I've stolen this simple one, so no googling allowed:
There are three logicians who are able to reason and deduce with perfect accuracy, their names are A, B, and C. They each know this as well. In a bag there are seven colored stickers. Two yellow, two red, and three green. The logicians know that too. Each logician reaches into the bag, grabs one sticker and slaps it on his forehead without looking to see what color it is. Any one logician is able to see the stickers on his compatriot's heads, but not the sticker on his own.
Jerry the interrogator asks logician A if he knows what color sticker is definitely not on his forehead.
"No.", A responds. Jerry asks logician B the same question, and receives the same answer.
Why must logician Cs sticker be green?
because if C were red and A said no, then B knows that their color cannot be red, because if B and C were red then A would be able to say that their color was not red.
if C were yellow and A said no, then B knows their color isn't yellow.
if C were green and A said no, then B cannot make a determination. Therefore, C must be green.