1. Suppose you are offered one of four prizes. Prize A is the
best of the four, Prize B is average, and prizes C and D are booby
prizes. You are invited to make a statement. According to the
rules, if the statement is true, you will get either A or B, and if
it is false, you will get either C or D.
(a) Suppose you have your heart set on prize A, what statement
could you make to ensure that you will get prize A?
(b) Suppose that for some reason, you prefer the booby prize C to
everything else. What statement could you make to ensure that you
will get prize C?
2. In a certain county jail, there are four innocent prisoners. One
day, the jailer takes them out and places them in line on, in such
a way that
(a) D can see A, B, and C
(b) C can see A and B, but not D
(c) B can see only A
(d) A can see none of the others
The jailer shows them 6 hats, of which 3 are white, 2 are black and
one is red. After this, he blindfolds the men, places one hat on
each of their heads, and removes the blindfolds again. The jailer
tells his four prisoners that if one of them is able to determine
the color of his hat within two minute, all of them are released.
Otherwise, they will all be executed. Assume that all four are
intelligent, and all want to be released. After 1 min 59 secs, A
shouts out the color of his hat. The jailer then releases all the
prisoners. What is the color of As hat and how does he
know?
