Toward a Unified Theory of Proper Egg Use
Remember my obsession with maintaining balance within the egg carton? That goal, it turns out, comes down to a mathematical equation.
Editor’s Note: This post includes several video slideshows that are essential to the story, so I strongly urge you to read the web version, not the emailed version. Phone is fine for this one, however — no computer needed. Enjoy! — Paul
Monday’s post about the best sequence for removing eggs from their carton — “best” being defined as a sequence that preserves symmetry and balance within the carton throughout the egg-removal process — prompted a a lot of good discussion, plus I’ve had some important revelations in the wake of that piece, so I’ve decided that a follow-up post is warranted.
First, as you can see above, I’ve assigned a number to each egg in the carton. I initially did this because I thought it would make it easier to discuss some of the egg-removal sequences (i.e., instead of saying, “Top-right, then bottom-left, then next-to-bottom-right,” we can just say, “6, 7, 11,” or whatever the sequence might be). But once I assigned the numbers, I realized that the key to a balanced egg-removal sequence is simple: Always remove the eggs in pairs that add up to 13.
I had already been following this rule without realizing it, before I even came up with the numerical designations. For example, my preferred sequence, which I showed in Monday’s post, begins by removing eggs 12 and 1, followed by 6 and 7, and then 11 and 2, and so on, always in pairs that add up to 13. Check this out:
The alternate method I presented on Monday also hews to what I’m now calling the Rule of 13, beginning with eggs 10 and 3 and then proceeding like so:
A few readers said they use a different sequence, one that maintains symmetry and balance while leaving a very pleasing zigzag pattern when you’re halfway through the carton. And sure enough, this method also adheres to the Rule of 13 — take a look:
I love that my instinctive urge to maintain symmetry and balance — an urge that many of you said you share — turns out to have a mathematical corollary. I think I felt this on an implicit or intuitive level all along (symmetry and balance are essentially mathematical concepts, after all), but it’s really fun to see it play out explicitly.
This leads us to two questions, the first of which is pretty obvious: What other sequences could we come up with that follow the Rule of 13? I’ll let you folks play around with those possibilities.
The second question, which I find more intriguing, is this: If a 12-egg carton follows the Rule of 13, would the proper sequences for an 18-egg carton follow a Rule of 19?