A terrible despot governing one small country decided tocheck
how smart are people living in his country. He gathered 20 smartestpeople
and put hats on their heads. Everybody could see all hats excepttheir own.
Then the despot said: \"Some of the hats have a red stripe on them.I will
give you one minute to think and then ask who has a red stripe ontheir
hat? If nobody answers, then I will give one more minute and askthe same
question again. I will repeat it 100 times. If you guess somehowthat you got
stripe on the hat you have to wait till I ask my question and sayimmediately
about that, because after somebody will gure out correctly that heor she
has a stripe on the hat, I will kill everybody else who has thestripe and did
not gure it out. If you say that you have a stripe and you don't ,I will kill
you. \" They know that each of them is really good at deduction (gotA for
Math 311W when they were in college) and nobody wants to die.
a) Prove that if 2 people have red stripes on their hats, thenafter the terrible
despot will ask them second time all of them will say that theyhave them,
and despot won't be able to kill anybody.
b) What happens if three people have stripes?
