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?
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it?
Amy has a box containing domino pieces but she does not think it is a complete set. She has 24 dominoes in her box and there are 125 spots on them altogether. Which of her domino pieces are missing?
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
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 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 article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?
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?
Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?
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 task combines spatial awareness with addition and multiplication.
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
The Man is much smaller than us. Can you use the picture of him next to a mug to estimate his height and how much tea he drinks?
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 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?
I'm thinking of a number. When my number is divided by 5 the remainder is 4. When my number is divided by 3 the remainder is 2. Can you find my number?
Can you work out what a ziffle is on the planet Zargon?
Can you each work out the number on your card? What do you notice? How could you sort the cards?
Here is a chance to play a version of the classic Countdown Game.
Using the statements, can you work out how many of each type of rabbit there are in these pens?
Four Go game for an adult and child. Will you be the first to have four numbers in a row on the number line?
Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?
What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
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?
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?
Use the information about Sally and her brother to find out how many children there are in the Brown family.
56 406 is the product of two consecutive numbers. What are these two numbers?
Bernard Bagnall recommends some primary school problems which use numbers from the environment around us, from clocks to house numbers.
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
Take the number 6 469 693 230 and divide it by the first ten prime numbers and you'll find the most beautiful, most magic of all numbers. What is it?
Using the numbers 1, 2, 3, 4 and 5 once and only once, and the operations x and ÷ once and only once, what is the smallest whole number you can make?
Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?
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?
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 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.
In this game, you can add, subtract, multiply or divide the numbers on the dice. Which will you do so that you get to the end of the number line first?
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?
The triangles in these sets are similar - can you work out the lengths of the sides which have question marks?
Annie and Ben are playing a game with a calculator. What was Annie's secret number?
Number problems at primary level that may require resilience.
This number has 903 digits. What is the sum of all 903 digits?
An old game but lots of arithmetic!