Wow, I am surprised #13 is listed as a 1-star problem.
I was told a story about this problem by a professor while in class. Supposedly, Edgser Djisktra couldn't sleep one night due to jet lag. He was currently going through a phase in which was exercising the power of thought, practicing thought-exercises such as these without a pencil and paper. While in bed that night, awake due to jet lag, he solved this problem. The professor told us that none of us were smart enough to solve this problem. Hardly seems worthy of one star. :)
I haven't solved it yet, but it seems to be solvable by sheer diligence? Is there a faster solution? I think in an interview I would ask to write a computer program that solves it. Wait - I guess now I have to try that :-(
Edit: which programming language has good support for primes? I thought I saw one recently, but can't find it now.
Update: OK, now I wrote the program, and in hindsight it was overkill. Just check the candidates for x+y starting from below, and the right solution appears pretty quickly (there are 24 candidates for x+y, but it is not necessary to check them all).
I was told a story about this problem by a professor while in class. Supposedly, Edgser Djisktra couldn't sleep one night due to jet lag. He was currently going through a phase in which was exercising the power of thought, practicing thought-exercises such as these without a pencil and paper. While in bed that night, awake due to jet lag, he solved this problem. The professor told us that none of us were smart enough to solve this problem. Hardly seems worthy of one star. :)