

```Page Part 1
First we filled A and got 6 lbs. Then we poured A to B to get 6 lbs. in B. A
is now empty. Then we filled A so now there was 6 lbs. in each container. Then
we poured A to B so now there was 10 lbs. in B and 2 lbs. in A  Then we
emptied B so there was only 2 lbs. in A. Then we poured A to B so there was 2
lbs.in B. Then we filled A so that there was 6 lbs. in it. Last, we poured A
to B so that B contained 8 lbs.
------------------------------------
```

 From: Keturah B., age 13 School: Frisbie Middle School, Rialto, CA

```Page Part 1
First I filled A, which equaled 6 pounds.  Next I poured A to B, now  B
had the six pounds.  After that I filled A again, and poured A to B.  That
left 2 lbs in the 6 lbs container and the 10 pound container was full.   Then
I emptied B.  So B had nothing and A had 2 pounds.  Next I poured A to B.  Now
A had no pounds and B had 2 pounds.  Next I filled A and poured A to B.  Now B
contained 8 pounds of diamonds.  I did the problem in eight steps.
------------------------------------
```

 From: Alicia W., age 13 School: Frisbie Middle School, Rialto, CA

```Page Part 1
First you fill container A with 6 pounds of diamonds . Pour the 6 pounds of
diamonds  in container A to container B so that it is filled with 6 pounds of
diamonds.  Fill container A again with 6 pounds of  diamonds. Pour the 6
pounds of diamonds from container A to container B again so that it is filled
with 10 pounds of diamonds. You should have 2 pounds of diamonds left in the A
container. Empty the B container . Pour the 2 pounds of diamonds in container
A to container  B so that it has 2 pounds of diamonds. Fill container A again
with 6 pounds, Pour container A with the 6 pounds  into container B. That's
how you make the purchase of  8 pounds.
------------------------------------
```

 From: Nicole L., age 13Nick G., age 13Victoria A., age 13Ryan-Grace C., age 13 School: JFK Middle School, Port Jefferson Station, NY

```Page Part 1
The first thing we did was was fill the ten pound container.  The next thing
we did was put the ten pounds of diamonds into the six pound container and
four pounds remained in the ten pound container, because the six pound
contaner can only hold six pounds.  After that we emptied the six pound
container.  Then we poured what was in the ten pound container into the six
pound container.  Then we filled the ten pound container again.  Then we
poured the ten pounds that was in the ten pound container into the six pound
container. After that we emptied the six pound container that had six pounds
in it and we were left with 8 pounds of diamonds in the 10 pound container.
------------------------------------
```

### 33 students received credit this week.

Atena A., age 13 - Lionville Middle School, Exton, PA
Mark A., age 13 - Frisbie Middle School, Rialto, CA
Reina A., age 13 - Frisbie Middle School, Rialto, CA
Victoria A., age 13 - JFK Middle School, Port Jefferson Station, NY
Chris B., age 14 - School of the Arts, San Francisco, CA
Jessie B., age 13 - Frisbie Middle School, Rialto, CA
Keturah B., age 13 - Frisbie Middle School, Rialto, CA
Miguel B., age 13 - Frisbie Middle School, Rialto, CA
Alan C., age 13 - School of the Arts, San Francisco, CA
Christina C., age 13 - School of the Arts, San Francisco, CA
Ryan-Grace C., age 13 - JFK Middle School, Port Jefferson Station, NY
Carson D., age 13 - School of the Arts, San Francisco, CA
Honora D., age 13 - School of the Arts, San Francisco, CA
Wil D., age 13 - School of the Arts, San Francisco, CA
Anna G., age 13 - School of the Arts, San Francisco, CA
Consuelo G., age 13 - Frisbie Middle School, Rialto, CA
Jeanette G., age 13 - School of the Arts, San Francisco, CA
Nick G., age 13 - JFK Middle School, Port Jefferson Station, NY
Bryant H., age 13 - Frisbie Middle School, Rialto, CA
Chelsea H., age 13 - School of the Arts, San Francisco, CA
Amanda L., age 13 - JFK Middle School, Port Jefferson Station, NY
Nicole L., age 13 - JFK Middle School, Port Jefferson Station, NY
Heather M., age 13 - JFK Middle School, Port Jefferson Station, NY
Nichole M., age 13 - JFK Middle School, Port Jefferson Station, NY
Kai N., age 13 - School of the Arts, San Francisco, CA
John O., age 25+ - W. R. Coile Middle School, Athens, GA
Noga P., age 13 - JFK Middle School, Port Jefferson Station, NY
Leah R., age 13 - Frisbie Middle School, Rialto, CA
Amanda S., age 13 - JFK Middle School, Port Jefferson Station, NY
Rachael S., age 13 - JFK Middle School, Port Jefferson Station, NY
Niranjani T., age 13 - JFK Middle School, Port Jefferson Station, NY
Alicia W., age 13 - Frisbie Middle School, Rialto, CA
Helen Y., age 13 - School of the Arts, San Francisco, CA

#### View most of the solutions submitted by the students above

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