System

Could someone help me with this word problem?

The Band Committee of 100 people wishes to set up a telephone call system. The initial contact person calls three other people, each of whom call three others and so on, until all the people in the Band Committee have been contacted. What is the maximum number of people they need to make the calls.

If you aren’t sure how to do this mathematically, it’s easy to do with a simple diagram.

The first person calls 3 people. (1×3) – 3 calls so far
Those 3 people in turn call 9 people. (3×3) – 12 calls total
Those 9 people in turn call 27 people 3×9) – 39 calls total
Those 27 people in turn would call 81 people except that you’d go over the 100 call mark. So 7 of the 27 will make 3 calls and the other 20 will only make 2 calls – 61 calls + previous 39 calls = 100

So 27+9+3+1=40 people would be the maximum number required to make the 100 calls.

One Response

1. PTF Says:
   May 31st, 2010 at 9:51 pm

   If you aren’t sure how to do this mathematically, it’s easy to do with a simple diagram.

   The first person calls 3 people. (1×3) – 3 calls so far
   Those 3 people in turn call 9 people. (3×3) – 12 calls total
   Those 9 people in turn call 27 people 3×9) – 39 calls total
   Those 27 people in turn would call 81 people except that you’d go over the 100 call mark. So 7 of the 27 will make 3 calls and the other 20 will only make 2 calls – 61 calls + previous 39 calls = 100

   So 27+9+3+1=40 people would be the maximum number required to make the 100 calls.
   References :

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