This riddle, one of the world's oldest, is still good for starting arguments.
A man is looking at a portrait. "Whose picture is that?" someone asks, and
the man replies: "Brothers and sisters have I none, but that man's father
is my father's son." At whose picture is the man looking?
Spoiler
The portrait is of the man's son. Many people mistakenly argue that the man
is looking at a picture of himself. If he had said, "... that man is my
father's son." then this solution would be correct, but he said, "... that
man's father is my father's son." One way out of the confusion is to
substitute the word "me" for the more cumbersome phrase "my father's son."
Then the statement becomes, "that man's father is me."
That Old, Old Story
The old riddle starts with the host pointing to a portrait on the wall.
In the modern version, which starts the same way, he might go on to say:
'Brothers and sisters have I none, but that man's father's a score and
one years older than that old son-of-a-gun, whose father of course is
my father's son.' Pausing a moment, he would continue: 'Forty was he
when his portrait was done, two years ago by an artist for fun.'
Now, how old would the speaker be?
Hunter, Fun with Figures, Problem 122
The riddle of the Sphinx
What walks on four legs in the morning, two legs in the afternoon, and three
legs in the evening?
Spoiler
The answer is man: crawling on four "legs" in early life, walking on two legs,
then using two legs and a cane in later life.
A new Sphinx riddle
What can make one man blind and another man see,
makes one building strong and tears another one down?
Spoiler
The answer to your riddle is "sand", because you can throw a handful in
someone's eyes to blind them, melt the sand to make glasses to help them
to see, and concrete makes buildings strong while sandstorms tear them
down. But glasses and concrete are quite a bit more recent than
Oedipus. Maybe they had other answers in mind, but I can't imagine sand
helping someone to see until many many years after the fall of the
Greeks.