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# What is the explicit rule for An equals An-1 plus 5n-1?

Updated: 12/24/2022

Wiki User

8y ago

It is not possible to give a conclusive answer because for a recursive relationship of order 1, the first (or 0th) term must be specified.

A(n) = (5*n^2 + 3*n + 2*A(1) - 8)/2 for n = 1, 2, 3, ...

Wiki User

8y ago

Wiki User

8y ago

It is not possible to give an explicit rule for a sequence which is defined recursively without the initial value(s).

In this case, it is

A(n) = 2.5*n^2 + 1.5*n - 4 + A(1)

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Q: What is the explicit rule for An equals An-1 plus 5n-1?
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### How many ways can you make a dollar out of change?

1 dollar coin2 half dollars1 HD 1Q 2D IN1 HD 1Q 2D 5P1 HD 1Q 1D 3N1 HD 1Q 1D 2N 5P1 HD 1Q 1D 1N 10P1 HD 1Q 1D 15P1 HD 1Q 5N1 HD 1Q 4N 5P1 HD 1Q 3N 10P1 HD 1Q 2N 15P1 HD 1Q 1N 20 P1 HD 1Q 25P1 HD 5D1 HD 4D 2N1HD 4D 1N 5P1 HD 4D 10P1 HD 3D 4N1 HD 3D 3N 5P1 HD 3D 2N 10P1 HD 3D 1N 15P1 HD 3D 20P1 HD 2D 6N1 HD 2D 5N 5P1 HD 2D 4N 10P1 HD 2D 3N 15P1 HD 2D 2N 20P1 HD 2D 1N 25P1 HD 2D 30P1 HD 1D 8N1 HD 1D 7N 5P1 HD 1D 6N 10P1 HD 1D 5N 15P1 HD 1D 4N 20P1 HD 1D 3N 25 P1 HD 1D 2N 30 P1 HD 1D 1N 35P1 HD 1D 40P1 HD 10N1 HD 9N 5P1 HD 8N 10P1 HD 7N 15 P1 HD 6N 20P1 HD 5N 25P1 HD 4N 30P1HD 3N 35P1 HD 2N 40P1 HD 1N 45P1 HD 50P4Q3Q 2D 1N3Q 2D 5P3Q 1D 3N3Q 1D 2N 5P3Q 1D 1N 10P3Q 1D 15P3Q 5N3Q 4N 5P3Q 3N 10P3Q 2N 15P3Q 1N 20 P3Q 25P2Q 5D2Q 4D 2N2Q 4D 1N 5P2Q 4D 10P2Q 3D 4N2Q 3D 3N 5 P2Q 3D 2N 10P2Q 3D 1N 15P2Q 3D 20P2Q 2D 6N2Q 2D 5N 5P2Q 2D 4N 10 P2Q 2D 3N 15P2Q 2D 2N 20P2Q 2D 1N 25P2Q 2D 30P2Q 1D 8N2Q 1D 7N 5P2Q 1D 6N 10P2Q 1D 5N 15P2Q 1D 4N 20P2Q 1D 3N 25P2Q 1D 2N 30P2Q 1D 1N 35P2Q 1D 40P2Q 50P2Q 10N2Q 9N 5P2Q 8N 10P2Q 7N 