Berengaria, Wanda, I don't think it is a coincidence.
If you know that 144 is a full sqaure, you react at it instinctively. Of course, everyone likes 144, for this very particualr reason. 169 and 196 and 225 and 256 and so on.
I think, likelyhood that a person remembers squares by heart depends on a country: fashions are different, math education is different. And also people with different education come here from different places. Consider also the likelyhood to answer such a question, it also depends on culture.
About the wording:
- such problems: "Vasia eats[likes, kisses, ....] this kind of cookies but doesn't eat that kind of cookies", with characters having math-based habits are familiar to me
- often in math numbers with 'unusual' or noteworthy properties are called 'good'. Informally and formally. It can be even a part of statemnt of a problem or even a serious theorem. "Let's call all Berengarias who satisfy the following condition ........... "good Berengarias". Prove that the number of good Berengarias is even".
P.S. In physics quarks have 'flavours' (which are: up, down, strange, charm, top, bottom). Just another example of application of terms you could find unusual. Point is that, they had to call them somehow:) And a boring 'scientific' word woul only be misleading, becasue they speak of somethign new.