Exploring and noticing

problem
Only connect

Age

11 to 14

Challenge level

The graph represents a salesman’s area of activity with the shops that the salesman must visit each day. What route around the shops has the minimum total distance?
problem
Tree tops

Age

14 to 16

Challenge level

Can you make sense of information about trees in order to maximise the profits of a forestry company?
problem
Marbles in a box

Age

11 to 16

Challenge level

How many winning lines can you make in a three-dimensional version of noughts and crosses?
problem
Exploring cubic functions

Age

14 to 18

Challenge level

Quadratic graphs are very familiar, but what patterns can you explore with cubics?
problem
Which scripts?

Age

7 to 11

Challenge level

There are six numbers written in five different scripts. Can you sort out which is which?
problem
3388

Age

11 to 14

Challenge level

Using some or all of the operations of addition, subtraction, multiplication and division and using the digits 3, 3, 8 and 8 each once and only once make an expression equal to 24.
problem
One to eight

Age

11 to 14

Challenge level

Complete the following expressions so that each one gives a four digit number as the product of two two digit numbers and uses the digits 1 to 8 once and only once.
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
Cut it out

Age

7 to 11

Challenge level

Can you dissect an equilateral triangle into 6 smaller ones? What number of smaller equilateral triangles is it NOT possible to dissect a larger equilateral triangle into?
problem
Fair shares?

Age

14 to 16

Challenge level

A mother wants to share a sum of money by giving each of her children in turn a lump sum plus a fraction of the remainder. How can she do this in order to share the money out equally?