These two group activities use mathematical reasoning - one is
numerical, one geometric.
What happens if you join every second point on this circle? How
about every third point? Try with different steps and see if you
can predict what will happen.
All strange numbers are prime. Every one digit prime number is
strange and a number of two or more digits is strange if and only
if so are the two numbers obtained from it by omitting either its
first or its last digit. Find all strange numbers.
This problem is taken from the UKMT Mathematical Challenges.