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Problem 2 (The Game Of Scoring Misere)
A misere game is a game played by the regular rules with one change; whoever wins the game according the regular rules is the loser. Consider again the game of Scoring, but this time we'll play it as a misere game.
- For which values of $n$ does the first player have a winning strategy when playing misere, provided each player must take 1, 2, or 3 objects?
- For which values of $n$ does the first player have a winning strategy when playing misere, provided each player must take 1, 2, 3, or 4 objects?
- If instead a player must take between 1 and $k$ objects, conjecture the values of $n$ for which the first player has a winning strategy when playing misere.
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