Friday, August 17, 2007

Unfair Coin and Die Challenge

[Challenge #1]

Imagine that you have a biased two-sided coin. However, while you know that the coin is biased, you are unsure as to how the coin is biased; that is, you do not know the probability of getting a head or tail.

The first challenge is to use the coin to make a binary decision that has a 50% probabilty. In other words, find a way to make a fair decision.

[Challenge #2]

Imagine that you have a biased 6 six-sided die. As before, you have no idea how the die is biased.

The second challenge is to think of a method to somehow transform (via mathematical, non-physical-manipulation methods) the die into a fair die.

It may be neccessary to flip the coin more than once. Same goes for the die.

[Super Hints]
"May be" ==> "is".