Math3096: Games and Puzzles
For my second honors experience I took a class called Games and Puzzles. In it we learned about the math behind several types of games and puzzles. We looked at card games, combinatorial games, logic puzzles, and Markovian games. Each type of game is distinguished by the number of players, amount of information given, and the presence of randomness or decisions.
We learned how to mathematically find the probability of a certain outcome within a card game. We first learned a simple trick game called Whist, and each day we added a new rule until we were playing a simplified version of Bridge.
One of the combinatorial games we learned is called Hackenbush. It consists of red and blue lines stacked on each other. Each player takes turns removing one of their color lines and any line that is disconnected from the base when that one is removed. The first player without a move loses. These games can be analyzed to determine the winner from the very beginning. Assuming a positive game meant red wins and negative game meant blue wins, we determined the games’ values. In a similar fashion we used nimbers to find the numerical values for the game Nim.
The logic puzzle unit was my favorite. Along with the well known puzzle Sodoku, we solved others such as Kakuro, Nurikabe, and Slitherlink. Our project for this unit was to develop our own puzzle. I have included below my puzzle along with a link to the answer.
Lastly we learned about Markovian games and how to represent the chain in a transition matrix. This way we could multiply matrixes to find the probability of the chain after a designated amount of iterations.
We learned how to mathematically find the probability of a certain outcome within a card game. We first learned a simple trick game called Whist, and each day we added a new rule until we were playing a simplified version of Bridge.
One of the combinatorial games we learned is called Hackenbush. It consists of red and blue lines stacked on each other. Each player takes turns removing one of their color lines and any line that is disconnected from the base when that one is removed. The first player without a move loses. These games can be analyzed to determine the winner from the very beginning. Assuming a positive game meant red wins and negative game meant blue wins, we determined the games’ values. In a similar fashion we used nimbers to find the numerical values for the game Nim.
The logic puzzle unit was my favorite. Along with the well known puzzle Sodoku, we solved others such as Kakuro, Nurikabe, and Slitherlink. Our project for this unit was to develop our own puzzle. I have included below my puzzle along with a link to the answer.
Lastly we learned about Markovian games and how to represent the chain in a transition matrix. This way we could multiply matrixes to find the probability of the chain after a designated amount of iterations.
My Puzzle
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