Pow Six Wirte Up

Process

The first thing I did was get the math book and opened it to page 132. I read the POW and I refreshed my memory to what I had to do for the POW and how the Linear Nim game was played. I understood that I had to play this game with a partner for quite a while so that I could pay attention to what we do to win the game and find the winning strategy. For this game you draw 10 line marks on a piece of paper and two players take turns crossing off only 1, 2, or 3 marks per turn. The person who crosses off the last mark is the winner. I played the game with Cinthia at school, and she always won even when I went first. This was probably because I only crossed off whatever number of marks: 1, 2, or 3 without thinking about winning. There was something I did notice after playing the game with her and her always winning, I noticed that whenever it was her turn to start the game most of the time she would cross off two marks and would win. Therefore, when it was my turn to go first I crossed off two marks and would win most of the time because I would try to leave the other person with four marks for their second turn. If they cross off 1 mark I am left with 3 and I can just cross all of them off and win, or if they cross off 2 or 1 mark I am still left with 1 or 2 marks and I still win.

I knew to always go first and cross off two marks so that I would win. I did this for any game I played. If I went first and crossed off one or three marks all I had to do was leave the other person with four marks always.

Strategies

A.) The winning strategy for the original game of Linear Nim that I developed is always play the game first and cross off two marks.

B.) 1. A variation of the game I tried was with five marks instead of 10 and only cross off 1, 2, or 3 marks per turn. The strategy I developed for this game is always plays the game first and cross off one mark.

2. Another variation of the game I tired was with 15 marks instead