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Posers and Puzzles

Posers and Puzzles

  1. Donation Anthem
    The Ferocious Camel
    27 Jul '11 21:16
    You and your roommate are trying to decide who gets the last piece of pizza. You decide to flip a coin to choose who gets the slice, but the only coin you have is biased (that is, there is a x% chance of the coin coming up heads on each flip where x is between 0 and 100, but is not 50).

    How can you use the results of flipping this coin to fairly decide who gets the slice?
  2. Standard member Palynka
    Upward Spiral
    27 Jul '11 21:40 / 2 edits
    Originally posted by Anthem
    You and your roommate are trying to decide who gets the last piece of pizza. You decide to flip a coin to choose who gets the slice, but the only coin you have is biased (that is, there is a x% chance of the coin coming up heads on each flip where x is between 0 and 100, but is not 50).

    How can you use the results of flipping this coin to fairly decide who gets the slice?
    Flip it twice with each player winning once with heads and once with tails. If one wins both, he gets the slice but if it's one each then repeat.
  3. 27 Jul '11 22:43
    Originally posted by Anthem
    You and your roommate are trying to decide who gets the last piece of pizza. You decide to flip a coin to choose who gets the slice, but the only coin you have is biased (that is, there is a x% chance of the coin coming up heads on each flip where x is between 0 and 100, but is not 50).

    How can you use the results of flipping this coin to fairly decide who gets the slice?
    I would reply but was looking into a question I had for you and saw the (or an) answer. Good one!
  4. Subscriber AThousandYoung
    It's about respect
    28 Jul '11 00:10
    Each player flips until one gets heads and one gets tails
  5. Subscriber sonhouse
    Fast and Curious
    28 Jul '11 00:35 / 1 edit
    Originally posted by AThousandYoung
    [hidden]Each player flips until one gets heads and one gets tails[/hidden]
    That could still be by chance. You need to correct for the coin bias.
    I would think that would only be the beginning, since now (assuming you captured the bias correctly) you would throw more tosses, say one side gets 3 tosses, the other 5 to compensate for the flip bias. I would assume you average the numbers then.
  6. 28 Jul '11 00:36
    does the coin bias change?
  7. Subscriber sonhouse
    Fast and Curious
    28 Jul '11 00:37
    Originally posted by Banana King
    does the coin bias change?
    That would be difficult unless it was coated with ice.....
  8. Subscriber AThousandYoung
    It's about respect
    28 Jul '11 02:28
    Originally posted by sonhouse
    That could still be by chance. You need to correct for the coin bias.
    I would think that would only be the beginning, since now (assuming you captured the bias correctly) you would throw more tosses, say one side gets 3 tosses, the other 5 to compensate for the flip bias. I would assume you average the numbers then.
    Both sides get the same number of flips. The bias will apply evenly to both sides because both sides win on heads. They flip seperately.
  9. Subscriber coquette On Vacation
    Already mated
    28 Jul '11 04:34 / 1 edit
    if neither player knows the coin bias, then the coin can be flipped and either player can select heads or tails. it doesn't matter. the guess of the coin is a 50:50 guess that you pick the favored bias side. then the flip uses the coin and the bias has already been neutralized by the random choice. the conditions for knowing or not knowing were not stated in the problem.

    if, however, both sides know the coin is biased and the decision is still to use the biased coin, the problem becomes interesting. So, let's say that tails is favored over heads to some degree and both sides know it. the use of the biased coin should be for the tip. the last piece of pizza should go to the winner of rock, scissors and paper
  10. Standard member Palynka
    Upward Spiral
    28 Jul '11 08:30
    Strange, why doesn't my answer appear when I hover over the spoiler? Well, if someone is interested click reply and quote.
  11. 28 Jul '11 11:34
    Originally posted by sonhouse
    That would be difficult unless it was coated with ice.....
    how is the coin biased in the first place?
  12. Donation Anthem
    The Ferocious Camel
    28 Jul '11 14:39 / 1 edit
    A solution:
    If I am understanding his post correctly, AThousandYoung got the solution that I was thinking of. In more detail: You each flip the coin once. If one person gets heads and the other gets tails the one who got heads wins. Repeat until someone wins. Palynka's solution also works.


    sonhouse - You do not know what the bias is. If you try to figure it out experimentally (e.g. by flipping the coin a bunch of times), you can only approximate the bias and thus cannot assure that the toss is completely fair.
  13. Standard member Palynka
    Upward Spiral
    28 Jul '11 15:03
    Your solution (and ATY's) is more economical than mine. I like it.
  14. Subscriber roma45
    st johnstone
    28 Jul '11 16:16
    Originally posted by Anthem
    You and your roommate are trying to decide who gets the last piece of pizza. You decide to flip a coin to choose who gets the slice, but the only coin you have is biased (that is, there is a x% chance of the coin coming up heads on each flip where x is between 0 and 100, but is not 50).

    How can you use the results of flipping this coin to fairly decide who gets the slice?
    cut it in half, a bit each
  15. Subscriber AThousandYoung
    It's about respect
    28 Jul '11 16:40
    Originally posted by Palynka
    [hidden]Flip it twice with each player winning once with heads and once with tails. If one wins both, he gets the slice but if it's one each then repeat.[/hidden]
    Probably too long, or perhaps you're not allowed to use punctuation.