0
13 ways - 5 pennies, 2 dimes - 1 quarter - 25 pennies - 1 nickel, 2 dimes - 5 nickels - 5 pennies, 4 nickels - 5 pennies, 2 nickels, 1 dime -3 nickels, 1 dime -15 pennies, 1 dime -10 pennies, 1 nickel, 1 dime - 10 pennies, 3 nickels - 15 pennies, 2 nickels - 20 pennies, 1 nickel
Using pennies, nickels, dimes, quarters, half-dollars and dollar coins, there are 293 ways to make change for 1 US dollar.
Method 1:
Using pennies, nickels, dimes, quarters, half-dollar and dollar coins there are 293 ways to make change for one dollar. In general, to make change for d dollars using these coins there are (1 + d) (6 + 121 d + 362 d^2 + 310 d^3 + 80 d^4 )/ 6 ways. Without using the dollar coin, there are (6 + 55 h + 119 h2 + 95 h3 + 25 h4)/6 ways of making change for h dollars. For example, putting h=1 gives 50 ways of making change for fifty cents, or h=2 gives 292 ways of making change for a dollar.
Method 2:
Take the Taylor expansion of 1 over (1-x)*(1-x5)*(1-x10)*(1-x25)*(1-x50)*(1-x100), and jot down the coefficient of x100. This is the generating function for the ways to partition 100 into subsets of size 1, 5, 10, 25, 50, or 100, so there are 293 ways to make change for 1 US dollar.
Method 3:
Make a list as below. Using only pennies, nickels, dimes, and quarters, there are 242 ways to make a dollar; these begin with line 52.
- 1 dollar coin
- 2 half dollars
- 1 HD 2Q
- 1 HD 1Q 2D IN
- 1 HD 1Q 2D 5P
- 1 HD 1Q 1D 3N
- 1 HD 1Q 1D 2N 5P
- 1 HD 1Q 1D 1N 10P
- 1 HD 1Q 1D 15P
- 1 HD 1Q 5N
- 1 HD 1Q 4N 5P
- 1 HD 1Q 3N 10P
- 1 HD 1Q 2N 15P
- 1 HD 1Q 1N 20P
- 1 HD 1Q 25P
- 1 HD 5D
- 1 HD 4D 2N
- 1 HD 4D 1N 5P
- 1 HD 4D 10P
- 1 HD 3D 4N
- 1 HD 3D 3N 5P
- 1 HD 3D 2N 10P
- 1 HD 3D 1N 15P
- 1 HD 3D 20P
- 1 HD 2D 6N
- 1 HD 2D 5N 5P
- 1 HD 2D 4N 10P
- 1 HD 2D 3N 15P
- 1 HD 2D 2N 20P
- 1 HD 2D 1N 25P
- 1 HD 2D 30P
- 1 HD 1D 8N
- 1 HD 1D 7N 5P
- 1 HD 1D 6N 10P
- 1 HD 1D 5N 15P
- 1 HD 1D 4N 20P
- 1 HD 1D 3N 25 P
- 1 HD 1D 2N 30 P
- 1 HD 1D 1N 35P
- 1 HD 1D 40P
- 1 HD 10N
- 1 HD 9N 5P
- 1 HD 8N 10P
- 1 HD 7N 15P
- 1 HD 6N 20P
- 1 HD 5N 25P
- 1 HD 4N 30P
- 1 HD 3N 35P
- 1 HD 2N 40P
- 1 HD 1N 45P
- 1 HD 50P
- 4Q
- 3Q 2D 1N
- 3Q 2D 5P
- 3Q 1D 3N
- 3Q 1D 2N 5P
- 3Q 1D 1N 10P
- 3Q 1D 15P
- 3Q 5N
- 3Q 4N 5P
- 3Q 3N 10P
- 3Q 2N 15P
- 3Q 1N 20P
- 3Q 25P
- 2Q 5D
- 2Q 4D 2N
- 2Q 4D 1N 5P
- 2Q 4D 10P
- 2Q 3D 4N
- 2Q 3D 3N 5P
