Using some or all of the operations of addition, subtraction, multiplication and division and using the digits 3, 3, 8 and 8 each once and only once make an expression equal to 24.
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?
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?
Grandma found her pie balanced on the scale with two weights and a quarter of a pie. So how heavy was each pie?
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?
Go through the maze, collecting and losing your money as you go. Which route gives you the highest return? And the lowest?
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?
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?
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.
Imagine you were given the chance to win some money... and imagine you had nothing to lose...
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.
If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?
Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.
Use your logical reasoning to work out how many cows and how many sheep there are in each field.
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.
Using the statements, can you work out how many of each type of rabbit there are in these pens?
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?
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?
Use the information to work out how many gifts there are in each pile.
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?
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?
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?
What is happening at each box in these machines?
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?
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
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?
Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?
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?
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
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?
This number has 903 digits. What is the sum of all 903 digits?
56 406 is the product of two consecutive numbers. What are these two 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?
How would you count the number of fingers in these pictures?
If the answer's 2010, what could the question be?
This task combines spatial awareness with addition and multiplication.
This challenge combines addition, multiplication, perseverance and even proof.
Number problems at primary level that may require resilience.
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
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?
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 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?
What is the sum of all the three digit whole numbers?
Here is a chance to play a version of the classic Countdown Game.
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 the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
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.