I Want To Know!

\(N\) generals received \(N\) letters at the same time, each one having received only one letter with one piece of information. They telephone each other to exchange news:

  • Only 2 generals are on one telephone line at a time.
  • Each general is on at most one telephone line at a time.
  • Each telephone conversation lasts an hour.
  • During each conversation, the 2 generals can exchange any number of pieces of information.

What is the minimum number of hours needed for each general to learn all of the information, an be ready to crush the enemy? Consider three cases:

\(A) N=64\).
\(B) N=55\).
\(C) N=100\).

Input your answer as the sum of the cases, i.e. \(A+B+C\).


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