15P2Q 6N 20P2Q 5N 25P2Q 4N 30P2Q 3N 35P2Q 2N 40P2Q 1N 45P1Q 7D 1N1Q 7D 5P1Q 6D 3N1Q 6D 2N 5P1Q 6D 1N 10P1Q 6D 15P1Q 5D 5N1Q 5D 4N 5P1Q 5D 3N 10P1Q 5D 2N 15P1Q 5D 1N 20P1Q 5D 25P1Q 4D 7N1Q 4D 6N 5P1Q 4D 5N 15P1Q 4D 4N 20P1Q 4D 3N 25P1Q 4D 2N 30P1Q 4D 1N 35P1Q 4D 40P1Q 3D 9N1Q 3D 8N 5PQ 3D 7N 10P1Q 3D 6N 15P1Q 3D 5N 20P1Q 3D 4N 25P1Q 3D 3N 30P1Q 3D 2N 35P1Q 3D 1N 40P1Q 3D 45P1Q 2D 11N1Q 2D 10N 5P1Q 2D 9N 10P1Q 2D 8N 15P1Q 2D 7N 20 P1Q 2D 6N 25P1Q 2D 5N 30P1Q 2D 4N 35P1Q 2D 3N 40P1Q 2D 2N 45P1Q 2D 1N 50P1Q 2D 55P1Q 1D 13N1Q 1D 12N 5P1Q 1D 11N 10P1Q 1D 10N 15P1Q 1D 9N 20P1Q 1D 8N 25P1Q 1D 7N 30P1Q 1D 6N 35P1Q 1D 5N 40P1Q 1D 4N 45P1Q 1D 3N 50P1Q 1D 2N 55P1Q 1D 1N 60P1Q 1D 65P1Q 15N1Q 14N 5P1Q 13N 10P1Q 12N 15P1Q 11N 20P1Q 10N 25P1Q 9N 30P1Q 8N 35P1Q 7N 40P1Q 6N 45P1Q 5N 50P1Q 4N 55P1Q 3N 60P1Q 2N 65P1Q 1N 70P1Q 75P10D9D 2N9D 1N 5P9D 10P8D 4N8D 3N 5P8D 2N 10P8D 1N 15P8D 20P7D 6N7D 5N 5P7D 4N 10P7D 3N 15P7D 2N 20P7D 1N 25P7D 30P6D 8N6D 7N 5P6D 6N 10P6D 5N 15P6D 4N 20P6D 3N 25P6D 2N 30P6D 1N 35P6D 40P5D 10N5D 9N 5P5D 8N 10P5D 7N 15P5D 6N 20P5D 5N 25P5D 4N 30P5D 3N 35P5D 2N 40P5D 1N 45P5D 50P4D 12N4D 11N 5P4D 10N 10P4D 9N 15P4D 8N 20P4D 7N 25P4D 6N 30P4D 5N 35P4D 4N 40P4D 3N 45P4D 2N 50P4D 1N 55P4D 60P3D 14N3D 13N 5P3D 12N 10P3D 11N 15P3D 10N 20P3D 9N 25P3D 8N 30P3D 7N 35P3D 6N 40P3D 5N 45P3D 4N 50P3D 3N 55P3D 2N 60P3D 1N 65P3D 70P2D 16N2D 15N 5P2D 14N 10P2D 13N 15P2D 12N 20P2D 11N 25P2D 10N 30P2D 9N 35P2D 8N 40P2D 7N 45P2D 6N 50P2D 5N 55P2D 4N 60P2D 3N 65P2D 2N 70P2D 1N 75P2D 80P1D 18N1D 17N 5P1D 16N 10P1D 15N 15P1D 14N 20P1D 13N 25P1D 12N 30P1D 11N 35P1D 10N 40P1D 9N 45P1D 8N 50P1D 7N 55P1D 6N 60P1D 5N 65P1D 4N 70P1D 3N 75P1D 2N 80P1D 1N 85P1D 90P20N19N 5P18N 10P17N 15P16N 20P15N 25P14N 30P13N 35P12N 40P11N 45P10N 50P9N 55P8N 60P7N 65P6N 70P5N 75P4N 80P3N 85P2N 90P1N 95P100P1 HD 2Q

