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

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

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

Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.

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?"

Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?

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.

Can you find a cuboid that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.

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

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

Different combinations of the weights available allow you to make different totals. Which totals can you make?

Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

Can you shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line?

What is the best way to shunt these carriages so that each train can continue its journey?

Seven friends went to a fun fair with lots of scary rides. They decided to pair up for rides until each friend had ridden once with each of the others. What was the total number rides?

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?

If these elves wear a different outfit every day for as many days as possible, how many days can their fun last?

How will you go about finding all the jigsaw pieces that have one peg and one hole?

Can you work out how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

Hover your mouse over the counters to see which ones will be removed. Click to remove them. The winner is the last one to remove a counter. How you can make sure you win?

Design an arrangement of display boards in the school hall which fits the requirements of different people.

Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.

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

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.

These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.

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.

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

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 Vikings communicated in writing by making simple scratches on wood or stones called runes. Can you work out how their code works using the table of the alphabet?

Each of the main diagonals of this sudoku must contain the numbers 1 to 9 and each rectangle width the numbers 1 to 4.

Two sudokus in one. Challenge yourself to make the necessary connections.

Two sudokus in one. Challenge yourself to make the necessary connections.

A Sudoku that uses transformations as supporting clues.

Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

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 problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?

In this challenge, buckets come in five different sizes. If you choose some buckets, can you investigate the different ways in which they can be filled?

When I fold a 0-20 number line, I end up with 'stacks' of numbers on top of each other. These challenges involve varying the length of the number line and investigating the 'stack totals'.

Time for a little mathemagic! Choose any five cards from a pack and show four of them to your partner. How can they work out the fifth?

Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?

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

How many different triangles can you make on a circular pegboard that has nine pegs?

This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .