Originally Posted by

**Guitarist**
I am just back from a funeral (nobody close, thank heavens), so I want to have some FUN.

A friend posted the following puzzle on another forum to which I subscribe, so I copy/paste without permission or attribution. This is clearly against the rules here, but hey! I'm the boss, and, as a friend here pointed out, I can do as I please. So I quote:

*A star system contains an odd number of planets. One (and only one) astronomer on each planet gazes at some other planet in this star system. Each astronomer looks at the planet closest to the planet on which the astronomer lives. Assuming the distances between pairs of planets are unique, show that at least one planet is not gazed upon by any of the astronomers.*

I offered a slightly frivolous argument, using no math, which was nonetheless based on logic as I saw it. It was semi-rejected on the grounds that it was a **non-constructivist** argument, in that it used the well ordering principle.

So in the name of FUN, I invite you all to have a go using *verbal* logic (no math), then I'll show you my frivolity on the subject.

PS I did also attempt a math proof, which I can show if desired......