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The Number Game
  
The Society of Misplaced Mathematicians likes to play a
game called TNG, The Number Game, which is like tictac
toe, except that at each stage there are only two pos
sible moves, + and , and instead of a board, there is
a single nonnegative integer n.
The two moves are:
+:n = ( n + e**n ) mod p
:n = ( n  e**n ) mod p
There is a set of goals g, for example, g = {8, 9},
which means that a player whose move makes n equal to 8
or 9 wins.
A game is specified by giving a prime number p, an inte
ger e, an initial value n0 for n, a maximum number of
rounds to be played, r, and a set of goals, g.
Each
round consists of a move by player X followed by a move
by player Y.
The player who first moves to a goal wins.
Because the number of rounds is limited, ties are
possible.
p
An example is:
Game:n0 = 3, r = 2, e = 7, p = 11, g = { 8, 9 }
7**0
mod 11 = 17**1 mod 11 = 7
7**2
mod 11 = 57**3 mod 11 = 2
7**4
mod 11 = 37**5 mod 11 = 10
7**6
mod 11 = 47**7 mod 11 = 6
7**8
mod 11 = 97**9 mod 11 = 8
7**10 mod 11 = 1
Initial State:n = n0 = 3
Round 1:
X moves +:n = ( 3 + 7**3 ) mod 11 = 5
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 Spring '11
 k.v.arya

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