Who Ate My Cake?
Eileen bought a cake, and she put it on a table and left. There were four persons around, Andy, Brian, Calvin and Danny. One of them ate the cake while the others saw him eating it. When Eileen returned and saw the cake was missing, she asked who ate the cake and the replies were as follows:
Andy
: Brian ate the cake.
Brian
: Andy didn't eat the cake.
Calvin
: Andy ate the cake.
Danny
: Either Andy or Brian ate the cake.
If we know that exactly two of them were lying, then who ate the cake?
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Relevant wiki: Truth-Tellers and Liars
We are given that exactly of two of these 4 people are lying.
Because Brian and Calvin told contradictory statements, then exactly one of these two is telling the truth, while the other lied.
This leaves us with exactly one of Andy or Danny to be telling the truth while the other lied.
Suppose Brian ate the cake, then Andy is telling the truth and Danny is also telling the truth well,
which contradicts the condition that only one of them is telling the truth. So Brian couldn't have eaten the cake.
In other words, Andy is lying. This means that Danny must be telling the truth. From Danny's claim, we know that Andy or Brian ate the cake.
Because we have ruled out the fact that Brian could have eaten the cake, then Andy must be the only one that ate the cake .
Double checking shows that Andy and Brian lied, while Calvin and Danny told the truth. Hence, all the conditions are satisfied.