a REALLY HARD math problem, can anyone help?

Question

Ms. Smith wanted to plan how to contact her class by phone in case their field trip was cancelled. She decided to call one student who would then call 2 other students. Each of these students would then call 2 other students. This would continue untill all students had been called. Ms. Smith has 31 students.

How many students would need to make phone calls if Ms.Smith calls the first student?

thanks :)

Answer 1

Mrs Smith calls the first student = 0 student calls.
The first student calls the next two = two calls, three students notified.
The next two students call the next four = 6 calls total, 7 students notified.
The next four call the next 8 = 14 calls total, 15 notified
Next 8 call the next 16 = 30 calls total, 31 notified.

There are a total of 30 phone calls. There are a total of 1+2+4+8 = 15 "outbound" phone callers to a total of 31 students.

Answer 2

15

Answer 3

15

Answer 4

I would say 15 students though am not sure .My assumption is that if every two students are calling each other then the whole class is divided into groups of 2.Divide 31 by 2 you get 15.5 the .5 is the 1st student called by the teacher.That leaves us with 15 students .am open to correction.

Answer 5

15 because the last 16 called will have no other students to call. Here is a kinda graph thing to help.

I
I I
I I I I
II II II II
II II II II II II II II Shows how each student called 2 more and the last 16 don't call anyone so only 15 of the students make calls.

Answer 6

15 students would have to make phone calls

Answer 7

15 students.

Ms Smith would ring 1 student who would ring 2 more (total 3), those 2 would ring 4 (total 7), those 4 would ring 8 (total 15) and finally those 8 would ring the last 16 who would not have to ring anybody.

Answer 8

15 students would need to make phone calls

Answer 9

15 students need to call

Answer 10

1 2 4 8 16

5 calls