### How many ways can you make a dollar?

1 dollar coin2 half dollars1 HD 1Q 2D IN1 HD 1Q 2D 5P1 HD 1Q 1D 3N1 HD 1Q 1D 2N 5P1 HD 1Q 1D 1N 10P1 HD 1Q 1D 15P1 HD 1Q 5N1 HD 1Q 4N 5P1 HD 1Q 3N 10P1 HD 1Q 2N 15P1 HD 1Q 1N 20 P1 HD 1Q 25P1 HD 5D1 HD 4D 2N1HD 4D 1N 5P1 HD 4D 10P1 HD 3D 4N1 HD 3D 3N 5P1 HD 3D 2N 10P1 HD 3D 1N 15P1 HD 3D 20P1 HD 2D 6N1 HD 2D 5N 5P1 HD 2D 4N 10P1 HD 2D 3N 15P1 HD 2D 2N 20P1 HD 2D 1N 25P1 HD 2D 30P1 HD 1D 8N1 HD 1D 7N 5P1 HD 1D 6N 10P1 HD 1D 5N 15P1 HD 1D 4N 20P1 HD 1D 3N 25 P1 HD 1D 2N 30 P1 HD 1D 1N 35P1 HD 1D 40P1 HD 10N1 HD 9N 5P1 HD 8N 10P1 HD 7N 15 P1 HD 6N 20P1 HD 5N 25P1 HD 4N 30P1HD 3N 35P1 HD 2N 40P1 HD 1N 45P1 HD 50P4Q3Q 2D 1N3Q 2D 5P3Q 1D 3N3Q 1D 2N 5P3Q 1D 1N 10P3Q 1D 15P3Q 5N3Q 4N 5P3Q 3N 10P3Q 2N 15P3Q 1N 20 P3Q 25P2Q 5D2Q 4D 2N2Q 4D 1N 5P2Q 4D 10P2Q 3D 4N2Q 3D 3N 5 P2Q 3D 2N 10P2Q 3D 1N 15P2Q 3D 20P2Q 2D 6N2Q 2D 5N 5P2Q 2D 4N 10 P2Q 2D 3N 15P2Q 2D 2N 20P2Q 2D 1N 25P2Q 2D 30P2Q 1D 8N2Q 1D 7N 5P2Q 1D 6N 10P2Q 1D 5N 15P2Q 1D 4N 20P2Q 1D 3N 25P2Q 1D 2N 30P2Q 1D 1N 35P2Q 1D 40P2Q 50P2Q 10N2Q 9N 5P2Q 8N 10P2Q 7N 15P2Q 6N 20P2Q 5N 25P2Q 4N 30P2Q 3N 35P2Q 2N 40P2Q 1N 45P1Q 7D 1N1Q 7D 5P1Q 6D 3N1Q 6D 2N 5P1Q 6D 1N 10P1Q 6D 15P1Q 5D 5N1Q 5D 4N 5P1Q 5D 3N 10P1Q 5D 2N 15P1Q 5D 1N 20P1Q 5D 25P1Q 4D 7N1Q 4D 6N 5P1Q 4D 5N 15P1Q 4D 4N 20P1Q 4D 3N 25P1Q 4D 2N 30P1Q 4D 1N 35P1Q 4D 40P1Q 3D 9N1Q 3D 8N 5PQ 3D 7N 10P1Q 3D 6N 15P1Q 3D 5N 20P1Q 3D 4N 25P1Q 3D 3N 30P1Q 3D 2N 35P1Q 3D 1N 40P1Q 3D 45P1Q 2D 11N1Q 2D 10N 5P1Q 2D 9N 10P1Q 2D 8N 15P1Q 2D 7N 20 P1Q 2D 6N 25P1Q 2D 5N 30P1Q 2D 4N 35P1Q 2D 3N 40P1Q 2D 2N 45P1Q 2D 1N 50P1Q 2D 55P1Q 1D 13N1Q 1D 12N 5P1Q 1D 11N 10P1Q 1D 10N 15P1Q 1D 9N 20P1Q 1D 8N 25P1Q 1D 7N 30P1Q 1D 6N 35P1Q 1D 5N 40P1Q 1D 4N 45P1Q 1D 3N 50P1Q 1D 2N 55P1Q 1D 1N 60P1Q 1D 65P1Q 15N1Q 14N 5P1Q 13N 10P1Q 12N 15P1Q 11N 20P1Q 10N 25P1Q 9N 30P1Q 8N 35P1Q 7N 40P1Q 6N 45P1Q 5N 50P1Q 4N 55P1Q 3N 60P1Q 2N 65P1Q 1N 70P1Q 75P10D9D 2N9D 1N 5P9D 10P8D 4N8D 3N 5P8D 2N 10P8D 1N 15P8D 20P7D 6N7D 5N 5P7D 4N 10P7D 3N 15P7D 2N 20P7D 1N 25P7D 30P6D 8N6D 7N 5P6D 6N 10P6D 5N 15P6D 4N 20P6D 3N 25P6D 2N 30P6D 1N 35P6D 40P5D 10N5D 9N 5P5D 8N 10P5D 7N 15P5D 6N 20P5D 5N 25P5D 4N 30P5D 3N 35P5D 2N 40P5D 1N 45P5D 50P4D 12N4D 11N 5P4D 10N 10P4D 9N 15P4D 8N 20P4D 7N 25P4D 6N 30P4D 5N 35P4D 4N 40P4D 3N 45P4D 2N 50P4D 1N 55P4D 60P3D 14N3D 13N 5P3D 12N 10P3D 11N 15P3D 10N 20P3D 9N 25P3D 8N 30P3D 7N 35P3D 6N 40P3D 5N 45P3D 4N 50P3D 3N 55P3D 2N 60P3D 1N 65P3D 70P2D 16N2D 15N 5P2D 14N 10P2D 13N 15P2D 12N 20P2D 11N 25P2D 10N 30P2D 9N 35P2D 8N 40P2D 7N 45P2D 6N 50P2D 5N 55P2D 4N 60P2D 3N 65P2D 2N 70P2D 1N 75P2D 80P1D 18N1D 17N 5P1D 16N 10P1D 15N 15P1D 14N 20P1D 13N 25P1D 12N 30P1D 11N 35P1D 10N 40P1D 9N 45P1D 8N 50P1D 7N 55P1D 6N 60P1D 5N 65P1D 4N 70P1D 3N 75P1D 2N 80P1D 1N 85P1D 90P20N19N 5P18N 10P17N 15P16N 20P15N 25P14N 30P13N 35P12N 40P11N 45P10N 50P9N 55P8N 60P7N 65P6N 70P5N 75P4N 80P3N 85P2N 90P1N 95P100P1 HD 2Q

