Pirates & Diamonds 3
posted October 15, 1999 as a Math Forum EPoW

Introduction: This problem challenges students to develop logic skills and problem-solving strategies by figuring out sequences of steps that will allow them to accomplish tasks not obviously possible with the tools provided.

Where's the Math: This problem draws on students' logical thinking skills and encourages use of measurement and geometry concepts. Standards: Measurement, algebra, geometry Role of Components: The Pirates & Diamonds series uses Geometer's Sketchpad to animate the containers, which are monitored via number entry fields (labeled with ESCOT labels) and triggered by a button panel. Instructions are displayed via the HTML viewer, and solutions are entered in a text entry box. Javascript handles communication among components.

(The applet for this problem is currently unavailable) 

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Sample submitted solution:

From: Atena, age 13
School: Lionville Middle School, Exton, Pennsylvania

Instructions: 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?  
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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