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Droqen
Droqen
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I'm going to say it's not possible, given these assumptions about the rules are correct:

  1. Each wizard can see every other wizard's hat. Apart from that, no knowledge or information may be imparted to one between getting a hat and making a guess. The wizards aren't able (or allowed) to notice any other details about the other wizards, like for example whose hat they're looking at.

  2. The coin flips (& therefore the hats assigned) truly are completely random & independent.

If these facts are true... each wizard receives absolutely no relevant information about their own hat before making his or her guess. Every wizard who guesses really is guessing, and has a 50% chance of being correct. An infiniteAny non-infinite number of guesses are infinitely unlikely to all be correct. Anything not infinite fails to satisfy the first condition of victory, so [edited replacing my 'infinite number of guesses' bit which dshin responded to]...

The probability of two unrelated events A and B occurring is P(A) * P(B). The accuracy (even if not the contents) of a wizard's guess is not related to that of another wizard's guess. Therefore as the number of wizards approaches infinity, the probability of all their guesses being correct -- P(A Wizard Guesses Correctly) ^ Number of Wizards Guessing -- approaches 0.

Short answer: No. The wizards lose.

EXCEPT I'M A BIG DUMMY AND

i did NOT do my hat-counting puzzle research

also infinity is weird and i forgot to take that into account as well

I'm going to say it's not possible, given these assumptions about the rules are correct:

  1. Each wizard can see every other wizard's hat. Apart from that, no knowledge or information may be imparted to one between getting a hat and making a guess. The wizards aren't able (or allowed) to notice any other details about the other wizards, like for example whose hat they're looking at.

  2. The coin flips (& therefore the hats assigned) truly are completely random & independent.

If these facts are true... each wizard receives absolutely no relevant information about their own hat before making his or her guess. Every wizard who guesses really is guessing, and has a 50% chance of being correct. An infinite number of guesses are infinitely unlikely to all be correct. Anything not infinite fails to satisfy the first condition of victory.

Short answer: No. The wizards lose.

I'm going to say it's not possible, given these assumptions about the rules are correct:

  1. Each wizard can see every other wizard's hat. Apart from that, no knowledge or information may be imparted to one between getting a hat and making a guess. The wizards aren't able (or allowed) to notice any other details about the other wizards, like for example whose hat they're looking at.

  2. The coin flips (& therefore the hats assigned) truly are completely random & independent.

If these facts are true... each wizard receives absolutely no relevant information about their own hat before making his or her guess. Every wizard who guesses really is guessing, and has a 50% chance of being correct. Any non-infinite number of guesses fails to satisfy the first condition of victory, so [edited replacing my 'infinite number of guesses' bit which dshin responded to]...

The probability of two unrelated events A and B occurring is P(A) * P(B). The accuracy (even if not the contents) of a wizard's guess is not related to that of another wizard's guess. Therefore as the number of wizards approaches infinity, the probability of all their guesses being correct -- P(A Wizard Guesses Correctly) ^ Number of Wizards Guessing -- approaches 0.

Short answer: No. The wizards lose.

EXCEPT I'M A BIG DUMMY AND

i did NOT do my hat-counting puzzle research

also infinity is weird and i forgot to take that into account as well

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Droqen
Droqen
  • 1
  • 1

I'm going to say it's not possible, given these assumptions about the rules are correct:

  1. Each wizard can see every other wizard's hat. Apart from that, no knowledge or information may be imparted to one between getting a hat and making a guess. The wizards aren't able (or allowed) to notice any other details about the other wizards, like for example whose hat they're looking at.

  2. The coin flips (& therefore the hats assigned) truly are completely random & independent.

If these facts are true... each wizard receives absolutely no relevant information about their own hat before making his or her guess. Every wizard who guesses really is guessing, and has a 50% chance of being correct. An infinite number of guesses are infinitely unlikely to all be correct. Anything not infinite fails to satisfy the first condition of victory.

Short answer: No. The wizards lose.