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?

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

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?

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.

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

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?

Amy has a box containing domino pieces but she does not think it is a complete set. She has 24 dominoes in her box and there are 125 spots on them altogether. Which of her domino pieces are missing?

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.

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.

Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?

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?

This addition sum uses all ten digits 0, 1, 2...9 exactly once. Find the sum and show that the one you give is the only possibility.

The sum of the first 'n' natural numbers is a 3 digit number in which all the digits are the same. How many numbers have been summed?

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

Ann thought of 5 numbers and told Bob all the sums that could be made by adding the numbers in pairs. The list of sums is 6, 7, 8, 8, 9, 9, 10,10, 11, 12. Help Bob to find out which numbers Ann was. . . .

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

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?

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?

Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.

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

What is the largest number you can make using the three digits 2, 3 and 4 in any way you like, using any operations you like? You can only use each digit once.

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.

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

If you wrote all the possible four digit numbers made by using each of the digits 2, 4, 5, 7 once, what would they add up to?

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 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?

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

Number problems at primary level that may require determination.

Number problems at primary level that require careful consideration.

Number problems at primary level to work on with others.

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

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.

This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.

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 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?

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?

The value of the circle changes in each of the following problems. Can you discover its value in each problem?

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.

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?

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