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There are a lot of interview questions that involve inductive logic. The following is a good example:

Let's say there are 5 blue dragons on the island. The dragons are smart in a way that whenever they are given a statement, they can deduce the statement to its fullest. They die 24 hours after they know their own color, so they keep their mouths shut about it. However, one day, someone tells them 'hey. at least one of you is red.' Five days later, all dragons died.

This seems a bit counter-intuitive since the dragons already know that at least one of the dragons have the red color, so why would they die if someone tells them what they already know, but if we think about it from the beginning, it makes sense.

N=1 one dragon. after someone tells them 'hey. at least one of you is red,' the dragon dies next day.

N=2 two dragons. Let's call them dragon I, dragon II. Both dragons swill two days after someone tells them 'hey. at least one of you is red' because of the following reason:

If dragon I is not red, then we could reduce the problem to N=1 case right away, and the dragon II would've died next day, but if the dragon I saw dragon II alive next day, that means dragon I must also have red color, so they both die next day.

Following similar line of inductive logical reasoning, we can see that for N=5, all five dragons will die 5 days after they heard that 'at least one of you is red.'

Of course, When there's a color-blind dragon or a super-dumb dragon who cannot deduce anything from any statement or observation, every dragon will survive.

Now, however, I saw the following case where inductive reasoning cannot apply.

A good example is this:

https://en.wikipedia.org/wiki/Unexpected_hanging_paradox

Basically, it's the following:

A judge tells a condemned prisoner that he will be hanged at noon on one weekday in the following week but that the execution will be a surprise to the prisoner. He will not know the day of the hanging until the executioner knocks on his cell door at noon that day. Having reflected on his sentence, the prisoner draws the conclusion that he will escape from the hanging. His reasoning is in several parts. He begins by concluding that the "surprise hanging" can't be on Friday, as if he hasn't been hanged by Thursday, there is only one day left - and so it won't be a surprise if he's hanged on Friday. Since the judge's sentence stipulated that the hanging would be a surprise to him, he concludes it cannot occur on Friday. He then reasons that the surprise hanging cannot be on Thursday either, because Friday has already been eliminated and if he hasn't been hanged by Wednesday noon, the hanging must occur on Thursday, making a Thursday hanging not a surprise either. By similar reasoning he concludes that the hanging can also not occur on Wednesday, Tuesday or Monday. Joyfully he retires to his cell confident that the hanging will not occur at all. The next week, the executioner knocks on the prisoner's door at noon on Wednesday — which, despite all the above, was an utter surprise to him. Everything the judge said came true.

Are there any more cases (famous or interesting) like this in which the applications of inductive logic fails? I found that wiki page on unexpected hanging paradox super-interesting.

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It's not that the inductive logic fails in the case of the surprise hanging. Rather, a false assumption (namely, that the prisoner knows that he will be hanged) is being made that, together with the inductive argument, leads to the false conclusion that the prisoner cannot be hanged. So don't blame the inductive logic!

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  • $\begingroup$ I apologize for my poor wording there. I didn't mean that inductive logic 'fails' in this case, but it's just that it's one of those cases where inductive logic cannot be applied, but with faulty assumptions that look reasonable in the first glance, inductive logic can be applied and can lead to erroneous conclusion. $\endgroup$ – user98235 Feb 12 '17 at 5:42
  • $\begingroup$ I think that with a definition for "surprised" as opposed to a vague one inductive logic could still be applied. $\endgroup$ – user400188 Feb 12 '17 at 7:21

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