Linear Nim

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Problem statement. There’s this game called linear nim where 2 players who have 10 marks and so they have to figure out a strategy. Then who ever crosses out the last mark wins. You can also play it with 15 marks. But you have to figure what to do while playing this game and try to find patterns or strategies to win.

Process. So what I did to attempt the problem is that I played the game a few times with my partner with the 10 marks and 15. So we can find some patterns and strategies that we can discuss. Then some strategies that we came up with were that we had to think ahead of our partner and see what next move will they make or see the amount of marks are left over.

Solution. So while playing the game my partner had won every game. I could see she had a great strategy and we had took turns like if she went first then I would go first the next round. Then I saw that if we played 10 marks I had crossed out 2 she would cross out 3 then 5 were left over so I couldn’t cross out 4 or 5 only 1,2 or 3 . So I cross out 2 and she would cross out the rest. But when we played 15 I could see that if there were 5 left and I have crossed out 1 she could cross out the other 4.

Extension. Mary and Louie are playing the same game but there are 20 marks so they can only mark out even numbers and the last person to cross out the last even number wins.

Self Assessment. My strongest points were that you could think ahead . Also seeing what marks were left over. My weakest points were trying to find a strategy of beatin my partner. My grade should be an A+ because I worked really hard.

Emma Irwin

Linear Nim

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