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

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## Topic review (newest first)

bobbym
2013-04-28 22:30:18

Hi;

I am going to get a little sleep. See you later.

gAr
2013-04-28 22:05:37

Yes.

bobbym
2013-04-28 22:03:25

There are a lot of possibilities here.

gAr
2013-04-28 21:56:48

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..

In python, we need to convert it to float.