Since trivial problems bore me, I thought I might make a weekly programming challenge for a bit of fun. Sometimes I find it fun to solve a problem, and compair it to other peoples solutions.
Let me know what you think about the idea (if you like the idea, if the problems are too easy/hard, or if I should just stop).
Rules: There are no rules. You may use any programming language, or any other method of finding the answer (even by hand).
Warning! Don't read the comments if you don't want to see other peoples solutions. You should probably try the problem out yourself before reading the comments.
Challenge #1: Graph Colourability
Consider the following two graphs: Click Here
The graph on the left is said to be two-colourable (or bipartite), because you are able to colour the nodes with two colours such that no adjacent nodes are the same colour.
It is impossible to colour the graph on the right with two colours such that no adjacent nodes share the same colour. Thus, it is not two-colourable.
Out of all possible graphs with 7 nodes, how many are two-colourable?