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.

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

Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?

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!

Number problems at primary level that require careful consideration.

This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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

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?

What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.

Using the statements, can you work out how many of each type of rabbit there are in these pens?

If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?

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

Can you substitute numbers for the letters in these sums?

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.

Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?

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

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

On my calculator I divided one whole number by another whole number and got the answer 3.125. If the numbers are both under 50, what are they?

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?

A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?

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?

Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?

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?

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

Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99 How many ways can you do it?

This dice train has been made using specific rules. How many different trains can you make?

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

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?

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

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

Alice and Brian are snails who live on a wall and can only travel along the cracks. Alice wants to go to see Brian. How far is the shortest route along the cracks? Is there more than one way to go?

Can you use this information to work out Charlie's house number?

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

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?

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

This article for primary teachers suggests ways in which to help children become better at working systematically.

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?

Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

Add the sum of the squares of four numbers between 10 and 20 to the sum of the squares of three numbers less than 6 to make the square of another, larger, number.

Place this "worm" on the 100 square and find the total of the four squares it covers. Keeping its head in the same place, what other totals can you make?

Can you make square numbers by adding two prime numbers together?

The discs for this game are kept in a flat square box with a square hole for each. Use the information to find out how many discs of each colour there are in the box.

These eleven shapes each stand for a different number. Can you use the number sentences to work out what they are?

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

What is the smallest number of coins needed to make up 12 dollars and 83 cents?

There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?

There are lots of different methods to find out what the shapes are worth - how many can you find?

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

Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?