how many combo's for 28 cents, using penies, nickles, dimes, and quarters?

Answer 1

You can solve this problem using generating functions. A generating function is an infinite polynomial whose coefficients are the numbers you're interested in.

For instance, the infinite polynomial
1 + x + x^2 + x^3 + x^4 + .,.. = 1/(1-x)
has all ones for each coefficient on the powers of x. You can interpret the coefficient of x^n as the number of ways to make change for n cents with pennies.

You can also do this for nickles. If we are allowed to use only nickels, then the only amounts that can be changed are the multiples of 5, each of which can thus be changed in a single way
1 + x^5 + x^10 + x^15 + x^20 + ... = 1/(1-x^5)

dimes, and quarters are similar
1 + x^10 + x^20 + x^30 + ... = 1/(1-x^10)
1 + x^25 + x^50 + x^75 + ... = 1/(1-x^25)

The product of these functions lists the number of ways in which various amounts could be changed with pennies, nickels, dimes, and quarters. So you're interested in the coefficient of the x^28 term in the expansion of:

1/(1-x) * 1/(1-x^5) * 1/(1-x^10) * 1/(1-x^25)

Expanding this out, you get 13 for the coefficient.

You can check this by being clever with binomial coefficients.

Answer 2

The two above answers are missing a couple combos.
I get 13:
P=pennies, D=dimes, N=nickels, and Q=quarters

28 P
1 N + 23 P
2 N + 18 P
3 N + 13 P
4 N + 8 P
5 N + 8 P
1 D + 18 P
2 D + 8 P
1 Q + 3 P
1 N + 1 D + 13 P
2 N + 1 D + 8 P
3 N + 1 D + 3 P
1 N + 2 D + 3 P

Answer 3

1 quarter + 3 pennies
2 dimes + 1 nickel +3 pennies
2 dimes + 8 pennies
1 dime + 3 nickels +3 pennies
1 dime + 2 nickels + 8 pennies
1 dime + 1 nickel + 13 pennies
1 dime + 18 pennies
5 nickels + 3 pennies
4 nickels + 8 pennies
3 nickels + 13 pennies
2 nickels + 18 pennies
1 nickel + 23 pennies
28 pennies

I make that 13 ways of making up 28 cents using quarters, dimes, nickels and pennies.

As a tip for doing another question start by choosing the max possible number of the largest coin. Then add the max number of the next coin and so on. Then one at a time you break the coins into the smaller ones.

Answer 4

i could tell human beings to place a coin on my nostril and with my tongue in basic terms i visit seize it and slide it into my mouth..i myself can try this...I tell them beforehand hand that quarters are lots much less confusing and then afterwards I provide them a small flag and a tootsie roll or a jolly rancher.

Answer 5

I've got thirteen:

1Q and 3 P
2D and 1N and 3P
2D and 8P
1D and 2N and 8P
1D and 3N and 3P
1D and 1N and 13 P
1D and 18P
5N and 3P
4N and8P
3N and 13P
2N and 18P
1N and 23P
28 P

Answer 6

Well now, that depends on if you SUPERSIZE your fries or not.