generally game nim twoplayer game perfect information number row quotheapsquot object legal consist remove number object single heap nontrivial game start heap quotstandard playquot player turn object remain loser general farreache theory game develop berlekamp conway guy win way mathematical playsin commercial version picture player turn remove peg row appear picture quotrowsquot run direction mean quotheapsquot intersect people know nim accord original description version loser player remove peg socalle quotmisere playquot standard win condition combinatorial game allow misegravere play variationnim solve mean initial configuration readily determine player previous player win strategy identify good case nim determine surprisingly readily matter size heap go secret mea interested nim know solution nt game nim play central role theory combinatorial game twoplayer finite impartial game sense nim disguise position game correspond unique nimheap play disguised game perfectly make move correspond win move nim sprout example mean sprout solve quotdisguisequot partially reveal

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