Answer to December 6, 1999 Problem

The Candy Factory Problem

The Winchester Candy Factory manufactures Apple Candy, and they want to be able to fill any demand for candy that ranges between 1 and 1000 pieces.

The production manager, a retired math teacher from the local high school, determined that they only needed 10 different size bags of candy on hand to be able to fill any order!

If all the bags are to hold a different amount of candy, and if you want to be able to fill any order of candy from 1 to 1000 pieces (without breaking any of the bags),
How many pieces of candy should be put into each of the ten bags?


Solution:

The ten bags should hold the following amounts of candy:

Bag 1:   1  
Bag 2:   2  
Bag 3:   4  
Bag 4:   8  
Bag 5:   16  
Bag 6:   32  
Bag 7:   64  
Bag 8:   128  
Bag 9:   256  
Bag 10: any amount from 489 to 512

For example, to fill an order of 63 pieces of candy, you would give the customer bags 1 through 6!
To fill an order of 300 pieces, you would give bags 3, 4, 6, and 9.
This is based on the binary (base 2) number system.

Correctly solved by:

1. Tom Marino Winchester, VA
2. Richard Mocarski Winchester, VA
3. Jon Pence Winchester, VA
4. Chris Moats Winchester, VA
5. Bob Hearn Winchester, VA
6. Chip Crawford Winchester, VA
7. Michael Webber Winchester, VA
8. Sam Stiebel Winchester, VA
9. Si Schiavone Winchester, VA
10. Ben Burdick Winchester, VA
11. Josh Grewal Winchester, VA
12. Ricky Patel Winchester, VA
13. Nataniel Ruiz-Mier La Paz, Bolivia
14. Brandon Jaycox Winchester, VA