Working systematically

problem
What's possible?

Age

14 to 16

Challenge level

Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?
problem
Funny factorisation

Age

11 to 16

Challenge level

Using the digits 1 to 9, the number 4396 can be written as the product of two numbers. Can you find the factors?
problem
ABC

Age

7 to 11

Challenge level

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
problem
Professional circles

Age

7 to 11

Challenge level

Six friends sat around a circular table. Can you work out from the information who sat where and what their profession were?
problem
Neighbours

Age

7 to 11

Challenge level

In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?
problem
Ones only

Age

11 to 14

Challenge level

Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.
problem
Fair shares?

Age

14 to 16

Challenge level

A mother wants to share some money by giving each child in turn a lump sum plus a fraction of the remainder. How can she do this to share the money out equally?
problem
Of all the areas

Age

14 to 16

Challenge level

Can you find a general rule for finding the areas of equilateral triangles drawn on an isometric grid?
problem
How old are the children?

Age

11 to 14

Challenge level

A student in a maths class was trying to get some information from her teacher. She was given some clues and then the teacher ended by saying, "Well, how old are they?"
problem
Medal muddle

Age

11 to 14

Challenge level

Countries from across the world competed in a sports tournament. Can you devise an efficient strategy to work out the order in which they finished?