Math Induction:
Step 1 Prove that the solution is valid for some n>=4
Step 2 For N=N+1, have the 'new' person call any one person (1 call)
Step 3 For the N persons excluding the 'new' person, share the secret as
before. All N people now know the 'new' persons secret. (2N-4 calls) per
formula
Step 4 One from this N calls up the 'new' person (1 call)
Step 5 Total for N+1 = 1+2N-4+1 = 2N-2 = 2(N+1) -4. Hence valid for N=>
valid for N+1

In the third step, how did you come up with 2n-4?

Or intuitive one ...
Number the people from 1...n. Have person 1 call all people greater than 4.
(N-4) calls.
Now 1..4 share the secret in 4 calls (4 calls)
Now the person 1 calls all people greater than 4 again. (N-4 calls)
Total = N-4+4+N-4 = 2N-4.

How can 4 people share their secrets in 4 calls?

One more question.
I simply don't understand how you came up with this:
2n-4 is for 4<n<=16

I would appreciate if someone would answer my questions.

-Liliya