Sets and Groups - March 2005, Stage 4&5

Problems

problem icon

Arithmagons

Age 14 to 16 Challenge Level:

Can you find the values at the vertices when you know the values on the edges?

problem icon

Spot the Card

Age 14 to 16 Challenge Level:

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?

problem icon

Sheffuls

Age 14 to 16 Challenge Level:

Discover a handy way to describe reorderings and solve our anagram in the process.

problem icon

Zodiac

Age 14 to 16 Challenge Level:

problem icon

Groups of Sets

Age 16 to 18 Challenge Level:

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.

problem icon

What's a Group?

Age 16 to 18 Challenge Level:

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.

problem icon

Binary Sequences

Age 16 to 18 Challenge Level:

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.