Go through the maze, collecting and losing your money as you go. Which route gives you the highest return? And the lowest?
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?
Look on the back of any modern book and you will find an ISBN code. Take this code and calculate this sum in the way shown. Can you see what the answers always have in common?
Use the information to work out how many gifts there are in each pile.
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.
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.
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?
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.
Can you score 100 by throwing rings on this board? Is there more than way to do it?
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 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!
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.
This challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?
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?
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
What is happening at each box in these machines?
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.
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!
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?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?
Using the statements, can you work out how many of each type of rabbit there are in these pens?
Use your logical reasoning to work out how many cows and how many sheep there are in each field.
This number has 903 digits. What is the sum of all 903 digits?
Number problems at primary level that may require resilience.
Find the next number in this pattern: 3, 7, 19, 55 ...
If the answer's 2010, what could the question be?
How would you count the number of fingers in these pictures?
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?
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.
Watch this animation. What do you notice? What happens when you try more or fewer cubes in a bundle?
Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?
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?
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?
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?
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?
What is the sum of all the three digit whole numbers?
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.
We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?
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?
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
This task combines spatial awareness with addition and multiplication.
All the girls would like a puzzle each for Christmas and all the boys would like a book each. Solve the riddle to find out how many puzzles and books Santa left.
This challenge combines addition, multiplication, perseverance and even proof.
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?