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.
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.
There are four unknown numbers. The mean of the first two numbers
is 4, and the mean of the first three numbers is 9. The mean of all
four numbers is 15. If one of the four numbers was 2, what were. . . .
This Sudoku requires you to do some working backwards before working forwards.