I don't think you understand the problem. Even if you manage to find 4, 4, 3, 1 and 6, 2, 2, 2, you still have to verify that if the sum is 12, then there is only 1 possible product. You'll note that nobody in the linked thread succeeds at this (one guy proves that 12 works by exhaustive search, not really a possibility in an interview...)
Well, I saw it before, and it took a several minutes then, maybe 5 or 15, I don't really remember. Then you have to consider that companies like D.E. Shaw end up hiring people who would end up giggling at how long somebody slow like me would take to solve the problem.
