Anyway, we can easily extend the recursion if not the formula for any number of variables and experiment with the terms.

bobbym

2013-04-28 21:44:54

Oh yes and quite useless unless you have exactly 4 colors.

gAr

2013-04-28 21:42:48

That's a good one!

bobbym

2013-04-28 21:23:47

Hi;

Looks like the worst is over. Now about that formula...

If we hold k = 4 and vary n then we come up with this:

for n = 2, 3, 4, ...

gAr

2013-04-28 21:19:00

Okay..

bobbym

2013-04-28 21:09:58

Hi;

I will play with it a little in a bit. Right now there is a little bit of an administrative matter to watch for.

gAr

2013-04-28 21:06:38

You're welcome! I think we can't write a formula like that when the number of marbles are different for different colors, since it involves permutation? Anyway, I'll stop here, spent almost a day on this one!

bobbym

2013-04-28 21:00:16

No problem! Thank you for the formula.

gAr

2013-04-28 20:52:45

Hi bobbym,

Ah yes, sorry!

Pearl2013

2013-04-28 20:46:37

Oop answer was wrong

bobbym

2013-04-28 20:44:31

Hi;

There is a typo in the formula. In post #26 there is (k-i), in post #34, (k-j).

gAr

2013-04-28 20:40:39

It causes problem like flooring if it's not written..