November 2018
Problem of the Month

Change for a (half) Dollar

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

Send any comments or questions to: David Pleacher