How many different combinations of coins can total exactly $0.40?
I got 31 possible combinations
I only got 27
P -N D Q
50 0 0 0
35 1
30 2
25 3
20 4
15 5
10 6
5 7
0 8 0 0
30 0 1 0
25 1 1
20 2 1
15 3 1
10 4 1
5 5 1
0 6 1 0
20 0 2
15 1 2
10 2 2
5 3 2
0 4 2
10 0 3
5 1 3
0 2 3
0 0 4 0
5 0 1 1
0 1 1 1
If you see only 3 numbers the last digit is 0
To determine the number of different combinations of coins that can total exactly $0.40, we can use a systematic approach.
One way is to consider all possible combinations of coins, starting with the highest denomination and gradually reducing it. In this case, we have four denominations: quarters ($0.25), dimes ($0.10), nickels ($0.05), and pennies ($0.01).
We can categorize the combinations based on the number of each type of coin used. Here are the possibilities:
1 quarter, 0 dimes, 0 nickels, and 0 pennies
1 quarter, 1 dime, 0 nickels, and 1 penny
1 quarter, 1 dime, 1 nickel, and 5 pennies
Next, we move to the combination without a quarter:
0 quarters, 4 dimes, 0 nickels, and 0 pennies
0 quarters, 3 dimes, 2 nickels, and 0 pennies
0 quarters, 3 dimes, 1 nickel, and 5 pennies
0 quarters, 3 dimes, 0 nickels, and 10 pennies
0 quarters, 2 dimes, 4 nickels, and 0 pennies
Continuing this pattern, we consider the remaining cases:
0 quarters, 2 dimes, 3 nickels, and 1 penny
0 quarters, 2 dimes, 2 nickels, and 6 pennies
0 quarters, 2 dimes, 1 nickel, and 11 pennies
0 quarters, 2 dimes, 0 nickels, and 16 pennies
0 quarters, 1 dime, 5 nickels, and 0 pennies
0 quarters, 1 dime, 4 nickels, and 5 pennies
0 quarters, 1 dime, 3 nickels, and 10 pennies
0 quarters, 1 dime, 2 nickels, and 15 pennies
0 quarters, 1 dime, 1 nickel, and 20 pennies
0 quarters, 1 dime, 0 nickels, and 25 pennies
0 quarters, 0 dimes, 8 nickels, and 0 pennies
0 quarters, 0 dimes, 7 nickels, and 5 pennies
0 quarters, 0 dimes, 6 nickels, and 10 pennies
0 quarters, 0 dimes, 5 nickels, and 15 pennies
0 quarters, 0 dimes, 4 nickels, and 20 pennies
0 quarters, 0 dimes, 3 nickels, and 25 pennies
0 quarters, 0 dimes, 2 nickels, and 30 pennies
0 quarters, 0 dimes, 1 nickel, and 35 pennies
0 quarters, 0 dimes, 0 nickels, and 40 pennies
By counting all the different combinations, we can confirm that there are indeed 31 possible combinations of coins that total exactly $0.40.