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flamebirde

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Posts posted by flamebirde


  1. Spoiler

    So the chances that the first two will match is 1/52. That much should be fairly obvious I think.

    If they do, then the chances of the next two matching is 1/51, and if they do then the chances of the next two are 1/50, and so on.

    If a pair doesn't match, then we're looking at an issue -- at least one more pair is guaranteed not to match... but there's some finicky stuff going on there, since you could have a loop of 3 or more unmatched pairs if it chains down a bit. So at minimum if you draw a non-matching card then you have at least 2 unmatched pairs right there and potentially more. Not to mention that you could spawn different "loops" in one run through.

    if a pair doesn't match, then the chances of the next pair matching are... what? That's where the riddle lies next I guess. If we number the first deck 1-52 and the second 1'-52' and the very first pair is 1-2', then we know that the next pair (the one starting with 2-) must also not match. Then there's a 1/51 chance that the loop ends there -- a 1/51 chance that the next pair is 2-1', in which case the probabilities continue as before. But there's also a 50/51 chance that the chain extends, and we draw something like 2-5', which means that now the fifth pair (the one starting with 5-) is guaranteed to be a non-match with a 1/45 chance of terminating.

    I'm sure there's an easier way to think about it, but I'm gonna let it percolate through the back of my head for now.

    Seems similar to that airplane seating problem a while back, I'll see if I can't find and link it here.

    Edit: here it is:

     

     


  2. 19 hours ago, rocdocmac said:

    Both Captain Ed and Thalia have transmitted vital clues in their previous remarks. Eish man, now you ought to get it!

    Spoiler

    ../ -  ....  ..  -.  -.-/ .. / ..-.  ..  --.  ..-  .-.  .  -../ ..  - / ---  ..- !

    What hath God wrought!

     


  3. 21 hours ago, Thalia said:

    fb- Joe is trying to sell you his share. You are paying him the $200... if you accept his offer. 

    A question

     

      Hide contents

    Who owns the car? If you take his offer and he owns the vehicle, you've got transportation issues. That said, I agree with flamebirde's reasoning so I guess either way, the odds are against you. Not owning the vehicle would just make it worse.

     

    whoops. In that case, I say refuse the offer. Assuming that the rest of the puzzle (i.e. the vehicle) is just story fluff and that the $1000 price tag of the rock is after processing, my answer remains the same. His share isn't even worth $100, let alone $200.


  4. Spoiler

    Yes. This is a question of Bayesian probability. The test results in a relatively large proportion of false positives. In fact, the majority of positives delivered by the test are actually false positives. Consider this case: say you scan a hundred rocks. Only 1%, or one rock, is actually gold. But your scan would result in ~9-10 false positives. That means you only have about a 10% chance that one particular positive rock actually has gold. Since the rock is worth $1,000 with a 10% chance or $0 with a 90% chance, the average value of the rock is just $100. Hence, it's a better deal to take the guaranteed $200 than the 10% chance at $1,000.

     


  5. assuming five apples in each bowl,

    Spoiler

    you have a 2/5*1/4 chance to survive in the first bowl, or 10%. You have a 3/5*2/4*1/3 chance to survive with the second bowl, or a 10% chance. Its the same chance either way. I say it doesn't matter. (I assume that after eating an apple you take it out of the bowl.)

     


  6. Spoiler

    It's very similar to the "read the line" solution, just in reverse.

    one

    one one

    two one

    one two, and one one

    one two, and three ones

    one three, one two, and two ones

    one three, two twos, and three ones (1 3 2 2 3 1)

    two threes, two twos, and two ones (2 3 2 2 2 1)

    one three, four twos, one one (1 3 4 2 1 1)

    and so on and so forth. The trick is that the largest number comes first, and then it descends. So instead of the read write sequence breaking up, say, 1 2 1 1 into one one, one two, two ones, this sequence breaks it up into one two and three ones.

     

     

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