Earlier quoted context omitted.
Thank you so much for this bit of humor. After ChatGPT first responds with the surgeon being the mom, I asked it to read the riddle more carefully, thinking it might figure it out with a little prompting. I got this gem of a response: Ah — now I see the twist. The patient is the cousin, but the surgeon says “He’s my son.” That means the man who died was the surgeon. So how is it possible? Because: The surgeon is the…
Now I really want to see that diagram…
(This is OEIS sequence A280873)
But it turns out that's overkill. Just giving them a single Ahnentafel number and asking if you could have inherited X DNA from them, trips them up.
But it turns out even that is overkill. Leave out X DNA entirely, and ask them to describe how Ahnentafel number 67 is related to you, and that's too recursive for them to figure it out.