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

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?

Try out some calculations. Are you surprised by the results?

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

Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?

Number problems at primary level that may require resilience.

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

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

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

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.

I throw three dice and get 5, 3 and 2. Add the scores on the three dice. What do you get? Now multiply the scores. What do you notice?

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

Number problems at primary level to work on with others.

On a calculator, make 15 by using only the 2 key and any of the four operations keys. How many ways can you find to do it?

On the table there is a pile of oranges and lemons that weighs exactly one kilogram. Using the information, can you work out how many lemons there are?

Rocco ran in a 200 m race for his class. Use the information to find out how many runners there were in the race and what Rocco's finishing position was.

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?

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?

Arrange three 1s, three 2s and three 3s in this square so that every row, column and diagonal adds to the same total.

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?

Fill in the numbers to make the sum of each row, column and diagonal equal to 34. For an extra challenge try the huge American Flag magic square.

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?

Fill in the missing numbers so that adding each pair of corner numbers gives you the number between them (in the box).

There are three buckets each of which holds a maximum of 5 litres. Use the clues to work out how much liquid there is in each bucket.

This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.

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

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?

Put a number at the top of the machine and collect a number at the bottom. What do you get? Which numbers get back to themselves?

Three dice are placed in a row. Find a way to turn each one so that the three numbers on top of the dice total the same as the three numbers on the front of the dice. Can you find all the ways to do. . . .

Investigate the different distances of these car journeys and find out how long they take.

Can you score 100 by throwing rings on this board? Is there more than way to do it?

Using 3 rods of integer lengths, none longer than 10 units and not using any rod more than once, you can measure all the lengths in whole units from 1 to 10 units. How many ways can you do this?

Generate large numbers then give the values of each digit.

Find a great variety of ways of asking questions which make 8.

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?

On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?

If each of these three shapes has a value, can you find the totals of the combinations? Perhaps you can use the shapes to make the given totals?

Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.

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?

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

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?

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

Mrs Morgan, the class's teacher, pinned numbers onto the backs of three children. Use the information to find out what the three numbers were.

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

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?