In the first round, one person chooses 3 people. In round 2, those 3 people choose 3 people each. Keeping with the pattern, how many people get chosen in round 6?
We have six Rounds of choosing people:
R1: 3 are chosen
R2: 3 choose 3, or
R3: 9 choose 3, or
and so on.
And so we can conclude that the pattern of the number of people being chosen in any given round is:
Therefore, in the 6th round, we'll have: