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?
Discover a handy way to describe reorderings and solve our anagram
in the process.
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.
Explore the properties of some groups such as: The set of all real
numbers excluding -1 together with the operation x*y = xy + x + y.
Find the identity and the inverse of the element x.
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.
Curt from Reigate College explains very well why this graph has a symmetrical pitchfork shape.
Go to last month's problems to see more solutions.
An introduction to the sort of algebra studied at university, focussing on groups.
An environment for exploring the properties of small groups.
Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?