> have people line up at the gate prior to boarding in accordance to the integer
Whenever I've had to queue way in advance of boarding in order just not to be at the end of my line, I've wished for this sort of solution—but, every time, it seems to me that you'd just run into the trouble where the lower-numbered folks wouldn't all show up on time, and then you'd have to (1) find a way to insert them into the line, which seems like it would have to slow them down, or (2) put them at the back of the line, in which case the whole point of the numbering scheme would be lost and we'd be right back to lines forming long before they need to do so.
If one had to print tickets, that might be a problem. But with cellphones, you could just have everyone et their seating at the gate. And "dynamically" move people that are late, out of the way.
So, lets say a plane seat 100, 75 show up on time - seat them automatically when the show up at the gate according to preferences. Those that remain, get what remains when they arrive. Want your seat? Want to sit with your group? Be at the gate 10 minutes before boarding (or however long it takes people to line up).
Whenever I've had to queue way in advance of boarding in order just not to be at the end of my line, I've wished for this sort of solution—but, every time, it seems to me that you'd just run into the trouble where the lower-numbered folks wouldn't all show up on time, and then you'd have to (1) find a way to insert them into the line, which seems like it would have to slow them down, or (2) put them at the back of the line, in which case the whole point of the numbering scheme would be lost and we'd be right back to lines forming long before they need to do so.