Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

Would you mind elaborating how you got the recurrence in a simpler way?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

Offline

**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,037

Okay, so, we think, how can we group the n snails into k groups, given a smaller grouping with n-1 snails. The first case is if we group the n-1 snails. If we do that, the last snail goes into a group of its own, and that group can be put in between any two other in k ways, so that would be k*a(n-1,k-1).

The other case is when the n-1 snails are already grouped into k groups. There we just have to put the last snails into one of those groups, which we can also do in k ways, so the total number of ways for this case is k*a(n-1,k). Just add the two, and there you have it.

*Last edited by anonimnystefy (2014-09-23 01:19:35)*

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

Offline

Thanks a lot

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

Offline

**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,037

No problem.

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

Offline

**gAr****Member**- Registered: 2011-01-09
- Posts: 3,481

Hi,

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

Offline

**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi gAr;

That is correct! Very good.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

Offline

**javanaut****Member**- Registered: 2016-02-02
- Posts: 5

Anybody,

How did gAr get that result?

Is there something like "combinatorics for dummies" on the web?

I did discover something exciting (to me, but seems trivial now). Distributing n snails among k people (where all the snails are the same):

Since we start with 1 for each person, it's n = 20 - 4 = 16

Any help on this notation gAr used would be appreciated.

Offline

**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Is it the sigma notation or the derivation of his result that is puzzling?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

Offline

**javanaut****Member**- Registered: 2016-02-02
- Posts: 5

Hi Bobby,

Actually, the derivation ...

Offline

**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Is there something like "combinatorics for dummies" on the web?

There are no smarties when it comes to Combinatorics, it is hard for everybody.

I think the best start is from the book Applied Combinatorics by Alan Tucker.

If you noticed each person solved the problem in a different way. I used a gf like EVW did. How gAr came up with his answer I do not know. I sometimes can not even describe my own methods to another person.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

Offline

**javanaut****Member**- Registered: 2016-02-02
- Posts: 5

Thank you gAr and Elaine these are beautiful solutions. I understand only the one with the double recurrence. Thanks for the explanation, anonymnistify.

Offline