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The title should read "... Kayles". OEIS A002186 Sprague-Grundy values for the game of Kayles (octal games .77 and .771).
kayles = (==0) . foldl1 xor . map (grundy!!)
grundy = map g [0..]
g 0 = 0
g n = mex n [grundy!!l `xor` grundy!!r | m<-[n-1,n-2],l<-[0..m`div`2],let r=m-l]
mex n = minimum . ([1..n] \\)
In test case 1, how are the last two "IXIXIII" and "XIIIXIXXIX" wins? And are there different test cases for different languages?
Winning moves for these cases:
IXIXIII -> IXIXIXI
XIIIXIXXIX -> XIXIXIXXIX
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