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  • en.wikipedia.org/wiki/Subset_sum_problem sounds similar Commented Sep 29, 2014 at 23:43
  • I'm wondering how you are defining the 'randomness' of the subset? Commented Sep 30, 2014 at 1:30
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    A subset of which set? An arbitrary set of integers of size >= N? Only positive integers? A subset of the set of all positive integers? Please clarify! Commented Sep 30, 2014 at 6:32
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    With the given example, 200 questions of which 50 are to be chosen, finding all the subsets of 50 that meet the requirement and choosing one at random is an unachievable task. There are 200 choose 50, or about 454 quattuordecillion (454*10^45), possible subsets. Some will be acceptable, others not. Your computer doesn't have the capacity to find all the acceptable subsets. Even Google or the NSA doesn't have that much storage (it's not even close). Commented Sep 30, 2014 at 15:37
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    Solutions to the knapsack problem inevitably use what you call "guess and check". Commented Sep 30, 2014 at 15:47