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?

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

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

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

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?

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

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?

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?

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?

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?

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

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

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.

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?

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 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?

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.

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?

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

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.

Number problems at primary level that may require resilience.

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.

How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?

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?

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.

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?

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.

Tell your friends that you have a strange calculator that turns numbers backwards. What secret number do you have to enter to make 141 414 turn around?

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.

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

Can you go through this maze so that the numbers you pass add to exactly 100?

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!

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?

Cassandra, David and Lachlan are brothers and sisters. They range in age between 1 year and 14 years. Can you figure out their exact ages from the clues?

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

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.

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

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.

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

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

Number problems at primary level to work on with others.

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?

This task follows on from Build it Up and takes the ideas into three dimensions!

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

Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?