Whose Picture Am I Looking At?

One of the first puzzles in the book we are required to solve, instead of just reading through the logic, is this:

A man was looking at a portrait. Someone asked him, “Whose picture are you looking at?” He replied: “Brothers and sisters have I none, but this man’s father is my father’s son.” Whose picture was the man looking at?

From the short story, with this man being the man in the portrait, the man and the man in the portrait is obvious somehow related, but how? Below is how we think of it:

Supposed the man is M, man in portrait is P, man’s father is F, this man’s father is PF. Since M does not have siblings, F’s son can only refer to M. As stated, PF = M, according to this logic, so the man was looking at the portrait of his son.

For the next little twist in the question:

The man had instead answered: “Brothers and sisters have I none, but this man’s son is my father’s son. Now whose picture is the man looking at?

To solve this, we change each characters to variables, with the man as M, man in portrait as P, portrait man’s son as PS, man’s father as F. Since M has no siblings as well, F’s son can only refer to M. PS = M, according to this story, so the man was actually looking at his own picture.

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