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Let n>1 be odd. A row of n spaces is initially empty. Alice and Bob alternate moves (Alice first); on each turn a player may either
1. Place a stone in any empty space, or
2. Remove a stone from a non-empty space S, then (if they exist) place stones in the nearest empty spaces immediately to the left and to the right of S.
Furthermore, no move may produce a position that has appeared earlier. The player loses when they cannot make a legal move.
Assuming optimal play, which move(s) can Alice make on her first turn?
1. Place a stone in any empty space, or
2. Remove a stone from a non-empty space S, then (if they exist) place stones in the nearest empty spaces immediately to the left and to the right of S.
Furthermore, no move may produce a position that has appeared earlier. The player loses when they cannot make a legal move.
Assuming optimal play, which move(s) can Alice make on her first turn?