Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?

How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?

Can you use the information to find out which cards I have used?

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?

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

What happens when you add three numbers together? Will your answer be odd or even? How do you know?

I was in my car when I noticed a line of four cars on the lane next to me with number plates starting and ending with J, K, L and M. What order were they in?

Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?

Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

This Sudoku, based on differences. Using the one clue number can you find the solution?

Number problems at primary level that require careful consideration.

Can you replace the letters with numbers? Is there only one solution in each case?

The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?

Find the values of the nine letters in the sum: FOOT + BALL = GAME

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?

My local DIY shop calculates the price of its windows according to the area of glass and the length of frame used. Can you work out how they arrived at these prices?

Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?

What happens when you round these three-digit numbers to the nearest 100?

Can you work out some different ways to balance this equation?

Have a go at balancing this equation. Can you find different ways of doing it?

Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?

Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?

How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

Can you draw a square in which the perimeter is numerically equal to the area?

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?

Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.

Hover your mouse over the counters to see which ones will be removed. Click to remover them. The winner is the last one to remove a counter. How you can make sure you win?

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

Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.

Cut differently-sized square corners from a square piece of paper to make boxes without lids. Do they all have the same volume?

George and Jim want to buy a chocolate bar. George needs 2p more and Jim need 50p more to buy it. How much is the chocolate bar?

Can you help the children find the two triangles which have the lengths of two sides numerically equal to their areas?

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?

Four small numbers give the clue to the contents of the four surrounding cells.

A merchant brings four bars of gold to a jeweller. How can the jeweller use the scales just twice to identify the lighter, fake bar?

This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?

This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.

Can you find all the different ways of lining up these Cuisenaire rods?

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?

Stuart's watch loses two minutes every hour. Adam's watch gains one minute every hour. Use the information to work out what time (the real time) they arrived at the airport.

In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?

Alice's mum needs to go to each child's house just once and then back home again. How many different routes are there? Use the information to find out how long each road is on the route she took.

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!

Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?

Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?

Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?

This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.