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

Given the products of adjacent cells, can you complete this Sudoku?

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 Zargoes use almost the same alphabet as English. What does this birthday message say?

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?

Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.

What is the smallest number of jumps needed before the white rabbits and the grey rabbits can continue along their path?

These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.

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?

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

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

Using the statements, can you work out how many of each type of rabbit there are in these pens?

If we had 16 light bars which digital numbers could we make? How will you know you've found them all?

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

Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?

If you take a three by three square on a 1-10 addition square and multiply the diagonally opposite numbers together, what is the difference between these products. Why?

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?

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

Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma and Emma passed a fifth of her counters to Ben. After this they all had the same number of counters.

This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

Six friends sat around a circular table. Can you work out from the information who sat where and what their profession were?

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

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.

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

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

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

A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.

Whenever a monkey has peaches, he always keeps a fraction of them each day, gives the rest away, and then eats one. How long could he make his peaches last for?

A mathematician goes into a supermarket and buys four items. Using a calculator she multiplies the cost instead of adding them. How can her answer be the same as the total at the till?

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

The challenge here is to find as many routes as you can for a fence to go so that this town is divided up into two halves, each with 8 blocks.

Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.

A merchant brings four bars of gold to a jeweller. How can the jeweller use the scales just twice to identify the lighter, fake bar?

Ana and Ross looked in a trunk in the attic. They found old cloaks and gowns, hats and masks. How many possible costumes could they make?

In this matching game, you have to decide how long different events take.

Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?

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.

This task follows on from Build it Up and takes the ideas into three dimensions!

Can you find all the ways to get 15 at the top of this triangle of numbers?

First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

If you have three circular objects, you could arrange them so that they are separate, touching, overlapping or inside each other. Can you investigate all the different possibilities?

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?

When newspaper pages get separated at home we have to try to sort them out and get things in the correct order. How many ways can we arrange these pages so that the numbering may be different?

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?

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