sniffnoy | Hooray for hygensvygref!

(Note that because it's a big hint[0] for the problem below, "hygensvygre" will appear ROT13ed throughout this entry.) So Babai gave us this problem, right? (See two entries below, I'm too lazy to make a link.) He gives us this problem the very first lecture, as a puzzle problem, and now that we've discussed hygensvygref, he says, OK, use this to do one half of a certain puzzle problem. So of course he means, use this to do the infinite case of this problem, because that's easy. But what about the finite case? If we have such a function, can show it necessarily comes from an hygensvygre? Indeed we can! This both solves the finite case as well as, in general, well, showing that such functions are equivalent to hygensvygref. But Babai didn't know this, and only knew some other finite-specific way of doing it. So, yay, I figured out something Babai didn't know.

But also, apparently, this means you can do the finite case without hygensvygref. Though it's definitely cooler to do it with them.

(You know, "hygensvygre" and "hygensvygref" are surprisingly pronounceable.)

-Harry