### How many ways can you make change for a dollar?

293 different ways to mke change for a dollar.There are quite a few ways to make change for a dollar. Here they are:1 dollar coin2 half dollars1 HD 2Q1 HD 1Q 2D IN1 HD 1Q 2D 5P1 HD 1Q 1D 3N1 HD 1Q 1D 2N 5P1 HD 1Q 1D 1N 10P1 HD 1Q 1D 15P1 HD 1Q 5N1 HD 1Q 4N 5P1 HD 1Q 3N 10P1 HD 1Q 2N 15P1 HD 1Q 1N 20P1 HD 1Q 25P1 HD 5D1 HD 4D 2N1 HD 4D 1N 5P1 HD 4D 10P1 HD 3D 4N1 HD 3D 3N 5P1 HD 3D 2N 10P1 HD 3D 1N 15P1 HD 3D 20P1 HD 2D 6N1 HD 2D 5N 5P1 HD 2D 4N 10P1 HD 2D 3N 15P1 HD 2D 2N 20P1 HD 2D 1N 25P1 HD 2D 30P1 HD 1D 8N1 HD 1D 7N 5P1 HD 1D 6N 10P1 HD 1D 5N 15P1 HD 1D 4N 20P1 HD 1D 3N 25 P1 HD 1D 2N 30 P1 HD 1D 1N 35P1 HD 1D 40P1 HD 10N1 HD 9N 5P1 HD 8N 10P1 HD 7N 15P1 HD 6N 20P1 HD 5N 25P1 HD 4N 30P1 HD 3N 35P1 HD 2N 40P1 HD 1N 45P1 HD 50P4Q3Q 2D 1N3Q 2D 5P3Q 1D 3N3Q 1D 2N 5P3Q 1D 1N 10P3Q 1D 15P3Q 5N3Q 4N 5P3Q 3N 10P3Q 2N 15P3Q 1N 20P3Q 25P2Q 5D2Q 4D 2N2Q 4D 1N 5P2Q 4D 10P2Q 3D 4N2Q 3D 3N 5P2Q 3D 2N 10P2Q 3D 1N 15P2Q 3D 20P2Q 2D 6N2Q 2D 5N 5P2Q 2D 4N 10P2Q 2D 3N 15P2Q 2D 2N 20P2Q 2D 1N 25P2Q 2D 30P2Q 1D 8N2Q 1D 7N 5P2Q 1D 6N 10P2Q 1D 5N 15P2Q 1D 4N 20P2Q 1D 3N 25P2Q 1D 2N 30P2Q 1D 1N 35P2Q 1D 40P2Q 50P2Q 10N2Q 9N 5P2Q 8N 10P2Q 7N 15P2Q 6N 20P2Q 5N 25P2Q 4N 30P2Q 3N 35P2Q 2N 40P2Q 1N 45P1Q 7D 1N1Q 7D 5P1Q 6D 3N1Q 6D 2N 5P1Q 6D 1N 10P1Q 6D 15P1Q 5D 5N1Q 5D 4N 5P1Q 5D 3N 10P1Q 5D 2N 15P1Q 5D 1N 20P1Q 5D 25P1Q 4D 7N1Q 4D 6N 5P1Q 4D 5N 15P1Q 4D 4N 20P1Q 4D 3N 25P1Q 4D 2N 30P1Q 4D 1N 35P1Q 4D 40P1Q 3D 9N1Q 3D 8N 5P1Q 3D 7N 10P1Q 3D 6N 15P1Q 3D 