Easy maths question

In a network with N nodes, what's the maximum number of connections you can make?

eg N=2, gives 1 connection, N=3 gives 3, N=4 gives 6, N=5 gives 10, N=6 gives lots etc

I think it's sum of N-i from i=1 to N-1

How many when N=100?

Can I simplify this in terms of N only and what's the function called in maths and/or in Excel or google sheets?

Probably easy but it's been years since i did maths.

Thanks!
xeniumAsked:
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Shaun VermaakTechnical Specialist/DeveloperCommented:
4950
Excel formula =A1+B1 and copy down
math.jpg
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xeniumAuthor Commented:
Thanks, I'm looking for a formula that gives the answer straight off.

Just guessing it seems to be N choose 2, that googles to the right answer for 100

Is that right?
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ShumsDistinguished Expert - 2017Commented:
In excel you can use below formula assuming  your data starts from A1:
=SUMPRODUCT(LARGE(A1:A100,ROW(INDIRECT("2:100"))))

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xeniumAuthor Commented:
I assume we don't need arrays.

If N choose 2 is the right answer then i can just use that formula, i assume Excel has the function, else a factorial version
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xeniumAuthor Commented:
eg
=FACT(100)/(2*FACT(100-2))
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xeniumAuthor Commented:
or
=COMBIN(100,2)
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xeniumAuthor Commented:
Now i think about it, it all makes sense. THe number of connections is the number of ways you can choose two nodes from the whole set.
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xeniumAuthor Commented:
Thanks all for your input and helping me get to an answer quickly.
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ShumsDistinguished Expert - 2017Commented:
Are you asking a question or testing us? If you already did your homework.
Why you need to send close request? right away accept Shaun's solution and it will close automatically.
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Fred MarshallPrincipalCommented:
In a network with N nodes, what's the maximum number of connections you can make?

 eg N=2, gives 1 connection, N=3 gives 3, N=4 gives 6, N=5 gives 10, N=6 gives lots etc

 I think it's sum of N-i from i=1 to N-1
Consider this:
Starting with "n" nodes, each node added gets N nodes.
Each node added, adds "n" connections.
So the formula is a sum of added connections.
The number of connections is a sequence: 1,2,3,6,12,
1 to 2 adds 1 for 1 total
2 to 3 adds 2 for 3 total
3 to 4 adds 3 for 6 total
4 to 5 adds 4 for 10 total
99 to 100 adds 99 >> so we will call M=N-1 as the sequence ends at N-1
SUM over k=1:M (1:k-1) which is done with a well-known formula M*(M+1)/2
Check:
M=1>>1*(1+1)/2=1
M=2>>2*(2+1)/2=3
M=3>>3*(3+1)/2=6
M=4>>4*(4+1)/2=10
.
M=99>>99*(99+1)/2=4,950

In this case, you have to be careful because there are N nodes and N-1 added connections.  Thus M=N-1
How many when N=100?
4,950

Can I simplify this in terms of N only
Yes. As above.
what's the function called in maths
Partial sum of integers
and/or in Excel or google sheets? SUM
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Fred MarshallPrincipalCommented:
Incomplete answer
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xeniumAuthor Commented:
Thanks Fred, that's a good point. I will request to defer closing so I can re-assign points.
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xeniumAuthor Commented:
n-choose-i.jpgNice formula btw, i see now how it's equivalent to the general case attached.
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Fred MarshallPrincipalCommented:
I believe ID: 42068924 answers the questions completely.  
The questions were:
How many when N=100?
Can I simplify this in terms of N only and what's the function called in maths and/or in Excel or google sheets?
I provided the answer to the first queston:
4,950
and to the second question:
M*(M+1)/2
where M=N-1 in the particular case given.
and
"Partial sum of integers
and/or in Excel or google sheets? SUM"
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Fred MarshallPrincipalCommented:
I rather hate to do this but it seems technically proper if not socially proper....
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