I think the intent is fine, it's an interesting problem to want to find the question or set of questions that is the best predictor of the other questions. But

I think the intent is fine, it's an interesting problem to want to find the question or set of questions that is the best predictor of the other questions. But I'd have thought there must be heuristics to help narrow the search. For example you could calculate how each question correlates to all the other questions[1]. If you picked the set of k questions with the best correlation, then you have a good sense of which will be in the actual "k-corr set". You could widen your search a little bit, but by chopping out any questions which correlate poorly to the overall score, you narrow your search greatly, going from 200 choose 5 to 10 choose 5 is a speedup factor of a million, and you've probably considered all the sets that are likely to be in the final bucket. It's been a while since I've worked in the domain, but OP might also want to check out https://en.wikipedia.org/wiki/Item_response_theory https://en.wikipedia.org/wiki/Item_response_theory and https://en.wikipedia.org/wiki/Classical_test_theory https://en.wikipedia.org/wiki/Classical_test_theory. [1] https://en.wikipedia.org/wiki/Point-biserial_correlation_coefficient https://en.wikipedia.org/wiki/Point-biserial_correlation_coe...