Probabilistic method problem

Question

100 people are sitting at a round table, they are from 25 countries (4 per country). Pick one from each so that no two are adjacent. Any thoughts?

@Prbmethod: Please try to frame something that looks like an explicit mathematical question. Here is one, which may not be what you have in mind. There are $100$ people in a room, from $25$ countries, $4$ per country. How many ways are there to seat them at a (large) round table, so that no two people from the same country are next to each other? (And you might want to specify when we should consider two seating arrangements to be the same. If you shift all the people in a good arrangement to the right by $1$ chair, is this the same seating arrangement?)

Yuval Filmus · Accepted Answer · 2011-04-30 03:41:48Z

up vote 2 down vote accepted

Use the Lovász local lemma. When I try to use it the parameters don't work, but I'm sure you can make it work...

answered Apr 30 '11 at 3:41

Yuval Filmus
25.9k2871

The example at the wikipedia page en.wikipedia.org/wiki/Lov%C3%A1sz_local_lemma might be instructive. I haven't tried working out the details, but it is very similar. – Aaron Apr 30 '11 at 4:17

1 Answer