Local Quiz

[grumpee]

At the grand summit, 1000 ambassadors meet to discuss important matters (and eat Ferrero Rocher obviously).



Every ambassador has a conversation with every other ambassador.



How many conversations take place?

[Sam1960]

Not sure about the "Ferrero Rocher" bit !!
And not sure I totally understand the question ..... ??

499,500

[JJ109]

First you need to sum (999 + 998 + 997+ ........+0) as the first ambassador has 999 conversations (he doesn't talk to himself)
The second has 998 different conversations (he doesn't talk to himself and has already talked to the first one)
The third has 997 different conversations. He doesn't talk to himself and already has spoken to the first two
The 4th has 996 different conversations
and so on down to number 1000 ambassador who has already spoken to them all = 0

To sum (999 + 998 + 997 +...........+2 + 1 + 0) simply add the first and last number 999 + 0 = 999
add the second and and second last = 998 + 1 = 999
add the third and third last = 997 + 2 = 999
and so on
There are 1000 /2 "pairs" of numbers that will all = 999
Therefore the sum of the conversations = 500 * 999 = 499,500
which is the figure that Sam has provided.

[JJ109]

An even simpler way of calculating it is to recognise that each ambassador is involved in 999 conversations (everybody but himself)
1000 * 999 = 999,000
However each conversation consists of 2 people
Therefore divide by two
999,000 / 2 = 499,500

[grumpee]

thanks for this and also the explanation - appreciate your help