SOLUTION: There were 100 politicians at certain convention.Each politician was either crooked or honest. we are given the following 2 facts. a. at least one of the politician was honest. b.

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Question 153226: There were 100 politicians at certain convention.Each politician was either crooked or honest. we are given the following 2 facts. a. at least one of the politician was honest. b. given any two of the politicians at least one of the two was crooked. Can it be determined from these facts how many were crooked? if so how many? If not why not?
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
All but that one are crooked. What a lousy problem for politicians :)
Why?
You are told that given 'any two' at least one is crooked. So let's take the one honest one and put him/her in our pair. Now, one by one, pick each of the other 99. Since 'at least one' must be crooked, then the one we add to our honest politician be crooked. Doing that for each of the 99 others folks, says they must ALL be crooked.