# POW 6: linear nim Essay

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Get AccessFor this game of Linear Nim 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. Firstly what I did was play a few games with my Mom and what I realized right away was that if you stopped just before the last four dashes in the game then you would always win. Since you aren’t always guaranteed of being the one who can put these dashes on the sixth line then I had to think of a strategy.

So I thought of a way to make it so I would be able to get the sixth dash as long as I started first. I found that starting with two lines crossed off would leave my mom with only one, two or three dashes that would give me the opportunity to get the sixth line no matter which number of lines she crossed off. I used this many times on her and it seemed to be undefeatable. When she went first and didn’t start with three I would try to get the six, which would make me win. Such as if she started with three then I would cross off three and I would get the six forcing her to lose.

For my variation of different games I did 11 lines and 23 lines. I chose eleven because it is right after ten. I chose 23 because it is my sister’s lucky number. I did both of these a few times to find a strategy that would fit any type of variation of linear nim game. My sister and I played a few games for eleven with no real strategy in mind. Then I found that in order to win I had to do the same thing as the last game except that I had to start with a three in order to get the 7th line.

This strategy worked exactly like the last strategy except that it was off a number. This would give me the last line(s). So my strategy was to cross off three but I knew that it wouldn’t be the same for every single variation of linear nim so I had to find a more complete strategy. The 23-lined linear nim was one that I had more trouble finding a solid edged strategy. When I played this a few times I found that there was no actual number that could force it to work like the last couple times with the ten and the eleven lines.

What I did was to break it into a ten and a nine after subtracting four. I subtracted four because that is reserved so that the opponent will have to lose. In this case, since it was 23 I subtracted 4 which made it 19. Since I already knew how to get the ten I put it into two parts of ten and nine. Over all there is an advantage when you go first for all of these games because it is when you go first that you get to force the other player not to be able to win if you have the right strategy.

This POW showed me how to plan strategies and the step that are needed in order to make a presentation on the POWs in the future. This POW I enjoyed much more than the others because of how it was formatted as a game and we could play it with other people to find a good strategy to always win. I felt this POW was a little easy but this, for me is a good thing because that meant that it was explained well enough for me to understand and clearly for me to find a way to generate answers. It was fun, easy and clear.