These problems invite students to find all possible solutions. One of the best answers to "How do you know you have found them all" is to be able to say "I worked systematically!"
problem
Shady symmetry
Age
11 to 14
Challenge level
How many different symmetrical shapes can you make by shading triangles or squares?
problem
Isosceles triangles
Age
11 to 14
Challenge level
Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?
problem
M, M and M
Age
11 to 14
Challenge level
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
problem
Peaches today, peaches tomorrow...
Age
11 to 14
Challenge level
A monkey with peaches, keeps a fraction of them each day, gives the rest away, and then eats one. How long can his peaches last?