PROBLEM:
A boy and a girl are sitting on the porch.  "I'm a boy," says the child with black hair.  "I'm a girl," says the child with red hair.

If at least one of them is lying, who is which?
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.


SOLUTION:
The black-haired child is a girl, and the red-haired child is a boy.

If at least one is lying, and there is one of each sex on the bench, then both must be lying.  If only one was lying, then there would be two children of the same sex.  Since the latter would not be following the given rules, then it is concluded that each child is of the opposite sex that they say they are.