List

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!"
Shady Symmetry
problem
Favourite

Shady symmetry

Age
11 to 14
Challenge level
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How many different symmetrical shapes can you make by shading triangles or squares?
Isosceles Triangles
problem
Favourite

Isosceles triangles

Age
11 to 14
Challenge level
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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
problem
Favourite

M, M and M

Age
11 to 14
Challenge level
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If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?

Peaches today, Peaches tomorrow...
problem
Favourite

Peaches today, peaches tomorrow...

Age
11 to 14
Challenge level
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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?