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J, L, M, N, O and P are members of a spy...

J, L, M, N, O and P are members of a spy network for security reasons, only certain spies are able to contact other spies. The only contacts allowed are:
J can contact both L and N.
O can be contacted by L, M and P.
N can contact M.
O can contact both L and N.
P can be contacted by M.
A spy can receive a message from any spy who can contact him and , in relay the message to any spy he is able to contact.
N can get a message from which of the following spies by using exactly one intermediate contact ?
`{:(" I. O II.L III.P"),("1) I only 2) III only 3) I and III only "),("4) II and III only 4) I, II and III "):}`

Text Solution

Verified by Experts

The correct Answer is:
3

Begin with the first condition.
J can contact both L and N:

Next, O can be contacted by L, M and P :

Next, N can contact M :

Then, O can contact both L and N :

Finally, P can be contacted by M:

With a "network" set, any further conclusions that you might need to draw are already implicit in the diagram. For Example, J can have N relay a message to M, who in turn can relay the message to O :

So there is no need to look for further conclusions. Go to the questions.
The diagram shows that N can contact M, who in turn can contact P and O .
So , using jsut one intermediate contact, N can contact those two spies.
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