How Many Hoops Will Kids Jump Through To Play Rock, Paper, Scissors?
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From Taylor Firman, the bell rings and itâs time for gym:
The following delightful video has been making the viral rounds:
Letâs call this game rock-paper-scissors-hop. Here is an idealized list of its rules:
- Kids stand at either end of N hoops.
- At the start of the game, one kid from each end starts hopping at a speed of one hoop per second until they run into each other, either in adjacent hoops or in the same hoop.
- At that point, they play rock-paper-scissors at a rate of one game per second until one of the kids wins.
- The loser goes back to their end of the hoops, a new kid immediately steps up at that end, and the winner and the new player hop until they run into each other.
- This process continues until someone reaches the opposing end. That playerâs team wins!
Youâve just been hired as the gym teacher at Riddler Elementary. Youâre having a bad day, and you want to make sure the kids stay occupied for the entire class. If you put down eight hoops, how long on average will the game last? How many hoops should you put down if you want the game to last for the entire 30-minute period, on average?
To get you started, hereâs how a single game might unfold:
