On Friday I set this puzzle…….
John wants to toss a coin to make a random decision.
However, he only has a biased coin (that is, a coin that does not have a 50:50 chance of coming up heads or tails). Even worse, John doesn’t know the extent of the bias, and thus has no idea about the likelihood of obtaining a head or tail.
How can John toss the coin to make a 50:50 random decision?
If you have not tried to solve it, have a go now. For everyone else the answer is after the break.
Imagine John tosses the coin twice. The chances of getting heads-tails is the same as tails-heads, no matter what the bias of the coin. Thus, all he has to do is toss the coin twice, assigning a ‘yes’ to HT and a ‘no’ to TH. If the coin comes up TT or HH he ignores the trial and repeats the process until he gets TH or HT.
Did you solve it? Any other solutions?
I have produced an ebook containing 101 of the previous Friday Puzzles! It is called PUZZLED and is available for the Kindle (UK here and USA here) and on the iBookstore (UK here in the USA here). You can try 101 of the puzzles for free here.