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.