I agree, if I met similar problem in real life I'd easily call it impossible. Maybe that's arrogance, but it's good to do these every once in a while to remembe

I agree, if I met similar problem in real life I'd easily call it impossible. Maybe that's arrogance, but it's good to do these every once in a while to remember that even if something seems "impossible" there still might be a solution. And the solution might be simpler than you think if you can just get rid of the tunnel-thinking. Also, in real life problem you usually agree that there might be no solution, which makes you give up even quicker. Here I knew (99% sure) that there is solution, but still I managed to miss it.