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

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?

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?

You have 5 darts and your target score is 44. How many different ways could you score 44?

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

You have two egg timers. One takes 4 minutes exactly to empty and the other takes 7 minutes. What times in whole minutes can you measure and how?

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!

There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.

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?

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

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

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

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

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!

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

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

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

Winifred Wytsh bought a box each of jelly babies, milk jelly bears, yellow jelly bees and jelly belly beans. In how many different ways could she make a jolly jelly feast with 32 legs?

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.

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

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?

Number problems at primary level that require careful consideration.

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

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?

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?

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

What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.

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?

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

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

Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.

My cube has inky marks on each face. Can you find the route it has taken? What does each face look like?

Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?

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

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

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

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

Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?

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

Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

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 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?

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?

Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?

This package contains a collection of problems from the NRICH website that could be suitable for students who have a good understanding of Factors and Multiples and who feel ready to take on some. . . .

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?

There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?

An investigation that gives you the opportunity to make and justify predictions.

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?