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 Gossip (Posted on 2012-07-26)
n people know each a different piece of gossip.

They can phone each other and exchange all they know so that after the call the parties know anything that either of them knew before the call.

What is the smallest number of calls needed so that everyone knows everything and how is this number achieved?

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 re(4): solution, some doubts, some doubts | Comment 8 of 12 |
(In reply to re(3): solution, some doubts by Dej Mar)

The sequence starts with 1, 3, 4, 7.

I suppose that 1 is the 1 call needed for 2 people sharing a gossip.
Which would make 7 the solution for 5 persons.  As I posted, you would only need 6 calls for 5 persons.

When I entered 1,3,4,6,8,10,12,14,16 Sloane gave A058992,
Gossip Problem: there are n people and each of them knows some item of gossip not known to the others. They communicate by telephone and whenever one person calls another, they tell each other all that they know at that time. How many calls are required before each gossip knows everything?

Editted to solve formatting problems.

Edited on July 27, 2012, 4:50 pm
 Posted by Hugo on 2012-07-27 16:46:48

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