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This only works with n=7 and n=8 yet.... Logic: This works because: Bonus #1 Bonus #2


Note: the question was answered before this edit. Whether it's good to edit questions after a loophole has been found or not is still undecided, as far as I can see. Maybe this is a bit of cheating (but I believe that it's still no lateral-thinking), but it easily works when


In your question you assume the standard peg solitaire rules. Then a solution is The game at the link however allows diagonal jumps as well.


Partial answer (a crude upper bound): Because


No, the fugitive cannot escape with large N Assume an arbitrarily large number of officers surrounding the fugitive, all standing 1 unit away from the fugitive on the perimeter of the unit circle centered on the fugitive. The fugitive cannot end his move within distance d of any officer, or that officer can catch him next turn. In the limit of an infinite ...


I've tried to anticipate some nitpicks at the process I present below. Nitpicks are in parentheses and set off from the main method. The core of the method can be found outside the parentheses. Set-up step: Then, they should follow these steps for each potential song: Why does this work? Or, in a wordier form:


I have a proposed process, which has the downside of allowing for cheating, but works if both sides want to keep the information transfer within the outlined parameters: This works because: We can modify this to enforce the secrecy better:


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: ...


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 ...


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


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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