Fascinating Frequencies 4

A physics simulation is needed to solve this challenge.

Diagram of Baffling Bungee Jump.

Bob the Bungee jumper from Baffling Bungee is upset about his bungee jumping experience. If you attempt the problem, you will soon see that Bob’s bungee jump will take too long. Far too long. This is because C5H8 is very springy. In fact, Bob’s bungee jump would take about 2 months … if you were thinking of a mathematical model. You see, the diagram shows a cliff behind Bob. The rubber is so springy he would bash into it, cutting his jump short. But set that problem aside for now. This challenge does not concern those. In bob’s jumps, the ups and downs would gradually, very gradually, become smaller and smaller. But they would still occur at the same frequency. Can you guess today’s challenge? Calculate that frequency.

Didactic Dice

Combinatorics is needed to solve today’s challenge.

Shown in the diagram to the right is the board for a dice game. The rules are as follows: start at the point. On your turn, roll 2 six sided dice. Move forward thet many spaces allong the path. The path is marked by the arrow and has 24 squares. If you reach the black square and have more moves, move back to the dot. You do not continue moving; your turn ends immediately. The first player to end exactly on the black square wins. You play this game with a friend. The challenge is to find the average number of turns the game will take. After 1 player wins, the other does not continue. This is very important.