I took the coin from out of the biased random number generators jar that had been collecting dust in the corner of the Den, but I needed to choose between two options with 50% probability each. I thought this would be easy since I already calculated the probability that heads would come up for this coin.

From ujjagrawal's puzzle: After flipping the coin 4 times, having heads come up 2 times is the same probability as heads coming up 3 times.

Also, assume the probability heads comes up on any given flip is neither 1 nor 0. Yeah, it's a coin so those are veritable impossibilities, but thought I'd spell it out regardless.

1) How can I choose between the two options with 50% probability?

2) I accidently drop ujjagrawal's coin in the jar, and now don't know which one it is. I grab another coin from the jar. How can I choose between the two options with equal probability using this new coin (assuming both heads and tails can be outcomes on any given flip and occur with constant probabilities)?

3) How can I use the coin from (2) to choose between N options, where N is a positive integer, with the fewest number of coin flips needed on average?

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## EventHorizon

I took the coin from out of the biased random number generators jar that had been collecting dust in the corner of the Den, but I needed to choose between two options with 50% probability each. I thought this would be easy since I already calculated the probability that heads would come up for this coin.

1) How can I choose between the two options with 50% probability?

2) I accidently drop ujjagrawal's coin in the jar, and now don't know which one it is. I grab another coin from the jar. How can I choose between the two options with equal probability using this new coin (assuming both heads and tails can be outcomes on any given flip and occur with constant probabilities)?

3) How can I use the coin from (2) to choose between N options, where N is a positive integer, with the fewest number of coin flips needed on average?

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