Take any whole number between 1 and 999, add the squares of the
digits to get a new number. Make some conjectures about what
happens in general.
Start with a large square, join the midpoints of its sides, you'll see four right angled triangles. Remove these triangles, a second square is left. Repeat the operation. What happens?
Laurinda Brown (1983) wrote about using this problem in the classroom: in Mathematics...with a Micro 1, pp.22-25, Waddingham, Jo (ed), Bristol, County of Avon, Resources for Learning Development Unit. The lesson notes above are adapted from her descriptions of using the problem.