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The survivor riddle can be found here and the evil geometry problem can be found here. I suggest that you read about those riddles there before you continue reading so that you will understand this question better.

For the airplane riddle, some people might be thinking they can assume there will be no survivors in the crash so it will actually be correct to say that all the survivors will be buried. For the evil geometry problem, they can directly deduce that the triangle has area 30. They were just given a mathematically impossible premise and didn't feel the need to check by doing math in their head that that the premise was mathematically possible. It's just like when somebody uses a computer to aid them in a proof, they put blind trust into the computer and don't feel the need to check by doing math in their head that some of the results the computer calculated for them is wrong and don't have to worry that if some of them were wrong, they wouldn't have noticed it.

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    $\begingroup$ What exactly are you asking? $\endgroup$ – PotatoLatte Jul 30 '18 at 15:41
  • $\begingroup$ I wasn't entirely sure myself, but I took a crack at it anyway -- seems to be asking about the premise of the riddles and how they try to trap people....(or at least, that's how I answered it). $\endgroup$ – El-Guest Jul 30 '18 at 15:43
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    $\begingroup$ Definitely relevant to both cases: XKCD 169. $\endgroup$ – Bass Jul 31 '18 at 4:23
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To me, the survivor riddle

hinges on the usage of language. By definition, a "survivor" is "a person who survives, especially a person remaining alive after an event in which others have died." The riddle uses misdirection by adding unnecessary detail (border of US and Canada) to obscure the fact that a survivor must be alive by definition and therefore does not need to be buried. If there are no survivors, then I guess mathematically the statement "All survivors were buried in the US" is vacuously true, but you would never say that in reality. The riddle should translate more closely to "Assuming that a crash occurred on the border between the US and Canada, and assuming that at least one occupant of the plane was alive after the crash occurred, where were all of the people who were alive after the crash occurred buried as a result of that crash?" (This last part eliminates the technically true answer of "Sweden, because Jimmy was on the plane and he survived, but then he lived another 50 years and died and was buried in Sweden").

The second problem preys on

the fact that most people have either (a) heard of the triangle area formula to find (6)(10)/2 = 30; or (b) heard of Pythagorean triples/triangles and know that there exists a 6-8-10 right triangle, so (6)(8)/2 = 24. People don't expect the fact that there is so much additional complexity behind this question - if I was asking you a quick math question about geometry, chances are you wouldn't expect to have to disprove the existence of the triangle in the question. There is an inherent simplicity bias as well here, since people want to give a quick answer without thinking too hard about it. My first thought certainly wasn't to prove that the maximum altitude of a triangle with hypotenuse 10 was 5.

I hope this helps - to your point, I certainly would agree with you that it isn't that big of a mistake. That said, in order to trick unsuspecting puzzlers, the puzzle relies on the puzzler making those specific mistakes in order to spring its trap, so to speak. So they are not big mistakes, but they are fundamental ones.

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    $\begingroup$ Though for example if you were to try using Heron's formula it would automatically tell you something was wrong (but I don't want to watch a Youtube video just to see what the problem was, so I'm not sure if that's applicable). On the other hand, if the hypotheses of the problem are contradictory, wouldn't that mean any answer is technically correct (ex falso quodlibet)? $\endgroup$ – Daniel Schepler Jul 30 '18 at 18:01
  • $\begingroup$ Essentially the problem requests that you find the area of a right triangle with hypotenuse 10 and altitude extending from the hypotenuse of 6. Heron's formula doesn't quite apply since you would determine that the side lengths were impossible before applying it, but you've got the right idea. Theoretically that may be true, but in this case I would believe that the more correct answer is "the triangle does not exist" rather than accepting any area of a hypothetical triangle as being correct. $\endgroup$ – El-Guest Jul 30 '18 at 18:33

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