### Whole Number Dynamics I

The first of five articles concentrating on whole number dynamics, ideas of general dynamical systems are introduced and seen in concrete cases.

### Whole Number Dynamics II

This article extends the discussions in "Whole number dynamics I". Continuing the proof that, for all starting points, the Happy Number sequence goes into a loop or homes in on a fixed point.

### Whole Number Dynamics III

In this third of five articles we prove that whatever whole number we start with for the Happy Number sequence we will always end up with some set of numbers being repeated over and over again.

# Odd Stones

##### Stage: 4 Challenge Level:

This could be a useful extension activity helping students to break away from too readily expecting odd or even to be the important characteristic. Odd or even-ness can be seen more generally as the remainder after a division by two, and this problem depends on remainders using a different divisor.

This context has more possibilities than the simple question posed in the problem. It is capable of building up into a rich dynamical system well within the scope of a Stage 4 student. The number of stones and more especially the number of circles are the key variables.