The Birthday Mystery - A Reportedly P6 Maths Question

Earlier this week, a colleague of my mine came to me and said, "Hey, you high IQ right? Can help with a question? My girlfriend wants to teach her P6 daughter and cannot solve this question." My colleague then showed me this on her phone.

Having prefixed her request with "you high IQ, right", my ego was at stake and I had to nonchalantly reply, "I think should be able to answer, just need some time." I asked my colleague to forward me the image and started to work on it. Initially, I thought it could be a calendar question where the confluence of month/day could be determined but after a few searches on the internet, I realised it was probably a logic question of some sort.

Once I looked at the logical relationship of the situation and the statements made by the characters, I figured it must be a process of elimination that would lead to the correct birth date. Thus, here is how you arrive at the answer.

Because Ben knows the month, he can deduce what 'day' values Mark cannot possibly have. Hence, since Ben says "I can ensure that Mark doesn't know", this means that the 'day' in the correct birth date does not appear just once among the 10 dates provided, thus we can deduce the correct birth date does not fall along the months including 7/6/1970 and 2/12/1970, which therefore eliminates both these rows.

Following Ben's statement, Mark too then knows that these two rows do not have the correct birth date, and since Mark says "now I know it", this means that of the remaining, he is able to pick the correct one because his 'day' value is no longer duplicated (i.e. the remaining birth dates would not have duplicate 'day' values, therefore eliminating 5/3/1970 & 5/9/1970).

And finally, since Ben can identify the birth date at this point, this means that there must be only one month value left which would eliminate 4/3/1970 and 8/3/1970, leaving 1/9/1970 as the correct birth date.

Of course, expecting this train of thought from of a 12-year-old is ridiculous.

Update:
I was alerted to the fact that MOE posted on twitter that the above is not a PSLE question (to be honest, I didn't think it was a PSLE question, to begin with). However, a few people have posted that they were indeed asked to try this question in school. In addition, this type of question is called an Impossible Puzzle and different variations do exist (if you're interested in this type of thing).