This puzzle was first posed by John von Neumann, and it is still quite tricky to work out.

You have a coin that is biased so that the probability of a head is not the same as the probability of a tail. The probabilities of each are fixed but you don't know the probabilities.

How can you use this coin to produce an outcome where both alternatives have a 50% probability?

The solution should work irrespective of the degree of bias in the coin, although clearly not if it lands heads 100% of the time!

If the probability of a head is h and the probability of a tail is t, then the probability of a head followed by a tail is h*t and the probability of a tail followed by a head is t*h. They are the same.

So one person calls head-tail or tail-head and you toss the coin twice. If it lands head-head or tail-tail, repeat until the two are different and you have your result.