Here is a puzzle put to me yesterday. I've not seen this before, so i thought i'd post it here, since some of you guys might be interested, or indeed may have already solved it!

There are `n' people at a party. Each person must talk to everyone else exactly once. The guests all talk in pairs, each for a minute then change to another person for the next minute. When n is even, it is possible to achieve this in `n' minutes. How many combinations are there for this optimum time given `n' and what is the best way to find a solution.

For example, there is exactly one solution for 4 people. Call them A, B, C and D. The solution can be tabulated as follows:

A B C D

B A D C

C D A B

D C B A

Columns represent time whilst rows list people. So, for example (row 1), A talks to B, then C then D, whilst (row 2) B talks to A then D then C, and so on.

Here is one solution for 6 people,

A B C D E F

B A D E F C

C E A F D B

D F B A C E

E C F B A D

F D E C B A

tip: there are 6240 solutions for 8 people.