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A276163 a(n) is the maximum first-player score difference of a "Coins in a Row" game over all permutations of coins 1..n with both players using a minimax strategy. 6

%I #14 Aug 25 2016 19:25:26

%S 1,1,2,4,5,9,6,16,9,25

%N a(n) is the maximum first-player score difference of a "Coins in a Row" game over all permutations of coins 1..n with both players using a minimax strategy.

%C a(2*n) = n^2 via [1, n+1, 2, n+2, ..., n, 2*n]

%D Peter Winkler, Mathematical Puzzles: A Connoisseur's Collection, A K Peters/CRC Press, 2003, pages 1-2.

%e a(1) = 1 via [1]

%e a(2) = 1 via [1,2]

%e a(3) = 2 via [1,2,3]

%e a(4) = 4 via [1,3,2,4]

%e a(5) = 5 via [1,2,4,3,5]

%e a(6) = 9 via [1,4,2,5,3,6]

%e a(7) = 6 via [1,2,3,4,6,5,7]

%e a(8) = 16 via [1,5,2,6,3,7,4,8]

%e a(9) = 9 via [1,2,3,4,6,5,8,7,9]

%e a(10) = 25 via [1,6,2,7,3,8,4,9,5,10]

%e For n=4, the first player would take 4, the second player would take 2, the first player would take 3, and the second player would take 1. The resulting score difference would be 4 - 2 + 3 - 1 = 4.

%o (Haskell)

%o minimax [] = 0

%o minimax as = max (head as - minimax (tail as)) (last as - minimax (init as))

%o a276163 n = maximum $ map minimax $ permutations [1..n]

%Y Cf. A276164.

%K nonn,more

%O 1,3

%A _Peter Kagey_, Aug 22 2016

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