The binary operation * for combining sets is defined as the union
of two sets minus their intersection. Prove the set of all subsets
of a set S together with the binary operation * forms a group.
How many tours visit each vertex of a cube once and only once? How
many return to the starting point?
Mr Smith and Mr Jones are two maths teachers. By asking questions, the answers to which may be right or wrong, Mr Jones is able to find the number of the house Mr Smith lives in... Or not!
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.
It is possible to identify a particular card out of a pack of 15
with the use of some mathematical reasoning. What is this reasoning
and can it be applied to other numbers of cards?