Suppose a group of people together are playing a trivia game on their smartphones.  The trivia game consist of 12 multiple choice questions of three choices for each question. The group splits into groups of 3. For each group, person 1 answers the first question with choice a, person 2 answers the first question with choice b, and person 3 answers the first question with choice c.  For each group of 3 people, 2 people get the answer wrong and are eliminated leaving 1 person in each original group of 3 people.  new groups of three people are formed from those who answered the first question right and then answer the second question the same way the first question was answered.  This continues for questions 3 - 12. At the end of the twelveth question, 1 person is left.  How many people were there before the first question is answered?  Please show step-by-step how you get to the answer.

gibsonj338  Aug 18, 2018

I think it is  531441


Let the number of people at the beginning be x

The number after question 1 is answered is x/3

the number after question 2 is answered is x/(3^2)


the number left after question 12 answered is  x/(3^12)


\(\frac{x}{3^{12}}=1\\ x=3^{12}\\ x=531441\)

Melody  Aug 18, 2018

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