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

This challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?

Watch this animation. What do you notice? What happens when you try more or fewer cubes in a bundle?

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

How many starfish could there be on the beach, and how many children, if I can see 28 arms?

Can you find different ways of creating paths using these paving slabs?

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

Number problems at primary level that require careful consideration.

Twizzle, a female giraffe, needs transporting to another zoo. Which route will give the fastest journey?

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.

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?

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

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?

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?

Where can you draw a line on a clock face so that the numbers on both sides have the same total?

Use the information to work out how many gifts there are in each pile.

EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.

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

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

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?

The Scot, John Napier, invented these strips about 400 years ago to help calculate multiplication and division. Can you work out how to use Napier's bones to find the answer to these multiplications?

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!

Find the next number in this pattern: 3, 7, 19, 55 ...

Here are the prices for 1st and 2nd class mail within the UK. You have an unlimited number of each of these stamps. Which stamps would you need to post a parcel weighing 825g?

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

A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.

Find out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf.

Go through the maze, collecting and losing your money as you go. Which route gives you the highest return? And the lowest?

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

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

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

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

Number problems at primary level that may require resilience.

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?

Look on the back of any modern book and you will find an ISBN code. Take this code and calculate this sum in the way shown. Can you see what the answers always have in common?

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!

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?

Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.

There are over sixty different ways of making 24 by adding, subtracting, multiplying and dividing all four numbers 4, 6, 6 and 8 (using each number only once). How many can you find?

Find another number that is one short of a square number and when you double it and add 1, the result is also a square number.

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

The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?

Annie cut this numbered cake into 3 pieces with 3 cuts so that the numbers on each piece added to the same total. Where were the cuts and what fraction of the whole cake was each piece?

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

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 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?