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:
(1+x^2)(1-x^3)
(1+x^2)(1-x^3)
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.
To solve the phone call system problem, we need to understand the pattern of how people are making calls.
Starting with the initial contact person, they call three persons. Each of those three persons also calls three persons, and so on, until all participants have been contacted.
Let's analyze the situation step by step.
1. The initial contact person calls three persons.
2. These three persons each call three persons, so there are now nine people who have been called.
3. These nine people each call three persons, resulting in 27 people being called.
4. Now, out of these 27 people, some may have already been called by someone before. To determine the number of people who do not need to make calls, we need to find out how many people have already been called.
To do this, let's subtract the total number of people who have been called from the total number of participants.
If we assume there are 100 people in total, then:
Total number of people who have been called = 1 (initial contact person) + 3 (first round) + 9 (second round) + 27 (third round) = 40
Total number of people who do not need to make calls = 100 - 40 = 60
So, in this scenario, the maximum number of people who do not need to make calls is 60.
Please note that these calculations are based on the assumption that each person can only be called once. If there are any additional constraints or rules, they may affect the final answer.