1 quarter = 25 cents
1 dime = 10 cents
1 nickel = 5 cents
1 penny = 1 cent
it would make sense to make a table of this working our way down from the highest denomination to the lowest denomination.
the total value of each row is equal to 50 cents.
quarters dimes nickels pennies
2 0 0 0
1 2 1 0
1 2 0 5
1 1 3 0
1 1 2 5
1 1 1 10 *** example 1
1 1 0 15
1 0 5 0
1 0 4 5
1 0 3 10
1 0 2 15
1 0 1 20
1 0 0 25
0 5 0 0
0 4 2 0
0 4 1 5
0 4 0 10
0 3 4 0
0 3 3 5 *** example 2
0 3 2 10
0 3 1 15
0 3 0 20
0 2 6 0
0 2 5 5
0 2 4 10
0 2 3 15
0 2 2 20
0 2 1 25
0 2 0 30
0 1 8 0
0 1 7 5
0 1 6 10
0 1 5 15
0 1 4 20
0 1 3 25
0 1 2 30
0 1 1 35
0 1 0 40
0 0 10 0
0 0 9 5
0 0 8 10
0 0 7 15
0 0 6 20
0 0 5 25 *** example 3
0 0 4 30
0 0 3 35
0 0 2 40
0 0 1 45
0 0 0 50
this counts out to be 49 possible combinations.
I couldn't figure out a formula to use so I just tabulated all the possible combinations I could think of.
The total is 49.
I believe I have them all covered.
Any combination you can think of should be in the table.
Example 1:
1 quarter 1 dime 1 nickel 10 pennies.
start with the quarter column and scan down until you see 1.
shift to the dime column and scan further down until you find 1.
shift to the nickel column and scan further down until you find 1.
shift to the penny column and you should see 10.
Example 2:
3 dimes 3 nickels 5 pennies.
start with the quarter column and scan down until you see 0.
shift to the dime column and scan further down until you find 3.
shift to the nickel column and scan further down until you find 3.
shift to the penny column ahd you should see 5.
Example 3:
5 nickels 25 pennies.
start with the quarter column and scan down until you see 0.
shift to the dime column and scan further down until you find 0.
shift to the nickel column and scan further down until you find 5.
shift to the penny column and you should see 25.