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III mex{0,1,2} = 3 means Win. Since mex of grundy numbers of all sub games. IXX = 1, IIX =2, IXI =0. You missed the grundy number of state IXI.
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Bowling Pins
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III mex{0,1,2} = 3 means Win. Since mex of grundy numbers of all sub games. IXX = 1, IIX =2, IXI =0. You missed the grundy number of state IXI.