Here's a numbers puzzle to think about during your idle cycles.
Let's start with some background. Say we have a spinner with 3 numbered sections. Each section in this spinner is equally likely to be picked when the spinner is spun. Now, say that this spinner had the numbers 1, 2, and 5. Let's take another spinner with the numbers 3, 7, and 9. If we put both the spinners in a heads-up competition against each other, the second spinner (3 7 9) would win in the long-run. So, we say that Spinner 3 7 9 dominates Spinner 1 2 5.
Onto the puzzle. We have 3 spinners just as described above. How can you assign the numbers from 1-9 to each of the sections, using each number exactly once, such that we have cyclical dominance? That is to say, Spinner A dominates Spinner B dominates Spinner C dominates Spinner A. Put yet another way... say we lay these spinners out on a table much like weapons prior to a duel. I then ask you to choose your weapon first. I will always be able to choose another that dominates yours (i.e. gives me the advantage) if there is a dominance cycle.
Follow-up question. There is more than one possible configuration that satisfies the cyclical dominance constraint. When you find one, check to see if your configuration is a fair one? A fair configuration being defined as one where any pair of spinners chosen will result in the same advantage for the dominant spinner.