Suppose you tell a story to two of your friends. Some people repeat the story to two others, and in turn some pass the story on. Each time the story is told, it is told to two new people and no one hears the story twice. Sometime later, 271 people know the story. How many people have related the story to others?
A)271
B)270
C)169
D)135

Question

Quizplus · Accepted Answer

The number of people who know the story follows a geometric progression: 1 (you) + 2 + 4 + 8 + ... = 2^n - 1. Solving 2^n - 1 = 271 gives n = 9. Thus, 2^9 - 1 = 511 people know the story, and 2^8 = 256 people have related the story to others. Subtracting the initial storyteller, 256 - 1 = 135 people have related the story to others.

Suppose You Tell a Story to Two of Your Friends