The APL Orchard

12:49 PM

(also, submitted the PR that we discussed earlier this week)

10 hours later…

10:30 PM

@RGS A personal challenge to you from Roger Hui:

> m people stand in a circle, each having a hat with a number from 0 to m-1 written on it. Everyone can see the numbers on other people’s hats but can not see his own number. They simultaneously write a number on a piece of paper and give it to the judge. If at least one of them wrote a number that is on his own hat then everyone wins, otherwise everyone loses. What strategy should they use to guarantee victory?

(Numbers on the hats do not have to be all different. People can not exchange any information during the procedure but can agree on some strategy beforehand.)

1 hour later…

11:44 PM

@Adám That's an honor! Interesting problem; are the rest of us allowed to answer it?

@AviF.S. Of course.

@Adám thanks for the forwarding :) 1: Roger may challenge me directly if he wants, you can give him my email; 2: his previous challenge is still on my TO SOLVE stack :)

I've heard a similar one where a bunch of mathematicians gather, and they want to figure out how much they collectively make (want to pitch in to get something together, or something), but they don't want to reveal how much they make to their coworkers....\

So I think they pass around one piece of paper, and then each write something on it, and at the end they should have the sum, but no one must be able to figure out what another makes, or something like that!

Know of it?

@AviF.S. I don't, not that one at least

Haven't heard of it before.

11:49 PM

Also, the infamous logicians/prisoners in a line riddle with either blue/red hat and each can only see what the one in front has...

If you google 'hat line puzzle' a million variations come up! Even mentioned in the NYT, haha

@AviF.S. with three in line? I know a generalization with an infinite line of mathematicians

Haha, of course there's one, lol

Don't know it!

I'm pretty sure it's central to the problem, in the other variations, that it's finite

Because then the one in front can't see anybody's

mathspp.blogspot.com/2018/04/…

That link of my old blog has the infinite mathematicians' variation on the bottom

Oh neat! That's your blog :)

(i should really finish migrating all my stuff to the new blog ⍨)

@Adám how big/small is m? 100% arbitrary?

11:56 PM

@RGS I imagine. He didn't specify.

Wasn't able to find the mathematician's salary problem, but found countless other 'can't-communicate-write-stuff-down' riddles. Guess it's a common problem type! Nevermind