Exploring and noticing

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?

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

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

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?

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

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

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

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.

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.

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