Hi:

Came accross an interesting problem. Dont know
if this is the right folder. Apologise if it isnt.
There are N people each of whom knows a unique
secret. Each person can make a call to exchange
secret(s) that they know. How many minimum calls
are required?

eg:
5 Guys - 6 calls
12,12,3,4,5
12,12,34,34,5
125,12,34,34,125
12345,12,12345,34,125
12345,12,12345,12345,12345
12345,12345,12345,12345,12345

7 Guys - 10 calls
12,12,34,34,56,56,7 - 3 Calls
127,12,34,34,56,56,127 - 1 Call
12347,12,12347,34,56,56,127 - 1 Call
1234567,12,12347,34,1234567,56,127 - 1 Call
1234567,12,1234567,34,1234567,1234567,127 - 1 Call
3 more calls.

What is the general solution/proof for finding the
number of calls for any given 'N'.

An interesting offshoot of this is the fact that
how does each node know which one to call to get
the complete information? Looks to me like along
with the signal information (ie secret), a control
information also needs to be passed. This 'constraint'
seems to increase the number of calls.

How can this problem be formulated and solved?

Manoj