It's just a matter of breaking the problem down Into an easier problem or set of problems.

All the additions are interchangable, so you could choose to add 1+2+3+4 or 4+1+2+3 and then 4+1=5 and 2+3=5 and then youve got 5+5 which is easy its 10. So you go ok you can do the conversion with 1 and 50 except it's still tough mental math so you say 1 and 100 to get 101 100 times, but that's twice too big so you slap it in half and you get the answer. It's solving a tough problem by splitting it into problems that aren't as tough.

The first step is knowing what tools you have in your belt. The second is knowing how they work in detail. The third part is the inspiration of using them in a way that solves a difficult problem.

I'm not a mathematician, but I've found interesting solutions to problems like this before, and it's fun when you understand your tools and understand the problem and it all comes together to find a solution nobody else would have.