Does this 'trick' for calculating multiples of 11 always work? Why or why not?
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?
Number problems at primary level that may require resilience.
56 406 is the product of two consecutive numbers. What are these two numbers?
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?
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?
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!
What is happening at each box in these machines?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?
Use the information to work out how many gifts there are in each pile.
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
This challenge combines addition, multiplication, perseverance and even proof.
This task combines spatial awareness with addition and multiplication.
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 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?
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?
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 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!
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 task offers an opportunity to explore all sorts of number relationships, but particularly multiplication.
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
If the answer's 2010, what could the question be?
Using the statements, can you work out how many of each type of rabbit there are in these pens?
Find the next number in this pattern: 3, 7, 19, 55 ...
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 require careful consideration.
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
This number has 903 digits. What is the sum of all 903 digits?
Can you work out what a ziffle is on the planet Zargon?
If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?
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?
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?
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
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?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Can you find different ways of creating paths using these paving slabs?
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.
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?
Can you score 100 by throwing rings on this board? Is there more than way to do it?
Watch this animation. What do you notice? What happens when you try more or fewer cubes in a bundle?
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
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.
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.