5N 20P1Q 3D 4N 25P1Q 3D 3N 30P1Q 3D 2N 35P1Q 3D 1N 40P1Q 3D 45P1Q 2D 11N1Q 2D 10N 5P1Q 2D 9N 10P1Q 2D 8N 15P1Q 2D 7N 20P1Q 2D 6N 25P1Q 2D 5N 30P1Q 2D 4N 35P1Q 2D 3N 40P1Q 2D 2N 45P1Q 2D 1N 50P1Q 2D 55P1Q 1D 13N1Q 1D 12N 5P1Q 1D 11N 10P1Q 1D 10N 15P1Q 1D 9N 20P1Q 1D 8N 25P1Q 1D 7N 30P1Q 1D 6N 35P1Q 1D 5N 40P1Q 1D 4N 45P1Q 1D 3N 50P1Q 1D 2N 55P1Q 1D 1N 60P1Q 1D 65P1Q 15N1Q 14N 5P1Q 13N 10P1Q 12N 15P1Q 11N 20P1Q 10N 25P1Q 9N 30P1Q 8N 35P1Q 7N 40P1Q 6N 45P1Q 5N 50P1Q 4N 55P1Q 3N 60P1Q 2N 65P1Q 1N 70P1Q 75P10D9D 2N9D 1N 5P9D 10P8D 4N8D 3N 5P8D 2N 10P8D 1N 15P8D 20P7D 6N7D 5N 5P7D 4N 10P7D 3N 15P7D 2N 20P7D 1N 25P7D 30P6D 8N6D 7N 5P6D 6N 10P6D 5N 15P6D 4N 20P6D 3N 25P6D 2N 30P6D 1N 35P6D 40P5D 10N5D 9N 5P5D 8N 10P5D 7N 15P5D 6N 20P5D 5N 25P5D 4N 30P5D 3N 35P5D 2N 40P5D 1N 45P5D 50P4D 12N4D 11N 5P4D 10N 10P4D 9N 15P4D 8N 20P4D 7N 25P4D 6N 30P4D 5N 35P4D 4N 40P4D 3N 45P4D 2N 50P4D 1N 55P4D 60P3D 14N3D 13N 5P3D 12N 10P3D 11N 15P3D 10N 20P3D 9N 25P3D 8N 30P3D 7N 35P3D 6N 40P3D 5N 45P3D 4N 50P3D 3N 55P3D 2N 60P3D 1N 65P3D 70P2D 16N2D 15N 5P2D 14N 10P2D 13N 15P2D 12N 20P2D 11N 25P2D 10N 30P2D 9N 35P2D 8N 40P2D 7N 45P2D 6N 50P2D 5N 55P2D 4N 60P2D 3N 65P2D 2N 70P2D 1N 75P2D 80P1D 18N1D 17N 5P1D 16N 10P1D 15N 15P1D 14N 20P1D 13N 25P1D 12N 30P1D 11N 35P1D 10N 40P1D 9N 45P1D 8N 50P1D 7N 55P1D 6N 60P1D 5N 65P1D 4N 70P1D 3N 75P1D 2N 80P1D 1N 85P1D 90P20N19N 5P18N 10P17N 15P16N 20P15N 25P14N 30P13N 35P12N 40P11N 45P10N 50P9N 55P8N 60P7N 65P6N 70P5N 75P4N 80P3N 85P2N 90P1N 95P100PHope that helped!!!!

