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Men of October


Prof. Templeton
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During a particular game of baseball between the Tri-City ValleyCats and the Auburn Doubledays, John Hinson was the lead off hitter for the ValleyCats. There were no substitutions or changes made to the nine man ValleyCats Rooster that day and Hinson stepped up to the plate every inning.

What is the fewest number of runs the ValleyCats could have scored that day?

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I might be missing some rule.

I believe the most at bats that can lead to no score in an inning is 6. Bases loaded and then 3 outs.

Going to use A23456789 to mark the batters.

1: {A23456} = 0

2: {789A23} = 0

3: 4{56789A} = 1

4: 234{56789A} = 3

5: 23456789A23{456789} = 11

6: A23{456789} = 3

7: A{234567} = 1

8: {89A234} = 0

9: {56789A} = 0

So I come up with a score of 19.

Which I suppose isn't great with a minimum 73 total at bats.

If a greater number of at bats can exist in an inning without scoring then take 73 - (9 * n)

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I guess I'm supposed to explain.

If Hinson leads off the first they can put three runners on and make three outs before running out of bases.

The seven hitter will lead off the second. Meaning Hinson will bat fourth. If two batters make outs and one is on base when Hinson steps to the plate, that runner could then be caught stealing for the third out. Since Hinson was still batting at the end of the second he would also lead off the third and the whole cycle would start over.

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I guess I'm supposed to explain.

If Hinson leads off the first they can put three runners on and make three outs before running out of bases.

The seven hitter will lead off the second. Meaning Hinson will bat fourth. If two batters make outs and one is on base when Hinson steps to the plate, that runner could then be caught stealing for the third out. Since Hinson was still batting at the end of the second he would also lead off the third and the whole cycle would start over.

Yes. Well Done.

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