Problems No 2. Peg Game
Peg Game At the arcade, you can play a simple game where a ball is dropped into the top of the game, from a position of your choosing. There are a number of pegs that the ball will bounce off of as it drops through the game. Whenever the ball hits a peg, it will bounce to the left with probability 0.5 and to the right with probability 0.5. The one exception to this is when it hits a peg on the far left or right side, in which case it always bounces towards the middle.
When the game was first made, the pegs where arranged in a regular grid. However, it's an old game, and now some of the pegs are missing. Your goal in the game is to get the ball to fall out of the bottom of the game in a specific location. Your task is, given the arrangement of the game, to determine the optimal place to drop the ball, such that the probability of getting it to this specific location is maximized.
The image below shows an example of a game with five rows of five columns. Notice that the top row … Shopee photos :
When the game was first made, the pegs where arranged in a regular grid. However, it's an old game, and now some of the pegs are missing. Your goal in the game is to get the ball to fall out of the bottom of the game in a specific location. Your task is, given the arrangement of the game, to determine the optimal place to drop the ball, such that the probability of getting it to this specific location is maximized.
The image below shows an example of a game with five rows of five columns. Notice that the top row … Shopee photos :