Find all the triples of numbers a, b, c such that each one of them
plus the product of the other two is always 2.
Solve the system of equations: ab = 1 bc = 2 cd = 3 de = 4 ea = 6
Which rational numbers cannot be written in the form x + 1/(y +
1/z) where x, y and z are integers?
This problem is taken from the UKMT Mathematical Challenges.