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 |