New maths formula answers long-standing party problem

If you invite six people to a party, either at least three of them will all know each other, or at least three will have never met before. But how many people do you have to invite to make sure that any given number of them are all friends, or all strangers?

This is a long-standing problem in combinatorics, the branch of mathematics that counts the ways in which a set of objects can be arranged. The optimal answer is surprisingly hard, and unknown except for a few simple cases. But a team of four mathematicians has now found the best upper limit so far and the most substantial improvement to a previous solution dating back to 1935.

via www.nature.com

No doubt this will result in parties being more fun, which will certainly be a relief.