A combination mechanism for a safe comprises thirty-two tumblers numbered from one to thirty-two in such a way that the numbers in each wheel total 132... Could you open the safe?

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.

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?

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?

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.

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.

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.

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.

Whenever two chameleons of different colours meet they change colour to the third colour. Describe the shortest sequence of meetings in which all the chameleons change to green if you start with 12. . . .

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

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

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

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?

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

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?

Number problems at primary level that may require resilience.

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

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

Generate large numbers then give the values of each digit.

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

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

Can you draw a continuous line through 16 numbers on this grid so that the total of the numbers you pass through is as high as possible?

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?

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

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

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?

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?

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?

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

What is the sum of all the digits in all the integers from one to one million?

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

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?

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?

The picture shows a lighthouse and many underwater creatures. If you know the markings on the lighthouse are 1m apart, can you work out the distances between some of the different creatures?

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

Here is a chance to play a version of the classic Countdown Game.

I was looking at the number plate of a car parked outside. Using my special code S208VBJ adds to 65. Can you crack my code and use it to find out what both of these number plates add up to?

Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the numbers on each circle add up to the same amount. Can you find the rule for giving another set of six numbers?

Can you arrange the digits 1,2,3,4,5,6,7,8,9 into three 3-digit numbers such that their total is close to 1500?

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

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.

Max and Mandy put their number lines together to make a graph. How far had each of them moved along and up from 0 to get the counter to the place marked?

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?

Vera is shopping at a market with these coins in her purse. Which things could she give exactly the right amount for?