Doubt Classical Nim Game

Revision en2, by adzo261, 2018-09-11 09:17:56

In normal Nim game, the player taking the last object wins.
And terminal position here is always a P -position.
Now, I have a question where you are given the terminal P and N positions unlike the only terminal condition in normal Nim.
Is this a variation of Nim? If yes, how to analyze it, how should I go about assigning grundy numbers?

Formally:
I have n heaps with represented by a set S={a1,a2,a3, .... an}.
And, I have a set T which gives terminal positions and tell whether it is a P-position or N-position.
One element of the set can be {{k1,k2,k3, .... kn},P}
where,
k1<=a1
k2<=a2
k3<=a3
.
.
kn<=an

It means the set {k1,k2,k3, .... kn} is a terminal position.
And, the second parameter denotes either 'P' or 'N' as P-position or N-position.

Can this be made equivalent to Nim?
How to analyze this?

Tags game theory, nim games, impartial games, two player games

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en2 English adzo261 2018-09-11 09:17:56 739 (published)
en1 English adzo261 2018-09-11 09:08:56 448 Initial revision (saved to drafts)