Question

Suppose there are six people - J, M, R, S, T and W - who pass rumours among themselves. Each day J talks with M and W; M talks with J, R and S; R talks with M, S and T; S talks with M, R, T and W; T talks with R, S and W; W talks with J, S and T. Whatever people hear one day they pass on to others the next day.

(a) Model this rumour passing situation with a graph.

(b) How many days does it take to pass a rumour from J to S ? Who will tell it to S ?

(c) Is there any way that if two people stopped talking to each other, then it must take three days to pass a rumour from one person to all the others ?

Answer 1

A) see attached

B) it takes 2 days, can be tell by w or s

C) Yes

Explanation:

A) Image attached shows the situation, each arrow represents a talking between the 2 people.

B) As you can see, J has to tell M or W, that will take a day. Then, M or W have to tell S, that will take another day. In total it takes 2 days. As explanined, it can be tell by M or W.

C) Lets suppose that M and R stop talking to each other, this means they won't tell rumors. So, if the rumour begans with J, we would tell to W, one day, W will tell S, 2 days and S will tell T, 3 days. it would take 3 days to arrive to T.