Use this grid to shade the numbers in the way described. Which numbers do you have left? Do you know what they are called?
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
Using the statements, can you work out how many of each type of rabbit there are in these pens?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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.
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 is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
56 406 is the product of two consecutive numbers. What are these two numbers?
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?
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?
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
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.
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?
This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?
A game for 2 people using a pack of cards Turn over 2 cards and try to make an odd number or a multiple of 3.
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!
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?
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?
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?
Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?
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?
What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.
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!
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
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?
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
What is the sum of all the three digit whole numbers?
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?
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
Can you work out what a ziffle is on the planet Zargon?
There are four equal weights on one side of the scale and an apple on the other side. What can you say that is true about the apple and the weights from the picture?
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?
Ben’s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?
Can you find different ways of creating paths using these paving slabs?
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?
Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?
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?
An old game but lots of arithmetic!
Number problems at primary level that require careful consideration.
After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?
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?
If the answer's 2010, what could the question be?
Here is a chance to play a version of the classic Countdown Game.
Find the next number in this pattern: 3, 7, 19, 55 ...
Number problems at primary level that may require resilience.
This number has 903 digits. What is the sum of all 903 digits?
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?
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?