## Friday, September 07, 2007

### How Logical Are You?

 You Are Incredibly Logical Move over Spock - you're the new master of logicYou think rationally, clearly, and quickly.A seasoned problem solver, your mind is like a computer!

[Hat Tip: GrrlScientist at Living the Scientific Life (How Logical Are You?]

1. I am also incredibly logical.

2. I am also incredibly logical.

3. I am also incredibly logical.

4. I find all this credible, actually...

5. I too find all this credible, actually...

6. I don't think any of the answers to #2 "must" be true.

7. Actually for #2, there are 3 wrong statements. As there are four statements, only one of which can be correct - automatically making 3 incorrect!

8. I didn't fare as well. I think I read too much into the baseball question. What inning was it? How many on base? What if she had a base-clearing double?

9. I was "Incredibly Logical" but I wasn't real sure about the baseball question either. But it is correct. If the team didn't win, then she did not hit a homer. Correct. It was stipulated that if she did hit the homerun, they won. So if they lost, then she could not have hit a homerun. That was the only one I wasn't confident about. Of course, the score could have been tied, and she could have struck out. In the top of the 10th inning the opposing team could have scored 12 runs. Then, even if she did hit a homerun, they would have lost. Yep. Now I think there was not a correct answer.

I didn't fare as well. I think I read too much into the baseball question. What inning was it? How many on base? What if she had a base-clearing double?

If I recall correctly, the question said that if she hits a home run the team wins. This must mean it's the bottom of the ninth or the bottom of an extra inning. The other things depend on the exact score.

11. I've changed my mind on the baseball question. I now think answer #3 must be true, although it's peculiar and a bit misleading -- at least as a matter of baseball.

Here's the question:

If Jenny hits a home run, her team will win. Given that this is true, what else also must be true?
(1) If the team won, Jenny hit a home run.
(2) If Jenny didn't hit a home run, the team tied.
(3) If the team didn't win, Jenny didn't hit a home run.
(4) All of the above.

I think the "home run" reference is a red herring. A home run results in scoring 1, 2, 3, or 4 runs, depending on how many runners are on base at the time. There are other ways to score runs and there is nothing special about runs scored by a home run as differentiated from runs scored in some other way. Nor is there anything special about runs scored "all at once" by a home run rather than "one at a time" by some other plays. Nor is there any situation in baseball in which a team can win only if a player hits a home run.

With this in mind, consider the premise: "Jenny's team wins if she hits a home run" really means that her team wins if it scores at least one run more than the opponent. Since -- by stipulation -- a home run will do it, we know that Jenny's team is either tied, or behind by no more than three runs when she comes to bat (if there are runners on base). It doesn't matter whether Jenny's team scores the necessary runs by her hitting a home run. What matters is whether they score enough runs.

However, we also know that a home run will do the job. It's one way to score the necessary runs. It is not necessary that Jenny hit a home run for her team to win, but it would be sufficient for that purpose if she did.

Since hitting a home run is, by the terms of the premise, enough to win, it follows that if Jenny hits a home run her team will score at least one more run than the opponent. So if Jenny's team loses, it did not score at least one run more than the other team. Since the premise implies that a home run would assure a win, it follows that if Jenny's team loses she did not hit a home run (since if she had, her team would not lose).

Incidentally, if I'm right about this it does not matter what the inning is. It's purely arithmetic. The winning run(s) could be scored in any inning. All that matters is that the number of runs be sufficient to assure the victory at the end of the game.

Answer #1 need not be true. Jenny's team could win if it scored more runs than the opponent by any means, not just by a home run.

Answer #2 need not be true. Without knowing the score when Jenny came to bat, it does not follow that her team "must" have tied if she did not hit a home run. Her team could lose by 1, 2 or 3 runs (but not 4, since if her team were 4 runs down even a grand slam home run would not win the game).

12. Jeff Chambelain says,

Incidentally, if I'm right about this it does not matter what the inning is. It's purely arithmetic. The winning run(s) could be scored in any inning. All that matters is that the number of runs be sufficient to assure the victory at the end of the game.

I don't think this is correct. If the opposing team can still come to bat before the game is over then you cannot make the statement that, "If Jenny hits a home run, her team will win."

13. It helps if one knows nothing whatsoever about baseball. Try substituting "blows her nose" for "hits a home run" and it will becme clearer.

I am also incredibly logical, but I would like to know how many questions one can get wrong before being demoted.

14. You can have one question wrong before being demoted. Except question 7 has no effect on the result whatsoever! This test is not logical.

15. LM said: I don't think this is correct. If the opposing team can still come to bat before the game is over then you cannot make the statement that, "If Jenny hits a home run, her team will win."

That's one of the peculiarities of the original question. But you have to take that question as presented: According to the question, it is true that if Jenny hits a home run (or on my reformulation, if her team scores 1-3 runs by whatever means) her team will win. It need not be a "walkoff." Whether the opposing team has more at bats is irrelevant to the question as formulated. The only way more at bats could matter if if the opposing team scored enough runs to overcome Jenny's home run. But we know, because of the premise, that this "did not happen," since if it did Jenny's home run would not have resulted in the winning run(s) scoring -- a statement we are admonished to take as "true."

I agree with you that in a baseball context the statement in question would not likely be made except in a walkoff situation. But the questions were presented as matters of logic, not baseball.

16. Maybe 7 has no result on the answer because it's not really about logic, but about pattern recognition. It was certainly the one that I thought it would be boring to think about, so chose an answer randomly. Not sure why it would be included, though.

17. The only question that gave me pause was the last one (some tigers are not lions)... I almost selected "some tigers are lions" because, colloquially, saying that some X's are not Y's generally means that some other X's are Y's, but formally, this is not necessarily the case.

As for the home run question, it was straightforward... apart from the fact that it is not specified that they were playing baseball or softball (could have been a team home run derby, or it could have been any arbitrary game in which some particular action is called "hitting a home run"), it's all in the problem statement: a home run = a win. If they did not win, Jenny did not hit a home run--that's all that is relevant.