OT:Re: No IRC in Kopete for KDE 4.1?

Dotan Cohen dotancohen at gmail.com
Sun Aug 31 12:03:36 UTC 2008

2008/8/31 Sylviane et Perry White <spwhite at freesurf.ch>:
> On Saturday 30 August 2008 22:55, Dotan Cohen wrote:
>> Actually, I'm not. It should have been n*(n+1)/2. Young Gauss would be mad.
>> I knew as I posted that I had an error, because n^2 would be odd for
>> an odd n, and thus indivisible evenly by 2. Buy I had to hit that Send
>> button to find the mistake......
>> A = n/2(a1+an) according to young Gauss (I'm sure you know the story).
> We were both wrong,
> Me:
> in my previous post I wrote 2n*(n-1) instead of just n*(n-1) because I was
> trying to exagerate the figure by considering that A speaks to B and B speaks
> to A may be counted as 2 conversations.
> You:
> It is not n*(n+1)/2 but n*(n-1)/2
> How fast can it grow?
> Best I got was 2 to the power 2n,
> and that was by considering that any group (subset of n, including the whole
> group and void group) can have a distinct conversation with any same or
> different group subset of n.
> Well, if each hear voices, speak to god or to himself or to nobody or to any
> subgroup in a group containing a least 9 people, they couldn't hold 9!
> conversations.   :-)
> cheers          Perry

You are right! I was not accounting for the fact that the first person
starts 0 conversations. Easy way to look at it:

1 person in a room: 0 conversations

1 person enters the room -> 2 people now in room:
---- 1 new conversation + 0 current conversations = 1 conversation

1 person enters the room -> 3 people now in room:
---- 2 new conversations + 1 current conversations = 3 conversation

1 person enters the room -> 4 people now in room:
---- 3 new conversations + 3 current conversations = 6 conversation

You could use mathematical deduction to get to n people in a room
having A conversations:
A=n*(n-1)/2 for n>=1

Let's double check:
n=1 -> A=1*0/2=0
n=2 -> A=2*1/2=1
n=3 -> A=3*2/2=3
n=4 -> A=4*3/2=6
It fits!

Another way of looking at it is that the nth person to enter the room
adds (n-1) conversations. So you would sum 1,2,...,(n-1). According to
Gauss, the sum is A= n/2*(0+(n-1)) = n(n-1)/2

And that's why I should not have been posting at 01:00 instead of sleeping!

Dotan Cohen



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