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100 people set up a phone call system so that the initial contact person call three persons, each of whom calla three persons,and so on until all have been contacted. The maximum people who do not need to make calls is?

Very Simple Question

How would you solve it:


This is the same as
1*(1-x^3) + (x^2)*(1-x^3) = 1 - x^3 + x^2 - x^5

We have
1 who call 3
1+3 who call 3
1+3+9 who call 3
1+3+9+27 who call the remaining 60 who don't need to call anyone.
So it looks like 40 will need to call someone and 60 won't need to call anyone. If I understand the question correctly.

Check that, of the last 27 who need to call, not everyone made a call. There were 60 people remaining to be called and only 20 of the 27 needed to call someone. 7 of the 27 didn't need to call anyone, so 67 people total did not need to call anyone. Check this too.

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