### How many ways can you give change for one dollar?

293 ways.Using pennies, nickels, dimes, quarters, half-dollars and dollar coins, there are 293 ways to make change for one dollar in US currency.Method 1:Using pennies, nickels, dimes, quarters, and half-dollars there are 292 ways to make change for one dollar. In general, to make change for h half-dollars using these coins there are (6 + 55*h + 119*h2 + 95*h3 + 25*h4)/6 ways. For example, putting h=1 gives 50 ways of making change for fifty cents, or h=2 gives 292 ways of making change for dollar etc.[[ The 292 ways computed above, includes fifty-cent pieces but not the dollar coin so, we must add one more in order to agree with the second method shown below. ]]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 one us dollar.[[ if we use no dollar coins or half dollars (only pennies, nickels, dimes and quarters) the method 2 gives 242 ways to make a dollar. Those 242 ways begin with line 52. ]]Indisputable Tally of Combinations1 dollar coin2 half dollars1 HD 2Q1 HD 1Q 2D IN1 HD 1Q 2D 5P1 HD 1Q 1D 3N1 HD 1Q 1D 2N 5P1 HD 1Q 1D 1N 10P1 HD 1Q 1D 15P1 HD 1Q 5N1 HD 1Q 4N 5P1 HD 1Q 3N 10P1 HD 1Q 2N 15P1 HD 1Q 1N 20P1 HD 1Q 25P1 HD 5D1 HD 4D 2N1 HD 4D 1N 5P1 HD 4D 10P1 HD 3D 4N1 HD 3D 3N 5P1 HD 3D 2N 10P1 HD 3D 1N 15P1 HD 3D 20P1 HD 2D 6N1 HD 2D 5N 5P1 HD 2D 4N 10P1 HD 2D 3N 15P1 HD 2D 2N 20P1 HD 2D 1N 25P1 HD 2D 30P1 HD 1D 8N1 HD 1D 7N 5P1 HD 1D 6N 10P1 HD 1D 5N 15P1 HD 1D 4N 20P1 HD 1D 3N 25 P1 HD 1D 2N 30 P1 HD 1D 1N 35P1 HD 1D 40P1 HD 10N1 HD 9N 5P1 HD 8N 10P1 HD 7N 15P1 HD 6N 20P1 HD 5N 25P1 HD 4N 30P1 HD 3N 35P1 HD 2N 40P1 HD 1N 45P1 HD 50P4Q3Q 2D 1N3Q 2D 5P3Q 1D 3N3Q 1D 2N 5P3Q 1D 1N 10P3Q 1D 15P3Q 5N3Q 4N 5P3Q 3N 10P3Q 2N 15P3Q 1N 20P3Q 25P2Q 5D2Q 4D 2N2Q 4D 1N 5P2Q 4D 10P2Q 3D 4N2Q 3D 3N 5P2Q 3D 2N 10P2Q 3D 1N 15P2Q 3D 20P2Q 2D 6N2Q 2D 5N 5P2Q 2D 4N 10P2Q 2D 3N 15P2Q 2D 2N 20P2Q 2D 1N 25P2Q 2D 30P2Q 1D 8N2Q 1D 7N 5P2Q 1D 6N 10P2Q 1D 5N 15P2Q 1D 4N 20P2Q 1D 3N 25P2Q 1D 2N 30P2Q 1D 1N 35P2Q 1D 40P2Q 50P2Q 10N2Q 9N 5P2Q 8N 10P2Q 7N 