- 2Q 3D 2N 10P
- 2Q 3D 1N 15P
- 2Q 3D 20P
- 2Q 2D 6N
- 2Q 2D 5N 5P
- 2Q 2D 4N 10P
- 2Q 2D 3N 15P
- 2Q 2D 2N 20P
- 2Q 2D 1N 25P
- 2Q 2D 30P
- 2Q 1D 8N
- 2Q 1D 7N 5P
- 2Q 1D 6N 10P
- 2Q 1D 5N 15P
- 2Q 1D 4N 20P
- 2Q 1D 3N 25P
- 2Q 1D 2N 30P
- 2Q 1D 1N 35P
- 2Q 1D 40P
- 2Q 50P
- 2Q 10N
- 2Q 9N 5P
- 2Q 8N 10P
- 2Q 7N 15P
- 2Q 6N 20P
- 2Q 5N 25P
- 2Q 4N 30P
- 2Q 3N 35P
- 2Q 2N 40P
- 2Q 1N 45P
- 1Q 7D 1N
- 1Q 7D 5P
- 1Q 6D 3N
- 1Q 6D 2N 5P
- 1Q 6D 1N 10P
- 1Q 6D 15P
- 1Q 5D 5N
- 1Q 5D 4N 5P
- 1Q 5D 3N 10P
- 1Q 5D 2N 15P
- 1Q 5D 1N 20P
- 1Q 5D 25P
- 1Q 4D 7N
- 1Q 4D 6N 5P
- 1Q 4D 5N 15P
- 1Q 4D 4N 20P
- 1Q 4D 3N 25P
- 1Q 4D 2N 30P
- 1Q 4D 1N 35P
- 1Q 4D 40P
- 1Q 3D 9N
- 1Q 3D 8N 5P
- 1Q 3D 7N 10P
- 1Q 3D 6N 15P
- 1Q 3D 5N 20P
- 1Q 3D 4N 25P
- 1Q 3D 3N 30P
- 1Q 3D 2N 35P
- 1Q 3D 1N 40P
- 1Q 3D 45P
- 1Q 2D 11N
- 1Q 2D 10N 5P
- 1Q 2D 9N 10P
- 1Q 2D 8N 15P
- 1Q 2D 7N 20P
- 1Q 2D 6N 25P
- 1Q 2D 5N 30P
- 1Q 2D 4N 35P
- 1Q 2D 3N 40P
- 1Q 2D 2N 45P
- 1Q 2D 1N 50P
- 1Q 2D 55P
- 1Q 1D 13N
- 1Q 1D 12N 5P
- 1Q 1D 11N 10P
- 1Q 1D 10N 15P
- 1Q 1D 9N 20P
- 1Q 1D 8N 25P
- 1Q 1D 7N 30P
- 1Q 1D 6N 35P
- 1Q 1D 5N 40P
- 1Q 1D 4N 45P
- 1Q 1D 3N 50P
- 1Q 1D 2N 55P
- 1Q 1D 1N 60P
- 1Q 1D 65P
- 1Q 15N
- 1Q 14N 5P
- 1Q 13N 10P
- 1Q 12N 15P
- 1Q 11N 20P
- 1Q 10N 25P
- 1Q 9N 30P
- 1Q 8N 35P
- 1Q 7N 40P
- 1Q 6N 45P
- 1Q 5N 50P
- 1Q 4N 55P
- 1Q 3N 60P
- 1Q 2N 65P
- 1Q 1N 70P
- 1Q 75P
- 10D
- 9D 2N
- 9D 1N 5P
- 9D 10P
- 8D 4N
- 8D 3N 5P
- 8D 2N 10P
- 8D 1N 15P
- 8D 20P
- 7D 6N
- 7D 5N 5P
- 7D 4N 10P
- 7D 3N 15P
- 7D 2N 20P
- 7D 1N 25P
- 7D 30P
- 6D 8N
- 6D 7N 5P
- 6D 6N 10P
- 6D 5N 15P
- 6D 4N 20P
- 6D 3N 25P
- 6D 2N 30P
- 6D 1N 35P
- 6D 40P
- 5D 10N
- 5D 9N 5P
- 5D 8N 10P
- 5D 7N 15P
- 5D 6N 20P
- 5D 5N 25P
- 5D 4N 30P
- 5D 3N 35P
- 5D 2N 40P
- 5D 1N 45P
- 5D 50P
- 4D 12N
- 4D 11N 5P
- 4D 10N 10P
- 4D 9N 15P
- 4D 8N 20P
- 4D 7N 25P
- 4D 6N 30P
- 4D 5N 35P
- 4D 4N 40P
- 4D 3N 45P
- 4D 2N 50P
- 4D 1N 55P
- 4D 60P
- 3D 14N
- 3D 13N 5P
- 3D 12N 10P
- 3D 11N 15P
- 3D 10N 20P
- 3D 9N 25P
- 3D 8N 30P
- 3D 7N 35P
- 3D 6N 40P
- 3D 5N 45P
- 3D 4N 50P
- 3D 3N 55P
- 3D 2N 60P
- 3D 1N 65P
- 3D 70P
- 2D 16N
- 2D 15N 5P
- 2D 14N 10P
- 2D 13N 15P
- 2D 12N 20P
- 2D 11N 25P
- 2D 10N 30P
- 2D 9N 35P
- 2D 8N 40P
- 2D 7N 45P
- 2D 6N 50P
- 2D 5N 55P
- 2D 4N 60P
- 2D 3N 65P
- 2D 2N 70P
- 2D 1N 75P
- 2D 80P
- 1D 18N
- 1D 17N 5P
- 1D 16N 10P
