Challenge Level

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!

Challenge Level

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

Challenge Level

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

Challenge Level

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

Challenge Level

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

Challenge Level

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.

Challenge Level

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

This article for primary teachers encourages exploration of two fundamental ideas, exchange and 'unitising', which will help children become more fluent when calculating.

Challenge Level

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?

Challenge Level

Can you draw a continuous line through 16 numbers on this grid so that the total of the numbers you pass through is as high as possible?

Challenge Level

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?

Challenge Level

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

Challenge Level

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?

Challenge Level

I was looking at the number plate of a car parked outside. Using my special code S208VBJ adds to 65. Can you crack my code and use it to find out what both of these number plates add up to?

Challenge Level

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

Challenge Level

Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.

Challenge Level

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.

Challenge Level

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?

Challenge Level

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

Challenge Level

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

Challenge Level

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?

Challenge Level

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?

Challenge Level

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?

Challenge Level

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?

Challenge Level

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.

Challenge Level

Find the sum of all three-digit numbers each of whose digits is odd.

In this article for primary teachers, Lynne McClure outlines what is meant by fluency in the context of number and explains how our selection of NRICH tasks can help.

Challenge Level

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

Challenge Level

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.

Challenge Level

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!

Challenge Level

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?

Challenge Level

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?

Challenge Level

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.

Challenge Level

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?

Challenge Level

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?

Challenge Level

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

Challenge Level

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.

Challenge Level

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?

Challenge Level

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

Challenge Level

A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.

Challenge Level

In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?

Challenge Level

Number problems at primary level that may require resilience.

Challenge Level

Try out this number trick. What happens with different starting numbers? What do you notice?

Challenge Level

Number problems at primary level that require careful consideration.

Challenge Level

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.

Challenge Level

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?

Challenge Level

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?

Challenge Level

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