## 4. Whose portrait am I looking at?

When I was a child, this puzzle was incredibly popular. Now it is less well-known. This puzzle has one remarkable feature: most people give the wrong answer to the question and stubbornly defend their solution despite all arguments. I remember that about 50 years ago in one company, a multi-hour debate arose over this puzzle, but those who solved it correctly were unable to convince the others of the correctness of their solution. Here is the puzzle.

A person is looking at a portrait. "Whose portrait are you looking at?" they are asked, and the person replies: "I grew up alone, as a single person, alone. And yet, the father of the one in the portrait is the son of my father (you didn't mishear, everything is correct - the son!)."

Whose portrait is the person looking at?
4. It is amazing how many people give the wrong answer to the question of this puzzle. They mentally put themselves in the place of the person looking at the portrait and reason as follows: “Since I have no brothers or sisters, I must be the only son of my father. Therefore, I am looking at my own portrait.”

The first statement is absolutely correct: if I have no brothers or sisters, then I am the only son of my father. But it does not follow from this that the correct answer to the puzzle is “Myself.” We could have answered this way if the second premise had been “and yet the person we see in the portrait is the son of my father.” But this is not what the puzzle states. It asserts that “the father of the person in the portrait is the son of my father.” From this, it follows that the father of the person in the portrait is myself (since I am the only son of my father). Since I am the father of the person in the portrait, he must be my son. Therefore, the correct answer is that the person is looking at a portrait of his son.

If my reasoning has not convinced the skeptical reader (and I am sure that many readers will disagree with my arguments!), then it can be presented in a more visual form.

(1) The father of the person in the portrait is the son of my father.

Substituting the brief “I” for the more cumbersome expression “the son of my father,” we transform statement (1) into the following:

(2) The father of the person in the portrait is I.

Now are you convinced, dear reader?