Odd Stones

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.