This typpe of problem is nearly impossible for folks that have never heard a similar test and nearly trivial for someone who has heard ~3 like it.
The interviews were an in-depth back-and-forth discussion, as much as could be had in about 25 minutes. These interviews, of course, are just one component among many in regard to the difficult admissions decision, a chance for the candidate to show us how they think through a problem, how well they can explain their ideas, how well they take hints and suggestions. In every interview, we had paused at a certain stage, when the candidate had a fully formed argument for one of the variations, and asked them to undertake an integrative exercise, summarizing as clearly as they could the entire problem and solution and how they expected it to play out. Since these were interviews for joint philosophy degrees, in my view this step was a key part of the interview, measuring the ability of the candidate to integrate what they had learned from the discussion and to present a complete, coherent argument.
So it becomes a test of preparedness and ruthlessness. The winner is the one who finds out what the questions are and studies them. Or studies enough IQ stuff to get through.
Its leetcode basically.
Not sure what the solution is. I think additional on topic exams you study for and have past papers would be better.
I didnt apply for oxbridge because of this extra pressure. My worry was id screw up the bread and butter of the a levels with the extra study needed for this kind of test.
Being an interview scenario too means you need to act. I was shy but very passionate about maths. A London college gave me feedback I wasn’t passionate about maths and should consider another course. Based in half an hour with me.
My guess is that 'impossible problems' either pick up on people who know "Oh that's the 2 generals problem" (gold star) or can quickly cycle through ideas and then pick up on the shortcomings as they mentally explore. Maybe A+ if they can explain why it's impossible, A if they say it is, D- if come up with something that doesn't work.
The object is generally to explore how a candidate thinks. If it turns out they memorised logic puzzles and can’t explain them then they will not get through the interview.