BrainMan Posted February 24, 2004 Posted February 24, 2004 This was posted by someone else on another site. It is a fin problem that I now pose to you. You have to choose randomly (with a 50-50 chance) between two people using three unfair coins. How do you do it? The coins can be unfair in any specific specified way (they just cannot be 50-50 for heads and tails). And, for a nice start (and easier problem), how would you do it with three fair coins?
YT2095 Posted February 24, 2004 Posted February 24, 2004 1`stly determine in what way each is unfair (is one mostly Heads and another Tails). then match the opposites and occurance of these 2, and use that data to offset the results to a true 50/50 outcome. I`m no mathematician though, so I may be totaly wrong
BrainMan Posted February 24, 2004 Author Posted February 24, 2004 Actaully, I think I stated the problem wrong. It was supposed to be: How do you choose randomly between three people using a single unfair coin? Sorry for the mistake...
Sayonara Posted February 24, 2004 Posted February 24, 2004 ... What criteria do we have to fulfil to have chosen "correctly"? Just that the choice is random?
BrainMan Posted February 25, 2004 Author Posted February 25, 2004 What criteria do we have to fulfil to have chosen "correctly"? Just that the choice is random? Each of the people must have equal odds of being selected.
Hades Posted February 25, 2004 Posted February 25, 2004 ? i think what i would do is assign each player a specific combo of two turns. player one would be H/H, player two would be H/T and player three would be T/T .. if those particular combos did not come out then they would roll again until someone's specific combo hit.
BrainMan Posted February 25, 2004 Author Posted February 25, 2004 The problem is that your solution does not necessarily work. It is always possible that the flipping will go on forever hitting on combinations that have not been assigned. So you do not garauntee being able to pick a person at random.
BrainMan Posted February 25, 2004 Author Posted February 25, 2004 Also, the combinations you assigned (HH, HT, TT) would not choose randomly between three people even if they did come up. One person would have an advantage over the others- given that it is an unfair coin.
YT2095 Posted February 25, 2004 Posted February 25, 2004 throw the coin up in the air, the one that catches it is sellected. quite simple really
Pinch Paxton Posted February 25, 2004 Posted February 25, 2004 I think you mean choose just two people, and from their throws of a coin, decide which of the three people has a rigged coin. If the two people throw heads/Tails then the other has a rigged coin. If one of the people throws heads/tails, but the other always throws heads, then he has a rigged coin. But that is way too easy. Pincho.
BrainMan Posted February 25, 2004 Author Posted February 25, 2004 I think you mean choose just two people, and from their throws of a coin, decide which of the three people has a rigged coin. No, the second way I stated the problem is correct.
Pinch Paxton Posted February 25, 2004 Posted February 25, 2004 Oh, then they are all using an unfair coin, because there must be some weight difference between heads, and tails. Like the butter side down problem? Pincho.
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