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

Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?

This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

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

Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?

Use the information about Sally and her brother to find out how many children there are in the Brown family.

This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!

There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.

There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

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?

Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?

Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?

Can you each work out the number on your card? What do you notice? How could you sort the cards?

In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?

Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?

Which is quicker, counting up to 30 in ones or counting up to 300 in tens? 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?

Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?

Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?

Can you order the digits from 1-6 to make a number which is divisible by 6 so when the last digit is removed it becomes a 5-figure number divisible by 5, and so on?

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?

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

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

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

Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?

Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.

Try adding together the dates of all the days in one week. Now multiply the first date by 7 and add 21. Can you explain what happens?

What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.

What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?

How would you count the number of fingers in these pictures?

What happens when you add the digits of a number then multiply the result by 2 and you keep doing this? You could try for different numbers and different rules.

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

56 406 is the product of two consecutive numbers. What are these two numbers?

We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?

These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?

Well now, what would happen if we lost all the nines in our number system? Have a go at writing the numbers out in this way and have a look at the multiplications table.

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?

Bernard Bagnall recommends some primary school problems which use numbers from the environment around us, from clocks to house numbers.

There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?

If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?

A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?

48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?

These sixteen children are standing in four lines of four, one behind the other. They are each holding a card with a number on it. Can you work out the missing numbers?

Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?

If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?

At the beginning of May Tom put his tomato plant outside. On the same day he sowed a bean in another pot. When will the two be the same height?

This number has 903 digits. What is the sum of all 903 digits?

Use your logical reasoning to work out how many cows and how many sheep there are in each field.