I have six mugs in my office. I use them throughout the day, to drink coffee from, to drink hot water (with PureGrapefruit!) from. Because I like me a fresh mug, I go through three or four each day, and wash them at the end of the day.
For years, now, I have – after removing every other mug – moved one of the remaining mugs to maintain a visually satisfying x-y symmetry. (The shelf on which I keep them can’t accommodate all six lined up straight, though that possibility didn’t occur to me until I wrote this, and cogitated for a couple more days.)
In recent weeks, I’ve been pondering – idly, without any real focus – whether there might be an initial configuration of the mugs that would allow me to remove each of the six, sequentially, without ever leaving an asymmetric remaining pattern along either the x or the y axis.
The other morning, as I showered, I thought I had it figured out.
But as I wrote this, I realized, I hadn’t solved my puzzle yet, that this configuration – though it seems to satisfy my hunger for symmetry by preserving y-axis symmetry through all five removals – fails along the x-axis.
A couple of notes: my solution satisfies my visual hunger. It turns out, the y-axis symmetry was my visual quest, though I mis-constructed the puzzle. Interestingly (?), though, my mis-construction itself left me with a new hunger – to solve the puzzle I had thought I was trying to solve.
I’m not there yet. I’m a smart guy. I imagine that in less than five minutes with pen and paper and concentrated focus, I could definitively solve the puzzle, or establish conclusively that the puzzle has no solution, either of which would constitute a satisfying resolution of my situation.
But I won’t take this approach. Instead, I’ll continue what I’ve been doing, occasionally drifting into a geometric reverie.