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8

Pretty much all Nim games can be solved by starting at the end and working backwards. Let's first solve the basic Nim, with only one pile, and simple actions (take 1-4). Let's enumerate the endgame situations by how many sticks are left, and see what kind of pattern emerges: Rules: 2 players, one pile, take 1-4, taking last wins 0: loss, cannot take 1: ...


5

If player A starts then player B have a winning strategy because


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1. Four players In the four players case, regardless of what D says, C can make a statement to secure arbitrarily high surviving probability for themself. There're many ways C can do that, one of which is like the following: where 2. Five players The above analysis for 4 players gives us a leverage to handle the 5 players case. Notice that if E makes the ...


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4 player answer The best thing D can do is say: Why? How? Why does it work: Conclusion


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If the first player is the one who says either 2nd January or 1st February, then the winning player is Proof: The first player The strategy is to Note: I assumed that the game only goes over one year. If players can go on to the next January, then


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