A multiple-choice quiz
by xaosdog.
Estimated time: 21 mins.

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Quiz Answer Key and Fun Facts

Answer:
**don't consult a physician no matter how trivial your head injury may be.**

Pragmatic cues are powerful guides to how language should be interpreted, often more powerful than mere niceties of grammar. Actually parsing the sentence yields a meaning contrary to that implied by pragmatic cues or, specifically, here, what I refer to as 'keyword heuristics.'

"No head injury is too trivial to be neglected" is best parsed by eliminating some of the negations: We invert "No head injury" to "Every head injury" and then we need to invert one other clause to retain the original meaning. Let's change "is too trivial" to "is important enough". Thus, we can rewrite the premise as "Every head injury is important enough to be neglected" - certainly the opposite of what constitutes sound medical advice, but if we assume it to be true, we should avoid seeing a doctor!

Wordings of this kind unintentionally happen in practice quite a lot, so it is always best to avoid multiple negations in writing - you can easily wind up with the opposite of what you want to say!

Pragmatic cues are powerful guides to how language should be interpreted, often more powerful than mere niceties of grammar. Actually parsing the sentence yields a meaning contrary to that implied by pragmatic cues or, specifically, here, what I refer to as 'keyword heuristics.'

"No head injury is too trivial to be neglected" is best parsed by eliminating some of the negations: We invert "No head injury" to "Every head injury" and then we need to invert one other clause to retain the original meaning. Let's change "is too trivial" to "is important enough". Thus, we can rewrite the premise as "Every head injury is important enough to be neglected" - certainly the opposite of what constitutes sound medical advice, but if we assume it to be true, we should avoid seeing a doctor!

Wordings of this kind unintentionally happen in practice quite a lot, so it is always best to avoid multiple negations in writing - you can easily wind up with the opposite of what you want to say!

Answer:
**The horse raced past the barn fell jumped.**

'The horse raced past the barn fell' is a famous garden-path sentence, where 'raced past the barn' is used adjectivally (with respect to 'horse') rather than as a verb phrase. However, we cannot account for the additional "jumped" in a proper syntax.

'Buffalo buffalo buffalo buffalo' implies that bison from a particular city in New York tend to bewilder, deceive or confuse (other) bison. This strange sentence hinges on the relatively unknown use of "buffalo" as a verb, but it is otherwise correct.

The rat-cat-dog sentence is best verified starting at the ends, going inward:

The main clause is "The rat hides." Then, we have a modifier for the rat, namely that it is being hunted by the cat: "The rat the cat hunts hides." Finally "the dog chases" modifies the cat - three animals run after each other and the leading one manages to hide.

The horse-race-ringer-false sentence can be analyzed in a similar way: We start with "The claim was false". Next, we specify the claim: "The claim (that) the horse was a ringer was false." Finally, we have an additional qualifier on the horse, namely that an unknown "he" entered it (into a race).

'The horse raced past the barn fell' is a famous garden-path sentence, where 'raced past the barn' is used adjectivally (with respect to 'horse') rather than as a verb phrase. However, we cannot account for the additional "jumped" in a proper syntax.

'Buffalo buffalo buffalo buffalo' implies that bison from a particular city in New York tend to bewilder, deceive or confuse (other) bison. This strange sentence hinges on the relatively unknown use of "buffalo" as a verb, but it is otherwise correct.

The rat-cat-dog sentence is best verified starting at the ends, going inward:

The main clause is "The rat hides." Then, we have a modifier for the rat, namely that it is being hunted by the cat: "The rat the cat hunts hides." Finally "the dog chases" modifies the cat - three animals run after each other and the leading one manages to hide.

The horse-race-ringer-false sentence can be analyzed in a similar way: We start with "The claim was false". Next, we specify the claim: "The claim (that) the horse was a ringer was false." Finally, we have an additional qualifier on the horse, namely that an unknown "he" entered it (into a race).

Answer:
**None of the other options are correct.**

To solve a syllogism problem, it is best to find a way to refute each of the possible conclusions by making an assumption that does not contradict the givens. You will likely need different assumptions to deal with different conclusions

If we assume that chemists are exactly those beekeepers that aren't artists, we have disproven both "Some artists are chemists" and "Some chemists are artists" - in this case, no chemist is also an artist and vice versa. So these two must be wrong, but this doesn't help with "Some chemists are not artists".

For that one, we make a different assumption (that also does not contradict the givens): Chemists are male artists. In this case, all chemists are artists.

The two extra assumptions contradict each other, but that is not a problem: We want to prove that the conclusion can't always be true - we can make up a case where each of the conclusions must be false. Obviously "some chemists are artists" and "some chemists are not artists" can't both be false at the same time - but we can come up with a case where one is false and a different case where the other is, so neither is irrefutably true.

