Last April we published a Puzzle involving Black and White Hats, and now we have another one.
Three people are placed in chairs and blindfolded, and then a hat is placed on each of their heads. The hats are either black or white, and there could be three black hats, three white hats, or two of one colour and one of the other. The hats are picked at random from a bag and placed on heads.
The three blindfolds are removed and each person can now see the other two people, but not themselves or, more importantly, their hat. The people are not allowed to communicate in any way.
Each person can then try to guess the colour hat they are wearing, or they can elect not to guess - a pass. None of the three know what the other two have done.
If one of the people guesses correctly they each win $1 million; if any of the three guess incorrectly they leave with nothing.
They were allowed a meeting beforehand to decide on a method. What is the best method for them to use? Can they guarantee success? Or what is their best percentage chance?
The best method is to agree that anyone who sees two hats of the same colour guesses the other colour, and anyone who sees two hats of different colours passes.
There are eight different combinations - BBB, BBW, BWB, WBB, WWB, WBW, BWW and WWW.
For BBB and WWW the method fails, as all three people will guess, and guess incorrectly.
For the other six combinations one person and one person only will see two hats of the same colour, and will guess correctly. The other two people will see hats of different colours and pass.
Six wins out of eight possible combinations is a win percentage of 75%