THE PUZZLE....(Solution)

The Solution

It requires that once in the room  each one of the three inspects  the hat colours of the other two.

If  those colours are the same, then to guess his or her own hat to be the opposite colour.

Or if any one of the three sees that the hat colors of the other two differ, then he or she must

then remain silent and not make a guess.


Using the above strategy…….


The eight possibilities for the hat colors and the responses needed for an overall 75% chance of winning are…..

RRR, RRB, RBR, RBB  BRR, BBR, BRB, and BBB.


Red
(Incorrectly guesses Blue)   

Red
(Incorrectly guesses Blue)     

Red
(Incorrectly guesses Blue)


Three  incorrect  guesses   No Million Bucks Each
.....................................................................................

Red
(No guess)                           

Red
(No guess)                             

Blue
(Correctly guesses Blue)

One Correct   guess    WIN Million Each
……………………………………………………………..

Red
(No guess)                           

Blue
(Correctly guesses Blue)       

Red
(No guess)

One Correct  guess    WIN Million Each
……………………………………………………………..

Red
(Correctly guesses Red)       

Blue
(No guess)                           

Blue
(No guess)

One Correct  guess    WIN Million Each
……………………………………………………………..


Blue
(Correctly guesses Blue)     

Red
(No guess)                             

Red
(No guess)

One Correct guess     WIN Million Each
……………………………………………………………..


Blue
(No guess)                           

Blue
(No guess)                           

Red
(Correctly guesses Red)

One Correct guess     WIN Million Each
……………………………………………………………..

Blue
(No guess)                         

Red
(Correctly guesses Red)         

Blue
(No guess)

One Correct  guess    WIN Million Each
……………………………………………………………..

Blue
(Incorrectly guesses Red) 

Blue
(Incorrectly guesses Red)     

Blue
(Incorrectly guesses Red)

Three  incorrect  guesses   No Million Bucks Each



………………………………………………………………………….



In the top and bottom responses they do not win the Million Dollars each ,

But in the  6 other responses they each win the Million Dollars.


If one were to run this game repeatedly, the number of right and wrong guesses would be equal.

Even  though the group as a whole would win the money six out of eight times or 75 percent of the time.

That is, half of all individual guesses are wrong, but three-fourths of the group responses are right!


Go figure…..