Question 153226
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.