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I am not sure if you mean the fewest possible, or the fewest ever recorded. If each batter takes one pitch (ground out, fly out, hit by pitch or base hit), and the home team scores one run somewhere along the line with every other batter getting out (perhaps double play, caught stealing, etc.), there would be 27 (outs for the visiting team)+24 (outs for the home team) and 1 (perhaps a home run) for a total of 52 pitches. This would be the minimum. The home team would take no pitches in the ninth inning. I do not know the fewest recorded. It may be different in Major league, minor league, little league, NCAA... perhaps there was a 52 pitch game somewhere in history...
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