> I don't understand how to solve the king's dillema at all.

I had the same problem at first -- try converting to decimals; I found that helped me. Anyway, the question you're asking here is, "What is a notable characteristic of the numbers involved?" They all have something in common, and the remainder gives you a good idea what that is. In fact, it actually gives you the answer for the last digit.

Alternately, the three numbers (you can convert them to whole numbers) eventually share a number in common. That nunber is just a couple of steps removed from the answer you want.

By the way, you might want to have a calculator handy.

You know where to use the number, right?

I don't know how well I've explained that, as math is one of my weak points. But that's what worked for me.