Suppose a middle school student creates a game he calls Popular Ones. This is ho

Question

Suppose a middle school student creates a game he calls Popular Ones. This is how the game works: the student who starts the game puts $1 into a box, then he recruits two students who also put $1 in the box, and they must each recruit two more students, etc. The “Popular Ones” get to evenly divide the money that is put into the box from the students that are three levels below them. For example, the first student gets the money from the students that are on the fourth level.

7. Predict how much each third level student will earn as PROFIT if the game continues through the sixth level. Explain your reasoning.

8. If you were the first student, would you play the game again on the fifth level? Explain why or why not.

Challenge: If the game ended after the fifth level (and the payout was made to the second level), how much money would remain in the box?

Explanation / Answer

I level -- one student -- 1 dollar

II level -- 2 students -- 2 dollars

III level - 4 students -- 4 dollars

IV level -- 8 students -- 8 dollars

V level -- 16 --16

VI level 32 -- 32 dollars

Thus no of dollars increase in geometic progression as 1,2,4,8.... and also no of participants.

Hence nth level participants will get 23 dollars from the n+3th level participants.

7) Answer is 8 dollars

8) No I will not play on the 5th level. Though gain is the same, no of students should increase level by level which cannot be assured for upto the 8th level

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