Choose any three by three square of dates on a calendar page...
Make a set of numbers that use all the digits from 1 to 9, once and
once only. Add them up. The result is divisible by 9. Add each of
the digits in the new number. What is their sum? Now try some other
possibilities for yourself!
What happens to the perimeter of triangle ABC as the two smaller
circles change size and roll around inside the bigger circle?
Show that among the interior angles of a convex polygon there
cannot be more than three acute angles.
Show that if a convex polygon has more than six sides, then at
least one of the sides has an obtuse angle at both ends.