I read about this old, elegant puzzle, having forgotten about it nearly a decade ago and thought some here might enjoy it. It's trivial to google for the answer so I urge you to resist that temptation. PLEASE DON'T POST THE ANSWER (not like I can stop you), but feel free to brag if you figured it out.

On to the problem:

Let's assume you are handed a coin, and told that it is biased, but you are told neither in which direction the coin is biased (heads or tails) nor how strong the bias is (70%/30%, 51%/49%...). Your task - devise a procedure, using only the biased coin, that results in either HEADS or TAILS with a probability of exactly 50% for either outcome. You may use as many coin tosses as you want to generate a HEADS or TAILS.

Cheers,
bachfan

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Solution (I think):

von neumann corrector.

Nice job hep!

Indeed. Old tricks are the best tricks.

I thought of that and thought there must be a more elegant solution.

Try the one I asked spadebidder yesterday, it's more interesting:

You have a run calculator for which you can enter 3 numbers m,n,p and it will tell you the probability of at least 1 run of length at least m of events with probability p in n trials. For example, if n=100, m=5, p=0.5 it will tell you the probability that you will get at least 5 consecutive heads in 100 flips of a fair coin. What numbers would you enter to compute the probability of 5 consecutive heads OR tails in 100 coin flips? Note that these are not independent events.

That's how you generate an arbitrary probability given a fair coin.

My first 3 guesses are, without any checking or real thinking....
> Double the flips, otherwise unchanged
> 1 minus the probability squared, otherwise unchanged
> m = 4, otherwise unchanged

...will have a think now.

One of these guesses is very close.

Seriously, nobody?

Answer:

Yeah I got that Bruce, with a little help from your post. I used the inspection method (i.e. guesswork) to solve.

Nice puzzle. Wish I'd been on 2+2 to mull it over before you spoiled it (I have little self-control sometimes!)

Sooooo Eeezeeeeee, do I get to put another star on my wizard hat? Oh forgot my wizard hat has dollar signs...