Spreading a virus

Pi314

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stapel

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I came across this problem that I can’t solve. There’s this girl who has a set of computers. When you connect a computer with another computer their information will be shared so basically what the first computer knew the second computer will know as well and backwards. Then there’s this bad guy who wants to spread a virus on these computers. He can only activate the virus when all the computers know the information of the other computers and he can only connect two computers at a time. What’s the minimum of the times that the bad guy has to connect the computers to activate the virus when there are 4 computers? What if there are 5? And if there are 10?
I tried to solve it but I’m not always sure if I have the minimum. I had 4 for 4 computers and 6 for 5 computers. I couldn’t solve the one with 10 computers.
I would really like if someone could help me with this problem.
PS: my English isn’t that good.
What math class and topic generated this exercise? (Algebra? Calculus? Recursive series? etc) What have you tried so far? Where are you getting stuck?

Please be complete. Thank you! ;)
 
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