I’m addicted to riddles, and Russian riddles are vastly preferable to the ones I’ve heard in the States. My godfather gave me this one:
One hundred wise men are on a bus. A random number (not zero) of randomly selected wise men have had their faces marked with paint. The wise men can all see each other, but they cannot communicate in any way. They are told that the bus will make one hundred rest stops before they reach their destination. A painted wise man has the right to get off the bus to wash his face, but if a clean wise man gets off the bus, they are all killed. Without communicating, how do all the painted wise men wash their faces?
I’ll post the answer in the comments tomorrow. This isn’t a trick question — there isn’t a mirror in the bus, they can’t touch their faces, etc.
I am assuming those who have paint on their faces do not know they have paint on their faces. Are they allowed to forcibly stop each other from exiting the bus?
Nope — that’s communication.
ANSWER:
Each wise man looks around and counts the number of dirty faces he sees (N). If no one gets off the bus at or before stop number N, he gets off at stop N+1.
The riddle works according to inductive reasoning. If only one wise man has a painted face, he would look around and see only clean faces. He would immediately know he was the only marked one and get off the bus at the first stop. If two people (A and B) are marked, each of them would see one marked person. When A sees that B did not get off at the first stop, A knows that he must also be marked. Both A and B would then get off at stop number two. This pattern can be applied to any number of people. So, for example, if there are ten wise men with dirty faces, they would get off the bus at stop number ten.
i definitely think i could have gotten that if i realized that the wise men were told how many of their faces had been painted. i don’t know if i was stupid not to realize this, or if the question ought to have made it clear. both are likely (:
ha ha, never mind. this riddle - like all of yours - is a lot smarter than i am.
oh, i somehow thought that only one could get off the bus at a time. now i realize it doesn’t say or imply that at all.
” When A sees that B did not get off at the first stop, A knows that he must also be marked”
Is this not communication of a sort? Observing one another and responding based on the observation?
Boy did that riddle give me a headache and I wasn’t even close to getting the right answer.
Cool riddle!
I did not get the correct answer for it, though. Bummer.
I feel intrigued. It is a suspense story. I will wait until you public the answer in your next post.