I was thinking about this at work today as I was cracking eggs for various breakfast preparations. We typically buy 60-packs of eggs, which contain 2 flats of 30 eggs each in a 5x6 configuration. Since we nearly always use multiple full trays at a time, I'm not concerned in leaving them balanced and just pull them out by going right down the line. Though I've never tried it, you could presumably follow the Rule of 31 with this configuration.
Your "preferred" method actually makes total sense to me as a physics person and is my habit as well. At each step, you're removing the egg (or one of two eggs) that contributes most to the instability of the carton around its center of mass. Thus making the carton progressively less likely to take a tumble and destroy all the remaining eggs.
I discussed your previous post with co-workers and one pointed out that you can cut the box of 18 into sections of 12 and 6, then balance the 6 eggs in the spaces between the 12 and end up with a smaller box. I think I'm going to start doing this.
As an asymmetrical egg puller, I'm shocked to find out that I am in the minority. I found out my wife, though allergic to eggs, pulls eggs symmetrically. Fortunately, it has not put a strain on our marriage.
Seeding a tournament bracket, where you try to balance the top seeds in the various parts of the draw, follows a similar principle. In the familiar 16-team regions of the NCAA tournament, you have a Rule of 17 (1 vs. 16, 8 vs. 9, 4 vs. 13, 5 vs. 12...).
From there it's not particularly complicated to go up to 32 teams, and if you drop to 8 or 4, most of us have those pairings memorized. But if you wanted to, say, seed EVERY institution in the NCAA, down to Division III, there are 1,000-some schools and you'd need a 10-round tournament (plus some play-in games). And I really hope none of you have those pairings memorized. But you could use the Rule of 2,049 (2^11 + 1) to determine that the 961 seed would play the 1087 seed, then use the Rule of 1,025 (2^10 + 1) to match that game up with the 64 seed.
I've never thought more about how I remove eggs from the carton as I have since Monday. Does anyone else find themselves rearranging the eggs in the carton after a family member removes them "incorrectly"? Or is that just me?
As usual, Paul is dissecting the omelet by investigating the various ways to break the eggs. Or not break the eggs, as it were. Thus allowing us to safely keep all of the eggs in one basket.
I was thinking about this at work today as I was cracking eggs for various breakfast preparations. We typically buy 60-packs of eggs, which contain 2 flats of 30 eggs each in a 5x6 configuration. Since we nearly always use multiple full trays at a time, I'm not concerned in leaving them balanced and just pull them out by going right down the line. Though I've never tried it, you could presumably follow the Rule of 31 with this configuration.
Your "preferred" method actually makes total sense to me as a physics person and is my habit as well. At each step, you're removing the egg (or one of two eggs) that contributes most to the instability of the carton around its center of mass. Thus making the carton progressively less likely to take a tumble and destroy all the remaining eggs.
I discussed your previous post with co-workers and one pointed out that you can cut the box of 18 into sections of 12 and 6, then balance the 6 eggs in the spaces between the 12 and end up with a smaller box. I think I'm going to start doing this.
As an asymmetrical egg puller, I'm shocked to find out that I am in the minority. I found out my wife, though allergic to eggs, pulls eggs symmetrically. Fortunately, it has not put a strain on our marriage.
Same for us. The things one discovers!
Seeding a tournament bracket, where you try to balance the top seeds in the various parts of the draw, follows a similar principle. In the familiar 16-team regions of the NCAA tournament, you have a Rule of 17 (1 vs. 16, 8 vs. 9, 4 vs. 13, 5 vs. 12...).
From there it's not particularly complicated to go up to 32 teams, and if you drop to 8 or 4, most of us have those pairings memorized. But if you wanted to, say, seed EVERY institution in the NCAA, down to Division III, there are 1,000-some schools and you'd need a 10-round tournament (plus some play-in games). And I really hope none of you have those pairings memorized. But you could use the Rule of 2,049 (2^11 + 1) to determine that the 961 seed would play the 1087 seed, then use the Rule of 1,025 (2^10 + 1) to match that game up with the 64 seed.
Darn, this is what I was coming to say.
The hidden apartment immediately made me think of Dawn of the Dead
Carl Friedrich Gauss is smiling (https://letstalkscience.ca/educational-resources/backgrounders/gauss-summation)
I've never thought more about how I remove eggs from the carton as I have since Monday. Does anyone else find themselves rearranging the eggs in the carton after a family member removes them "incorrectly"? Or is that just me?
Yet another eggs-cellent post! (Of course, I would eggs-pect nothing less.)
As usual, Paul is dissecting the omelet by investigating the various ways to break the eggs. Or not break the eggs, as it were. Thus allowing us to safely keep all of the eggs in one basket.