A senior member of a 100-member society was informed about a certain change regarding the nearest convention and was forced to inform the rest of the members about such change. He calls 3 members and provides each of them with a detailed schedule of a "telephone tree": each of the recipients will call upon 3 new members ,those will address each 3 members and so on until the relevant information is known to each member of the society.

Assuming an optimal efficiency of the method, what is the greatest number of members who need not make a call?

As 99 members need to be called, there must be 99 phone calls. As the instructions are for each caller to make three calls, there need be 33 persons making the calls, including the first caller.  As there are 100 members altogether, 67 need not make a call.

Posted by Charlie on 2016-07-26 13:35:10