22. Three friends make the following statements.
Ben says, "Exactly one of Dan and Cam is telling the truth."
Dan says, "Exactly one of Ben and Cam is telling the truth."
Cam says, "Neither Ben nor Dan is telling the truth."
Which of the three friends is lying?
A Just Ben
B Just Dan
C Just Cam
D Each of Ben and Cam
E Each of Ben, Cam and Dan
Solution
C
If Cam's statement is true, then both Ben and Dan are lying. But then exactly one of Ben and Cam is telling the truth. So Dan is telling the truth. This is a contradiction.

We deduce that Cam is lying.
Hence at least one of Ben and Dan is telling the truth.
If Ben's statement is true, then exactly one of Ben and Cam is telling the truth. Hence Dan is telling the truth.

Similarly, if Dan's statement is true, then Ben is telling the truth.
We deduce that Ben and Dan are telling the truth and that Cam is lying.