15P2Q 6N 20P2Q 5N 25P2Q 4N 30P2Q 3N 35P2Q 2N 40P2Q 1N 45P1Q 7D 1N1Q 7D 5P1Q 6D 3N1Q 6D 2N 5P1Q 6D 1N 10P1Q 6D 15P1Q 5D 5N1Q 5D 4N 5P1Q 5D 3N 10P1Q 5D 2N 15P1Q 5D 1N 20P1Q 5D 25P1Q 4D 7N1Q 4D 6N 5P1Q 4D 5N 15P1Q 4D 4N 20P1Q 4D 3N 25P1Q 4D 2N 30P1Q 4D 1N 35P1Q 4D 40P1Q 3D 9N1Q 3D 8N 5P1Q 3D 7N 10P1Q 3D 6N 15P1Q 3D 5N 20P1Q 3D 4N 25P1Q 3D 3N 30P1Q 3D 2N 35P1Q 3D 1N 40P1Q 3D 45P1Q 2D 11N1Q 2D 10N 5P1Q 2D 9N 10P1Q 2D 8N 15P1Q 2D 7N 20P1Q 2D 6N 25P1Q 2D 5N 30P1Q 2D 4N 35P1Q 2D 3N 40P1Q 2D 2N 45P1Q 2D 1N 50P1Q 2D 55P1Q 1D 13N1Q 1D 12N 5P1Q 1D 11N 10P1Q 1D 10N 15P1Q 1D 9N 20P1Q 1D 8N 25P1Q 1D 7N 30P1Q 1D 6N 35P1Q 1D 5N 40P1Q 1D 4N 45P1Q 1D 3N 50P1Q 1D 2N 55P1Q 1D 1N 60P1Q 1D 65P1Q 15N1Q 14N 5P1Q 13N 10P1Q 12N 15P1Q 11N 20P1Q 10N 25P1Q 9N 30P1Q 8N 35P1Q 7N 40P1Q 6N 45P1Q 5N 50P1Q 4N 55P1Q 3N 60P1Q 2N 65P1Q 1N 70P1Q 75P10D9D 2N9D 1N 5P9D 10P8D 4N8D 3N 5P8D 2N 10P8D 1N 15P8D 20P7D 6N7D 5N 5P7D 4N 10P7D 3N 15P7D 2N 20P7D 1N 25P7D 30P6D 8N6D 7N 5P6D 6N 10P6D 5N 15P6D 4N 20P6D 3N 25P6D 2N 30P6D 1N 35P6D 40P5D 10N5D 9N 5P5D 8N 10P5D 7N 15P5D 6N 20P5D 5N 25P5D 4N 30P5D 3N 35P5D 2N 40P5D 1N 45P5D 50P4D 12N4D 11N 5P4D 10N 10P4D 9N 15P4D 8N 20P4D 7N 25P4D 6N 30P4D 5N 35P4D 4N 40P4D 3N 45P4D 2N 50P4D 1N 55P4D 60P3D 14N3D 13N 5P3D 12N 10P3D 11N 15P3D 10N 20P3D 9N 25P3D 8N 30P3D 7N 35P3D 6N 40P3D 5N 45P3D 4N 50P3D 3N 55P3D 2N 60P3D 1N 65P3D 70P2D 16N2D 15N 5P2D 14N 10P2D 13N 15P2D 12N 20P2D 11N 25P2D 10N 30P2D 9N 35P2D 8N 40P2D 7N 45P2D 6N 50P2D 5N 55P2D 4N 60P2D 3N 65P2D 2N 70P2D 1N 75P2D 80P1D 18N1D 17N 5P1D 16N 10P1D 15N 15P1D 14N 20P1D 13N 25P1D 12N 30P1D 11N 35P1D 10N 40P1D 9N 45P1D 8N 50P1D 7N 55P1D 6N 60P1D 5N 65P1D 4N 70P1D 3N 75P1D 2N 80P1D 1N 85P1D 90P20N19N 5P18N 10P17N 15P16N 20P15N 25P14N 30P13N 35P12N 40P11N 45P10N 50P9N 55P8N 60P7N 65P6N 70P5N 75P4N 80P3N 85P2N 90P1N 95P100PWHEW!!!

### How many different ways can you make 15 cents in change?

9 ways: 20 pennies 1 nickel 15 pennies 2 nickles 10 pennies 3 nickels 5 pennies 4 nickels 1 dime 10 pennies 1 dime 1 nickel 5 pennies 1 dime 2 nickels 2 dimes.