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Hi;

On the front page go into Help Me and look for the Post New Topic button. Hit that and you are ready.

Hi;

For 1)

Plugin the two irrational roots and determine b and c.

From the point of view of EM, the problem is solved.

I just did 1 pair out of 2,3,4,5,6,7,8,9,...players and looked up the form on the OEIS.

Then I did 2 pair out of 4,5,6,7,8,9,...players etc.

Hi adpqadpq;

Make the switch to Linux...

196, 218

440^3 = 85,184,000

Hi;

Thanks, my machine is the same as yours and runs out of memory too.

Coming at the problem in another way, I get for 5 pairs out of 13 players:

`(1/3840) (m - 9) (m - 8) (m - 7) (m - 6) (-5 + m) (-4 + m) (-3 + m) (-2 + m) (-1 + m) m /. m -> 13`

I have some confidence in the result now. I would like to have a solution in generating functions too but so far this has not been possible.

Hi;

Could you please run this when you get a chance and post a screenshot of the notebook that pops up.

```
Needs["Benchmarking`"]
BenchmarkReport[]
```

I agree. I am using a different method than you are so we can be pretty sure of those answers.

Hi;

Can you calculate 4 pairs out of 9 people?

I do not get that many. I think the difference in our answers is because you solved for 11 people.

I am glad you asked me that question. EM mean Experimental Mathematics.

I would say the first rule is this:

Get Your Hands Dirty: This is easy and fun to do. Stay loose and experiment. Plug in lots of numbers. Keep playing around until you see a pattern. Then play around some more, and try to figure out why the pattern you see is happening. It is a well-kept secret that much high-level mathematical research is the result of low-tech "plug and chug" methods. The great Gauss, widely regarded as one of the greatest mathematicians in history, was a big fan of this method. In one investigation, he painstakingly computed the number of integer solutions to x^2 + y^2 < 90,000

Today, we can be assisted by a computer to help with this type of research.

Hi bob bundy;

Thanks!

Hi;

I agree with 105. How about 1 more? Can you calculate 4 pairs out of 9 people?

I agree! How about 2 pairs out of 7 players?