Your second prompt was explicitly hinting Gemini towards what it had missed, highlighting the "his" rather than asking Gemini to double-check whether its first answer made sense without providing any clues:
> Are you sure this is correct? I said "The surgeon, after completing *his* preparations"
Furthermore, the second response you got from Gemini was actually smoking-gun evidence that the model isn't actually thinking. Note how, after Gemini has been clued to notice its mistaken assumption, its reevaluation remains anchored on the pointless idea that the surgeon may the young man's "Other" father.
What other father? There are only two characters in the prompt: the young man and a surgeon. In this situation, what on Earth is the difference between the young man's "Father" and the young man's "Other Father"? Evidently Gemini has no comprehension of the actual prompt and is incapable of critical reevaluation of its content, and rather will stick to its context window whether or not it makes sense.
The model actually answered this in the first prompt answer:
### Other Possibilities In the modern context, there is another valid answer: * The surgeon could be the young man's other father (in the case of a same-sex couple).
Exactly, but only because in the first prompt under the mistaken assumption that a father died in the crash, it would make sense to refer to another father. However, no father died in any car crash in your modified "riddle", which didn't stop Gemini from being anchored to the context window even after you asked it to correct itself.
Put it this way. Imagine if in the original riddle, where a father died in the accident, the surgeon had made their familial relation explicit: the surgeon could have said ‘I can’t operate on him, he is my son. I am his mother’ or, in a modern context, ‘he is my son. I am his father’. Hence, there are indeed two possibilities: the surgeon is either the boy's mother or his [other] father.
Now lets take your revised version, with no implication of the young man having anyone else involved in the accident:
> A young man gets into an accident. The surgeon, after completing his preparations, says: ‘I can’t operate on him, he is my son. I am the boy's ${PARENTAL_RELATIONSHIP}.’
Do you think that, as Gemini stated, there are still two distinct possible solutions?
>Wouldn't it be correct to have two fathers in a child adopted by gay parents?
Having two fathers doesn't mean having a father and an "other father". It means having two fathers, in the same way that having two parents doesn't mean having a parent and an "other parent".
In the original riddle it makes sense to refer to "another father", but not in the revised version in which there is no mention of a father involved in the car crash.
> Are you sure this is correct? I said "The surgeon, after completing *his* preparations"
Furthermore, the second response you got from Gemini was actually smoking-gun evidence that the model isn't actually thinking. Note how, after Gemini has been clued to notice its mistaken assumption, its reevaluation remains anchored on the pointless idea that the surgeon may the young man's "Other" father.
What other father? There are only two characters in the prompt: the young man and a surgeon. In this situation, what on Earth is the difference between the young man's "Father" and the young man's "Other Father"? Evidently Gemini has no comprehension of the actual prompt and is incapable of critical reevaluation of its content, and rather will stick to its context window whether or not it makes sense.