Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
Your vessel, the Starship Diophantus, has become damaged in deep space. Can you use your knowledge of times tables and some lightning reflexes to survive?
56 406 is the product of two consecutive numbers. What are these two numbers?
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.
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?
Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.
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.
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.
Using the statements, can you work out how many of each type of rabbit there are in these pens?
What is the sum of all the three digit whole numbers?
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!
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?
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.
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 arrange 5 different digits (from 0 - 9) in the cross in the way described?
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
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?
This task combines spatial awareness with addition and multiplication.
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!
Does this 'trick' for calculating multiples of 11 always work? Why or why not?
Can you work out what a ziffle is on the planet Zargon?
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?
Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?
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.
Use the information to work out how many gifts there are in each pile.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
This task offers an opportunity to explore all sorts of number relationships, but particularly multiplication.
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?
On my calculator I divided one whole number by another whole number and got the answer 3.125. If the numbers are both under 50, what are they?
What is happening at each box in these machines?
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
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?
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?
Here is a chance to play a version of the classic Countdown Game.
This challenge combines addition, multiplication, perseverance and even proof.
Four Go game for an adult and child. Will you be the first to have four numbers in a row on the number line?
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
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?
How would you count the number of fingers in these pictures?
Can you each work out the number on your card? What do you notice? How could you sort the cards?
If the answer's 2010, what could the question be?
If you take a three by three square on a 1-10 addition square and multiply the diagonally opposite numbers together, what is the difference between these products. Why?
Find the next number in this pattern: 3, 7, 19, 55 ...
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.
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?
Number problems at primary level that may require resilience.
This number has 903 digits. What is the sum of all 903 digits?