To solve a syllogism problem, it is best to find a way to refute each of the possible conclusions by making an assumption that does not contradict the givens. You will likely need different assumptions to deal with different conclusions

If we assume that chemists are exactly those beekeepers that aren't artists, we have disproven both "Some artists are chemists" and "Some chemists are artists" - in this case, no chemist is also an artist and vice versa. So these two must be wrong, but this doesn't help with "Some chemists are not artists".

For that one, we make a different assumption (that also does not contradict the givens): Chemists are male artists. In this case, all chemists are artists.

The two extra assumptions contradict each other, but that is not a problem: We want to prove that the conclusion can't always be true - we can make up a case where each of the conclusions must be false. Obviously "some chemists are artists" and "some chemists are not artists" can't both be false at the same time - but we can come up with a case where one is false and a different case where the other is, so neither is irrefutably true.

Answer:
**Fifty percent**

The problem uses three cards (R/R, R/W, W/W), each with two sides. Each time a card is drawn there is thus a 1 in 3 chance that any particular card will be drawn, but from a formal standpoint that is a red herring, because, relevantly, there is a 1 in 6 chance that any particular side will come up - keeping your eyes closed until you set the card down ensures it is a truly even random selection between the six sides.

Nevertheless, once you see that the top card is red, you've already eliminated the white-white card. By observing, the odds change. Sort-of. There always was a 50-50 chance that the downward facing side was red. There are six sides, three of them red, and randomly, 3 in 6 chance of it being red. Once observed, you've rejected one card and the odds change to... still 50-50. the bottom side of the card can either be red or it can be white.

The problem uses three cards (R/R, R/W, W/W), each with two sides. Each time a card is drawn there is thus a 1 in 3 chance that any particular card will be drawn, but from a formal standpoint that is a red herring, because, relevantly, there is a 1 in 6 chance that any particular side will come up - keeping your eyes closed until you set the card down ensures it is a truly even random selection between the six sides.

Nevertheless, once you see that the top card is red, you've already eliminated the white-white card. By observing, the odds change. Sort-of. There always was a 50-50 chance that the downward facing side was red. There are six sides, three of them red, and randomly, 3 in 6 chance of it being red. Once observed, you've rejected one card and the odds change to... still 50-50. the bottom side of the card can either be red or it can be white.

Answer:
**One out of three.**

This problem is tricky for reasons not well understood by psychologists. Some characteristic of human reasoning makes it difficult to grasp the logic, even once it has been laid out openly.

Tom has received some information, but he cannot use it to make any deductions about his own fate, because the guard always has an option to name someone, regardless of who has been chosen.

If Harry was the one selected to die (1 in 3 chance), the guard must name Dick as he can't name Tom.

If Dick was selected (also 1 in 3 chance), the guard must name Harry, for the same reason.

If Tom was selected, the guard can name either Dick or Harry, so each case has half of Tom's 1 in 3 death chance (i.e. 1 in 6) to be true.

That however does not change the relative probability of the cases we have not eliminated. Thus, we have to contrast the 1 in 6 chance of "Tom will die, the guard names Dick" and the 1 in 3 chance of "Harry will die, the guard names Dick". We have to multiply these chances by 2 (since half the original options were eliminated), thus Tom still has the 1 in 3 chance to die, with the remaining 2 in 3 now fully borne by poor Harry.

If you know the Monty Hall problem, you might have noticed this is the very same setup except that Tom doesn't get the option to make a new choice of doors. He's stuck with his 1/3 chance to "win" - and he probably appreciates it in that context!

This problem is tricky for reasons not well understood by psychologists. Some characteristic of human reasoning makes it difficult to grasp the logic, even once it has been laid out openly.

Tom has received some information, but he cannot use it to make any deductions about his own fate, because the guard always has an option to name someone, regardless of who has been chosen.

If Harry was the one selected to die (1 in 3 chance), the guard must name Dick as he can't name Tom.

If Dick was selected (also 1 in 3 chance), the guard must name Harry, for the same reason.

If Tom was selected, the guard can name either Dick or Harry, so each case has half of Tom's 1 in 3 death chance (i.e. 1 in 6) to be true.

That however does not change the relative probability of the cases we have not eliminated. Thus, we have to contrast the 1 in 6 chance of "Tom will die, the guard names Dick" and the 1 in 3 chance of "Harry will die, the guard names Dick". We have to multiply these chances by 2 (since half the original options were eliminated), thus Tom still has the 1 in 3 chance to die, with the remaining 2 in 3 now fully borne by poor Harry.

If you know the Monty Hall problem, you might have noticed this is the very same setup except that Tom doesn't get the option to make a new choice of doors. He's stuck with his 1/3 chance to "win" - and he probably appreciates it in that context!

This quiz was reviewed by FunTrivia editor spanishliz before going online.

Any errors found in FunTrivia content are routinely corrected through our feedback system.

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