This problem encourages students to think about the properties of numbers. It could be used to consolidate work on linear sequences.
This problem provides an introduction to summing geometric series, and allows students to discover for themselves the formulae used to calculate such sums.
This is an engaging investigation that quickly yields results and leads to conjectures and a lot of mathematical thinking and discussion.
This short problem can be given to students who have been working on sequences or algorithms.
This problem is suited to tenacious problem solvers who will relish the intellectual challenge. Although determining the rules will be very challenging, the mathematics required to verify the rules is elementary (KS3).