perplexus.info :: Just Math : Gossip

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?

No Solution Yet Submitted by Ady TZIDON

Rating: 4.5000 (2 votes)

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2n - 3.

Order the callers in some sequence. 1 calls 2, then 2 calls 3, ... , then n-1 calls n.

At this point there have been n-1 calls and the last two callers know all. Another n-2 calls (from somebody who knows all to somebody who doesn't) leave everybody fully informed.

I would be surprised if better than 2n-3 can be achieved (without using a conference call).

Posted by Steve Herman on 2012-07-26 11:35:30

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