h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

In US money, there are Pennies, Nickels, Dimes, and Quarters and Fifty Cents.
A Penny coin is one cent.
A Nickle is five cents.
A Dime is 10 cents.
A quarter is twenty-five cents.
A Fifty Cents coin is, you guessed it, fifty cents.

So... How many ways are there to make one dollar out of coins?
Can you make it out? Is there a reasonable approach to calculate it?

Y.

An algorithm wouldn't be difficult, but please don't ask me to write one now - I'll leave that, erm, as an exercise for my students.

Interesting. And more complicated in the UK where we also have an extra coin.

1p
2p
5p
10p
20p
50p

I'm off to raid my piggy bank to work it out.

Back in a couple of years.......

PP.

292 ways apparently in acording to Google

Now work it out if one of the pennies is a Lincoln cent.

No. You could make things vastly more complicated in all sorts of ways -- Wheat pattern patterns, Indian-head pennies, quarters for each of the fifty states -- but shouldn't a penny be *just* a penny? If it's worth one cent, it should be regarded as worth any other penny that's worth one cent. I think the concept is called fungibility.

Yes, but it shows the value of an algorithm - you can parametrise for this sort of thing.

I'm not saying it isn't useful in some ways. Chances are, though, that a shop clerk who has to make quick change for a dollar is going to go with the fastest and easiest way, not stop to calculate all the possible combinations. Occam's razor, that sort of thing.

Permutations and combinations maths - get thee back to the classroom - A level maths in the UK this sort of thing

The world is my classroom now. I learn lots of new things every day.