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
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.
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. 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:
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 ...
If the first player is the one who says either 2nd January or 1st February, then the winning player is
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