Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

I added together some of my neighbours' house numbers. Can you explain the patterns I noticed?

Given the products of diagonally opposite cells - can you complete this Sudoku?

Each clue in this Sudoku is the product of the two numbers in adjacent cells.

Throughout these challenges, the touching faces of any adjacent dice must have the same number. Can you find a way of making the total on the top come to each number from 11 to 18 inclusive?

Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

This Sudoku puzzle can be solved with the help of small clue-numbers on the border lines between pairs of neighbouring squares of the grid.

The clues for this Sudoku are the product of the numbers in adjacent squares.

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

This dice train has been made using specific rules. How many different trains can you make?

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?"

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

An investigation that gives you the opportunity to make and justify predictions.

What happens when you add three numbers together? Will your answer be odd or even? How do you know?

Add or subtract the two numbers on the spinners and try to complete a row of three. Are there some numbers that are good to aim for?

The puzzle can be solved by finding the values of the unknown digits (all indicated by asterisks) in the squares of the $9\times9$ grid.

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?

This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

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?

The items in the shopping basket add and multiply to give the same amount. What could their prices be?

Find out about Magic Squares in this article written for students. Why are they magic?!

Take 5 cubes of one colour and 2 of another colour. How many different ways can you join them if the 5 must touch the table and the 2 must not touch the table?

Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?

Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.

Investigate the different ways you could split up these rooms so that you have double the number.

Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.

These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

There are lots of different methods to find out what the shapes are worth - how many can you find?

You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.

Can you rearrange the biscuits on the plates so that the three biscuits on each plate are all different and there is no plate with two biscuits the same as two biscuits on another plate?

My dice has inky marks on each face. Can you find the route it has taken? What does each face look like?

Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.

On a digital clock showing 24 hour time, over a whole day, how many times does a 5 appear? Is it the same number for a 12 hour clock over a whole day?

Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.

Add the sum of the squares of four numbers between 10 and 20 to the sum of the squares of three numbers less than 6 to make the square of another, larger, number.

Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?

There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

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?

In the planet system of Octa the planets are arranged in the shape of an octahedron. How many different routes could be taken to get from Planet A to Planet Zargon?

How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?

In a bowl there are 4 Chocolates, 3 Jellies and 5 Mints. Find a way to share the sweets between the three children so they each get the kind they like. Is there more than one way to do it?

This task depends on groups working collaboratively, discussing and reasoning to agree a final product.

This challenge is to design different step arrangements, which must go along a distance of 6 on the steps and must end up at 6 high.

Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?