Math CentralQuandaries & Queries


Question from ryan, a parent:

Tuscan school has a fair. At the fair, Pia plays "what's your secret? The game starts with 3 players who are told the same secret. Each of those 3 players tells another 3 player, and so on. At the end of the 3rd round, everyone who knows the secret will compare what they have heard. What number in exponent form represents the number of people who know the secret after 3 rounds?
How many people is that?

Thank you very much.

P.S. I got 3 cube. which is 27

But when i map it out I end up with 39.

Hi Ryan,

Your number $3^3 = 27$ is the number of new people who learn the secret on the third round. $3^2 = 9$ new people learn the secret on the second round and $3$ people knew it at the start. Thus the number of people who know the secret after the third round is $3 + 3^2 + 3^3.$


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