The Baseball Mysteries: Challenging Puzzles for Logical Detectives by Jerry Butters & Jim Henle

Author:Jerry Butters & Jim Henle
Language: eng
Format: epub
Tags: Puzzles, Logic, Recreational Mathematics, Probability, Mathematical games, Baseball
Publisher: A K Peters/CRC Press
Published: 2023-03-15T00:00:00+00:00

146 The Baseball Mysteries Jim:

Because the box score would have told us. It would say:

“McMullen ph, p,” not just “McMullen p.” Box scores always tell you when somebody enters as a pinch hitter. Just look at Heineman’s line: “Heineman ph, ss.” It’s entirely analogous. In both cases a player pinch-hits for someone and replaces him at his fielding position. If McMullen had been a pinch hitter, it would have said so.

Jerry: OK, you’ve convinced me. McMullen couldn’t bat in the fifth, and can’t score 2 runs in the sixth, so he can’t be the second pitcher. He must be the starter, and High his replacement. We’ve got the Hornets pitching settled.

Hornets’ Pitching:

innings:

1 2 3 4

5 6 7 8 9 10 11 total

Hornet pitchers: McMullen High

Sax

Muskrat runs:

5

2

0

7

10.5

THE MUSKRATS’ PITCHING

Jerry: We already know the last three Muskrats pitchers: Brickell then Douthit then Hafey. We just have to order Suhr, Proudhomme, and Cuccinelli.

Jim:

I’ve been thinking about this. It just seems like the pieces can fit together in so many different ways.

We could use a hint.

Jerry: Hint? Who’s going to give us a hint?

The Final Problem 147

If you want a hint, there’s one on the next page.

And if you’re in a hurry, the solution follows after that.

148 The Baseball Mysteries Hint:

The key is when players are left on base. Look at the number of LOB in the ninth and tenth innings. And the key for that is seeing where Heineman bats (and drives in 2 runs) in the ninth. Keep in mind the number of players the Hornets leave on base at various points in the game and note the fact that slot 6

leads off in the eleventh.

Who bats in slot 6 is also important.

It’s all delicately balanced.

The Final Problem 149

The Hornets had 2 or 3 LOB when Proudhomme pitched, which was sometime in the first 6 innings—that’s what Jerry wanted remembered on page 140. The Hornets also had 3 LOB in the eleventh (p. 141). That leaves at most 2 LOB for the ninth and tenth innings.

Muskrats’ Pitching:

innings: 1 2 3 4 5 6 7 8

9

10 11 totals

Muskrat pitchers:

???

B B B/D H H

Hornet runs:

5

0 0

2

0 1

8

Hornet LOB:

≥2

≤2

3

7

The ninth and tenth innings have 2 runs, 6 outs, and 0–2 LOB for a total of 8–10 PA. Counting back from slot 6, which led off the eleventh, 9 and 10 11

1

5

2

4

3

3

4

2

5

10

1

slots 6

9

•

7

8

•

8

7

•

9

6

•

the ninth inning begins with slot 5, 6, or 7. But Heineman, who doesn’t homer, can’t get 2 rbis unless he bats third in the inning or later, that is, in slot 7, 8, 9, 1, 2, or 3. But it’s not slot 9, which is taken by Worthington and later by Watkins.

He also can’t be in slots 1, 2, or 3 which are taken by the guys 11

with 6 PA, Gruhe, Melillo, and Gustine. That leaves 7 or 8.

Now suppose Heineman was in slot 8. Then in the eleventh he would have batted with 2 runners on base. He has 2 hits, a double and a triple. Either one would have driven in a on

run—but the winning run must be driven in by Watkins’ HBP.

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