What is the greatest number of coins you can use to make 50 cents?
What is the smallest number of coins you can use?
In how many different ways can you make 50 cents?
You may only use pennies, nickels, dimes, and quarters.
Solution to the Problem:
The greatest number of coins is fifty pennies.The smallest number of coins is two quarters.
The number of ways in which you can make 50 cents is 49.
| pennies | nickels | dimes | quarters |
|---|---|---|---|
| 50 | 0 | 0 | 0 |
| 45 | 1 | 0 | 0 |
| 40 | 2 | 0 | 0 |
| 40 | 0 | 1 | 0 |
| 35 | 3 | 0 | 0 |
| 35 | 1 | 1 | 0 |
| 30 | 4 | 0 | 0 |
| 30 | 2 | 1 | 0 |
| 30 | 0 | 2 | 0 |
| 25 | 5 | 0 | 0 |
| 25 | 3 | 1 | 0 |
| 25 | 1 | 2 | 0 |
| 25 | 0 | 0 | 1 |
| 20 | 6 | 0 | 0 |
| 20 | 4 | 1 | 0 |
| 20 | 2 | 2 | 0 |
| 20 | 1 | 0 | 1 |
| 20 | 0 | 3 | 0 |
| 15 | 7 | 0 | 0 |
| 15 | 5 | 1 | 0 |
| 15 | 3 | 2 | 0 |
| 15 | 2 | 0 | 1 |
| 15 | 1 | 2 | 0 |
| 15 | 0 | 1 | 1 |
| 10 | 8 | 0 | 0 |
| 10 | 6 | 1 | 0 |
| 10 | 4 | 2 | 0 |
| 10 | 3 | 0 | 1 |
| 10 | 2 | 2 | 0 |
| 10 | 1 | 1 | 1 |
| 10 | 0 | 4 | 0 |
| 5 | 9 | 0 | 0 |
| 5 | 7 | 1 | 0 |
| 5 | 5 | 2 | 0 |
| 5 | 4 | 0 | 1 |
| 5 | 3 | 3 | 0 |
| 5 | 2 | 1 | 1 |
| 5 | 1 | 4 | 0 |
| 5 | 0 | 2 | 1 |
| 0 | 10 | 0 | 0 |
| 0 | 8 | 1 | 0 |
| 0 | 6 | 2 | 0 |
| 0 | 5 | 0 | 1 |
| 0 | 4 | 3 | 0 |
| 0 | 3 | 1 | 1 |
| 0 | 2 | 4 | 0 |
| 0 | 1 | 2 | 1 |
| 0 | 0 | 5 | 0 |
| 0 | 0 | 0 | 2 |
Correctly solved by:
| 1. James Alarie | Flint, Michigan |
| 2. Rob Miles | Northbrook, Illinois |
| 3. Mairany Jaracuaro |
Delta High School, Delta, Colorado |
| 4. Anna Vice | Landon School, Bethesda, Maryland |
| 5. Mikaela Williams |
Mountain View High School, Mountain View, Wyoming |
| 6. Daniel Harris |
Mountain View High School, Mountain View, Wyoming |
| 7. Caleb Frazier |
Delta High School, Delta, Colorado |
| 8. Triniti Rogers |
Mountain View High School, Mountain View, Wyoming |
| 9. Sameha Haque |
Delta High School, Delta, Colorado |