Exploring and noticing

problem
Highest and lowest

Age

7 to 11

Challenge level

Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
problem
Prison cells

Age

7 to 11

Challenge level

There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?
problem
Difference

Age

7 to 11

Challenge level

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
problem
Heads and feet

Age

5 to 7

Challenge level

On a farm there were some hens and sheep. Altogether there were 8 heads and 22 feet. How many hens were there?
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.