New answers tagged strategy
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This only works with n=7 and n=8 yet....
Logic:
This works because:
Bonus #1
Bonus #2
-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
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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.
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Partial answer (a crude upper bound):
Because
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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 ...
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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:
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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:
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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: ...
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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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