Efficient gossip by telephone

Suppose everybody has following gossip :
a,b,c,d,,e,f,g,h,j,k
now if person with knowledge a calls person with knowledge b , then person(a) will have a+b knowledge and same person(b) will have , Similarly in next 3 calls of person(a) with person(c) ,(d) and (e),, person(a) and person(e) will have a+b+c+d+e knowledge . If same scenario happens in other half row (k calling j,h,g,f) then person(k) and person (f) have f+g+h+j+k knowledge .
Till now 8 calls have been made . Now if person(a) and person(k) calls then they both will know every gossip , similarly if person(e) and person(f) calls then they will know every gossip.

Total calls : 10 and a,e,f,k knows full gossip . Now if remaining persons i.e (b,c,d,g,h,j ) will call anyone from (a,e,f,k) they will know every gossip .
So total calls will be 10+ 6 =16
Enjoy ;)

We need to find f(10). We can find by hand calculation that f(4) = 4.

we can point out f(n+1)<= f(n)+2 for people a 1,a 2,...a n, a n+1

first a n+1 calls a 1 then f(n) calls happen between a 1 to a n. Then we can see everyone except a {n+1} knows everything . One more call is required for a {n+1}

So, f(10) = f(4)+6*2=16