Cube Net

How many tours visit each vertex of a cube once and only once? How many return to the starting point?

Binary Sequences

Show that the infinite set of finite (or terminating) binary sequences can be written as an ordered list whereas the infinite set of all infinite binary sequences cannot.

Binomial Coefficients

An introduction to the binomial coefficient, and exploration of some of the formulae it satisfies.

Groups of Sets

Stage: 5 Challenge Level:
As defined in this question $A*B$ is the set of all elements belonging to one or other of the sets $A$ and $B$ but not to both.

For $G$ to be a group it must be closed and associative, it must contain an identity and all the elements must have inverses.