- 1D 15N 15P
- 1D 14N 20P
- 1D 13N 25P
- 1D 12N 30P
- 1D 11N 35P
- 1D 10N 40P
- 1D 9N 45P
- 1D 8N 50P
- 1D 7N 55P
- 1D 6N 60P
- 1D 5N 65P
- 1D 4N 70P
- 1D 3N 75P
- 1D 2N 80P
- 1D 1N 85P
- 1D 90P
- 20N
- 19N 5P
- 18N 10P
- 17N 15P
- 16N 20P
- 15N 25P
- 14N 30P
- 13N 35P
- 12N 40P
- 11N 45P
- 10N 50P
- 9N 55P
- 8N 60P
- 7N 65P
- 6N 70P
- 5N 75P
- 4N 80P
- 3N 85P
- 2N 90P
- 1N 95P
- 100P
Key: HD - Half Dollar ($0.50), Q - Quarter ($0.25), D - Dime ($0.10), N - Nickel ($0.05), P - Penny ($0.01)
- 1 dollar coin
- 2 half dollars
- 1 HD 2Q
- 1 HD 1Q 2D IN
- 1 HD 1Q 2D 5P
- 1 HD 1Q 1D 3N
- 1 HD 1Q 1D 2N 5P
- 1 HD 1Q 1D 1N 10P
- 1 HD 1Q 1D 15P
- 1 HD 1Q 5N
- 1 HD 1Q 4N 5P
- 1 HD 1Q 3N 10P
- 1 HD 1Q 2N 15P
- 1 HD 1Q 1N 20P
- 1 HD 1Q 25P
- 1 HD 5D
- 1 HD 4D 2N
- 1 HD 4D 1N 5P
- 1 HD 4D 10P
- 1 HD 3D 4N
- 1 HD 3D 3N 5P
- 1 HD 3D 2N 10P
- 1 HD 3D 1N 15P
- 1 HD 3D 20P
- 1 HD 2D 6N
- 1 HD 2D 5N 5P
- 1 HD 2D 4N 10P
- 1 HD 2D 3N 15P
- 1 HD 2D 2N 20P
- 1 HD 2D 1N 25P
- 1 HD 2D 30P
- 1 HD 1D 8N
- 1 HD 1D 7N 5P
- 1 HD 1D 6N 10P
- 1 HD 1D 5N 15P
- 1 HD 1D 4N 20P
- 1 HD 1D 3N 25 P
- 1 HD 1D 2N 30 P
- 1 HD 1D 1N 35P
- 1 HD 1D 40P
- 1 HD 10N
- 1 HD 9N 5P
- 1 HD 8N 10P
- 1 HD 7N 15P
- 1 HD 6N 20P
- 1 HD 5N 25P
- 1 HD 4N 30P
- 1 HD 3N 35P
- 1 HD 2N 40P
- 1 HD 1N 45P
- 1 HD 50P
- 4Q
- 3Q 2D 1N
- 3Q 2D 5P
- 3Q 1D 3N
- 3Q 1D 2N 5P
- 3Q 1D 1N 10P
- 3Q 1D 15P
- 3Q 5N
- 3Q 4N 5P
- 3Q 3N 10P
- 3Q 2N 15P
- 3Q 1N 20P
- 3Q 25P
- 2Q 5D
- 2Q 4D 2N
- 2Q 4D 1N 5P
- 2Q 4D 10P
- 2Q 3D 4N
- 2Q 3D 3N 5P
- 2Q 3D 2N 10P
- 2Q 3D 1N 15P
- 2Q 3D 20P
- 2Q 2D 6N
- 2Q 2D 5N 5P
- 2Q 2D 4N 10P
- 2Q 2D 3N 15P
- 2Q 2D 2N 20P
- 2Q 2D 1N 25P
- 2Q 2D 30P
- 2Q 1D 8N
- 2Q 1D 7N 5P
- 2Q 1D 6N 10P
- 2Q 1D 5N 15P
- 2Q 1D 4N 20P
- 2Q 1D 3N 25P
- 2Q 1D 2N 30P
- 2Q 1D 1N 35P
- 2Q 1D 40P
- 2Q 50P
- 2Q 10N
- 2Q 9N 5P
- 2Q 8N 10P
- 2Q 7N 15P
- 2Q 6N 20P
- 2Q 5N 25P
- 2Q 4N 30P
- 2Q 3N 35P
- 2Q 2N 40P
- 2Q 1N 45P
- 1Q 7D 1N
- 1Q 7D 5P
- 1Q 6D 3N
- 1Q 6D 2N 5P
- 1Q 6D 1N 10P
- 1Q 6D 15P
- 1Q 5D 5N
- 1Q 5D 4N 5P
- 1Q 5D 3N 10P
- 1Q 5D 2N 15P
- 1Q 5D 1N 20P
- 1Q 5D 25P
- 1Q 4D 7N
- 1Q 4D 6N 5P
- 1Q 4D 5N 10P
- 1Q 4D 4N 15P
- 1Q 4D 3N 20P
- 1Q 4D 2N 25P
- 1Q 4D 1N 30P
- 1Q 4D 35P
- 1Q 3D 9N
- 1Q 3D 8N 5P
- 1Q 3D 7N 10P
- 1Q 3D 6N 15P
- 1Q 3D 5N 20P
- 1Q 3D 4N 25P
- 1Q 3D 3N 30P
- 1Q 3D 2N 35P
- 1Q 3D 1N 40P
- 1Q 3D 45P
- 1Q 2D 11N
- 1Q 2D 10N 5P
- 1Q 2D 9N 10P
