Finding All Solutions

These problems invite you 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!"

Stage: 3 Challenge Level:

How many different symmetrical shapes can you make by shading triangles or squares?

Isosceles Triangles

Stage: 3 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?

M, M and M

Stage: 3 Challenge Level:

If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?

Peaches Today, Peaches Tomorrow....

Stage: 3 and 4 Challenge Level:

Whenever a monkey has peaches, he always keeps a fraction of them each day, gives the rest away, and then eats one. How long could he make his peaches last for?