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Gossip (Posted on 2012-07-26) Difficulty: 3 of 5
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?

No Solution Yet Submitted by Ady TZIDON    
Rating: 4.5000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re(2): solution, some doubts | Comment 5 of 12 |
(In reply to re: solution, some doubts by Hugo)

That's pretty convincing, Hugo.  I guess that it is less than 2n - 3, when n > 3

Using your approach,

2 people could do it in 1 phone call
4 people could do it in 2*1 + 4/2 = 4, which is less than 5
8 people could do it in 2*4 + 8/2 = 12, which is less than 13
16 people could do it in 2*12 + 16/2 = 32, which is more than 29

I guess we need to do some more work to get a general formula

  Posted by Steve Herman on 2012-07-26 18:52:32
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