- 1Q 2D 8N 15P
- 1Q 2D 7N 20P
- 1Q 2D 6N 25P
- 1Q 2D 5N 30P
- 1Q 2D 4N 35P
- 1Q 2D 3N 40P
- 1Q 2D 2N 45P
- 1Q 2D 1N 50P
- 1Q 2D 55P
- 1Q 1D 13N
- 1Q 1D 12N 5P
- 1Q 1D 11N 10P
- 1Q 1D 10N 15P
- 1Q 1D 9N 20P
- 1Q 1D 8N 25P
- 1Q 1D 7N 30P
- 1Q 1D 6N 35P
- 1Q 1D 5N 40P
- 1Q 1D 4N 45P
- 1Q 1D 3N 50P
- 1Q 1D 2N 55P
- 1Q 1D 1N 60P
- 1Q 1D 65P
- 1Q 15N
- 1Q 14N 5P
- 1Q 13N 10P
- 1Q 12N 15P
- 1Q 11N 20P
- 1Q 10N 25P
- 1Q 9N 30P
- 1Q 8N 35P
- 1Q 7N 40P
- 1Q 6N 45P
- 1Q 5N 50P
- 1Q 4N 55P
- 1Q 3N 60P
- 1Q 2N 65P
- 1Q 1N 70P
- 1Q 75P
- 10D
- 9D 2N
- 9D 1N 5P
- 9D 10P
- 8D 4N
- 8D 3N 5P
- 8D 2N 10P
- 8D 1N 15P
- 8D 20P
- 7D 6N
- 7D 5N 5P
- 7D 4N 10P
- 7D 3N 15P
- 7D 2N 20P
- 7D 1N 25P
- 7D 30P
- 6D 8N
- 6D 7N 5P
- 6D 6N 10P
- 6D 5N 15P
- 6D 4N 20P
- 6D 3N 25P
- 6D 2N 30P
- 6D 1N 35P
- 6D 40P
- 5D 10N
- 5D 9N 5P
- 5D 8N 10P
- 5D 7N 15P
- 5D 6N 20P
- 5D 5N 25P
- 5D 4N 30P
- 5D 3N 35P
- 5D 2N 40P
- 5D 1N 45P
- 5D 50P
- 4D 12N
- 4D 11N 5P
- 4D 10N 10P
- 4D 9N 15P
- 4D 8N 20P
- 4D 7N 25P
- 4D 6N 30P
- 4D 5N 35P
- 4D 4N 40P
- 4D 3N 45P
- 4D 2N 50P
- 4D 1N 55P
- 4D 60P
- 3D 14N
- 3D 13N 5P
- 3D 12N 10P
- 3D 11N 15P
- 3D 10N 20P
- 3D 9N 25P
- 3D 8N 30P
- 3D 7N 35P
- 3D 6N 40P
- 3D 5N 45P
- 3D 4N 50P
- 3D 3N 55P
- 3D 2N 60P
- 3D 1N 65P
- 3D 70P
- 2D 16N
- 2D 15N 5P
- 2D 14N 10P
- 2D 13N 15P
- 2D 12N 20P
- 2D 11N 25P
- 2D 10N 30P
- 2D 9N 35P
- 2D 8N 40P
- 2D 7N 45P
- 2D 6N 50P
- 2D 5N 55P
- 2D 4N 60P
- 2D 3N 65P
- 2D 2N 70P
- 2D 1N 75P
- 2D 80P
- 1D 18N
- 1D 17N 5P
- 1D 16N 10P
- 1D 15N 15P
- 1D 14N 20P
- 1D 13N 25P
- 1D 12N 30P
- 1D 11N 35P
- 1D 10N 40P
- 1D 9N 45P
- 1D 8N 50P
- 1D 7N 55P
- 1D 6N 60P
- 1D 5N 65P
- 1D 4N 70P
- 1D 3N 75P
- 1D 2N 80P
- 1D 1N 85P
- 1D 90P
- 20N
- 19N 5P
- 18N 10P
- 17N 15P
- 16N 20P
- 15N 25P
- 14N 30P
- 13N 35P
- 12N 40P
- 11N 45P
- 10N 50P
- 9N 55P
- 8N 60P
- 7N 65P
- 6N 70P
- 5N 75P
- 4N 80P
- 3N 85P
- 2N 90P
- 1N 95P
- 100P
The Data below is useless do not read or waist time the answer I could find is 13
I didn't put in the below information some assinide person did !
13
1.. H
2.. 2Q
3.. Q,2D,1N
4.. Q,2D,5P
5.. Q,1D,3N
6.. Q,1D,2N,5P
7.. Q,1D,1N,10P
8.. Q,1D,15P
9.. Q,5N
10 Q,4N,5P
11 Q,3N,10P
12 Q,2N.15P
13 Q,1N,20P
14 Q,25P
15 5D
16 4D,2N
17 4D,1N,5P
18 4D,10P
19 3D,4N
20 3D,3N,5P
21 3D,2N,10P
22 3D,1N,15P
23 3D,20P
24 2D,6N
25 2D,5N,5P
26 2D,4N,10P
27 2D,3N,15P
28 2D,2N,20P
