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!

Arrange the numbers 1 to 16 into a 4 by 4 array. Choose a number.
Cross out the numbers on the same row and column. Repeat this
process. Add up you four numbers. Why do they always add up to 34?

Convex Polygons

Age 11 to 14 Challenge Level

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.