How many ways can you make change for a quarter(25cents)?

Question

Is there a a pattern? How many ways????

Answer 1

Process of elimination?

There are lots of ways to do it...

I would start with the largest denomination and find all the ways to do it and work your way down.

Start with a dime (the largest) and then the second largest (nickel)

2d 1n

Then replace just the nickel with the next smallest (penny)

2d 5p

Now replace one of those dimes with the next smallest (nickels)

1d 3n

Now replace one of those nickels with the next smallest

1d 2n 5p

Now replace the second nickel with the next smallest

1d 1n 10p

Now the last nickel is replaced.

1d 15 p

Now replace your last dime with nickels

5n

4n 5p

3n 10p

2n 15p

1n 20p

Now replace your last nickel with the next smallest

25p

remember not to use 1n 1d 10p as that's the same as the 1d 1n 10p that you used earlier.

I think that results in 12 different ways.

Answer 2

I think the only way to do this is to list all of the ways, but it will help if you follow a pattern in doing that. I suggest you start with the biggest coin available, and work down. For each coin, take it off the total and work out the number of ways you can make the resulting amount using nothing bigger than the coin you started with. I'm not sure what coins you have in the USA -- is it 1c, 5c, 10c, 25c? Then start with 25c. In that case, job done. That's one way. Now start with 10c. Take that 10c off the total to get 15c, and you have a new problem: how many ways can you make 15c (using nothing bigger than 10c, but that's not an issue here). Well do the same trick: start high, with a 10c coin, and you're left with 5c to make. Now you have another new problem: How many ways can you make 5c? Just keep going like that, and you should end up with something like

25c

10c 10c 5c

10c 10c 1c 1c 1c 1c 1c

10c 5c 5c 5c

10c 5c 5c 1c 1c 1c 1c 1c

10c 5c 1c 1c 1c 1c 1c 1c 1c 1c 1c 1c

and so on. If you're doing a computer programming class, this sort of problem is a cinch, by the way!

Answer 3

are u trying to get us to do ur hmework cause if u are and i answer this question ur probably going to get the answer wrong cause i suck at math lol