29 2D,1N,25P
30 2D,30P
31 1D,8N
32 1D,7N,5P
33 1D,6N,10P
34 1D,5N,15P
35 1D,4N,20P
36 1D,3N,25P
37 1D,2N,30P
38 1D,1N,35P
39 1D,40P
40 10N
41 9N,5P
42 8N,10P
43 7N,15P
44 6N,20P
45 5N,25P
46 4N,30P
47 3N,35P
48 2N,40P
49 1N,45P
50 50P
1 dime, 1 nickel; 1 dime, 5 pennies; 3 nickels; 2 nickels, 5 pennies; 1 nickel, 10 pennies; 15 pennies. So there are six ways
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How many different ways can you make 50 cents in change?
how different ways can you make 50 cents in change
How many ways can you make change for 41 cents?
a lot of ways to change 41 cents
How many possible arrangements to make change for 35 cents?
The answer depends on the currency. The choice of coins for US cents is different to that for Euro cents, so the answer will be different.The answer depends on the currency. The choice of coins for US cents is different to that for Euro cents, so the answer will be different.The answer depends on the currency. The choice of coins for US cents is different to that for Euro cents, so the answer will be different.The answer depends on the currency. The choice of coins for US cents is different to that for Euro cents, so the answer will be different.
How many ways can you make 19 cents in change?
6
How many ways can you make 33 cents in change?
5
How many ways can you make change for 12 cents?
4
How many ways to make change for 22 cents?
Oh, what a happy little question! Let's see, to make 22 cents, you could use a combination of coins like 2 dimes and 2 pennies, or 1 dime, 3 nickels, and 2 pennies. There are several different ways to make change for 22 cents, so feel free to get creative and try out different combinations!
How many different ways can you make 185 cents?
11
How many ways to make 28 cents using nickels dimes pennies?
There are 13 different ways to make 28 cents.
How many different ways can you make change for 75 cents using quarters dimes and nickels?
Well, honey, let me break it down for you. You can use up to 3 quarters, 0-5 dimes, and 0-15 nickels to make 75 cents. So, there are a total of 4 ways to make change for 75 cents using quarters, dimes, and nickels. Hope that clears things up for ya!
How many different ways can you make 32 cents in US coins?
18
How many different combinations can you use to make 16 cents?
6 ways
