Monday, August 24, 2009
I Know You Can't Know That
A little puzzle I was offered today, which might perhaps be interesting. I will give what I think is the solution at the end of the week. A teacher says to their pupils, at some point this week I will give you a test, which you will not know is a test until I tell you afterwards. Given that if the test hasn't taken place in the last couple of minutes of Friday, the students will seemingly rightly think that it will take place then, and likewise for the couple of minutes before then, and so on, until the teacher is apparently compelled to say that the test has already been taken, can what the teacher says be true?
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6 comments:
I heard an alternative version, where the teacher promises a "surprise test" in that week (the surprise being in its timing). -- but it can't be a surprise if its on Friday afternoon, so on.
Yes, I also heard the version Alex mentions (but there the paradox seems dispelled because the test will indeed be a surprise if they conclude it cannot happen). On this version, perhaps the teacher's statement is itself the test.
That solution works here too, since as in the case of the surprise, you won't know something you think is impossible is happening.
Is the teacher's name Zeno by any chance?
Old joke. Zeno takes Achilles and a tortoise into a barn at the other end of which are Patroclus and rather cute lady tortoise with a come hither look. "You can advance across the barn" says Zeno "but every pace must be half the length of your previous one." Achilles sets off. "No point" says the philosophical chelonian. "Logic says you won't get across." "Logic be damned" says Achilles (who has been studying economics). "I can get close enough for all practical purposes."
I think that rather depends on how long Achilles' first stride was.
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