In this case the "arbitrary filter" was filtering applicants to a university for very basic math knowledge, so I think assuming that it's correlated with success at that university is not very far fetched.
I don't think after playing 20 or so levels I was much smarter for it. It turned out to be a bunch of rules that were extremely limited. You do begin to appreciate trig much more.
If you are being given a geometry subject test and are prepared for it, this is fair game. If the question is just given out of the blue as a brain teaser, then no, the university is not mining useful signals at all.
When I did my university entrance interview (for maths, at Cambridge) the interviewers were clear that they expected that some subset of candidates would have seen the problem before, and some wouldn't -- for those in the first set they'd get them to quickly go through the problem and move onto the later parts which would be new to them; for those in the second set they'd provide sufficient guidance to let the candidate walk through the problem. The point was to get any particular candidate to a point in the problem sequence where this was something new to them, and then see how they tackled things. The idea that some applicants (usually from public schools) would have been very highly prepped for interview and others (usually from state schools) would not was clearly something they were well aware of and setting their interview design up to handle.
But how do you know it's a new problem? You can always fake a little struggle and thinking your way to the solution for a problem that you know the answer already.
