# tng - The Number Game The Society of Misplaced...

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Sheet1 Page 1 The Number Game --- ------ ---- The Society of Misplaced Mathematicians likes to play a game called TNG, The Number Game, which is like tic-tac- toe, except that at each stage there are only two pos- sible moves, + and -, and instead of a board, there is a single non-negative 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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tng - The Number Game The Society of Misplaced...

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