# Minimum number of telephone calls needed to exchange information [duplicate]

There are 16 secret agents who each know a different piece of secret information. They can telephone each other and exchange all the information they know. After the telephone call, they both know everything that either of them knew before the call.

What is the minimum number of telephone calls required so that all of them know everything?
The answer is $28$.
But I don't know how?
I remember dividing them into $4$ groups of $4$ each. Then suppose in group $'A'$ there are $a,b,c,d$. Now $a$ calls $b$, $c$ calls $d$ and $a$ calls $c$. This happens in every group so that $2$ people in their respective groups know whole info about their group. But what to do next, I don't remember, or work out?

• If this is a duplicate, why does it have a different answer? The "original" has 2n-2 as an answer, this one has 2n-4 as an answer. So either the answers to the "original" are wrong, or this is not a duplicate question. Not the difference between email (one-way) and phone calls (two way communication!). Voting to re-open, although Davidenko's comment contains the full answer. – oerkelens Jul 16 '15 at 14:33
• @Davidenko Please remove your comment containing the answer. – JLee Jul 16 '15 at 15:05
• @oerkelens The original features two variants, one has $2n-2$ as answer (emails), the other $2n-4$ (phone calls, like this question). That being said, though leoll2's answer gave the method for attaining $2n-4$ calls, it didn't prove it was impossible with fewer, so there I think this issue could plauiably warrant more discussion – Mike Earnest Jul 16 '15 at 16:57