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.
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.
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?
Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
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 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.
Go through the maze, collecting and losing your money as you go. Which route gives you the highest return? And the lowest?
Can you find different ways of creating paths using these paving slabs?
What is happening at each box in these machines?
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?
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
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?
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?
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.
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
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.
Use the information to work out how many gifts there are in each pile.
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?
What is the sum of all the three digit whole numbers?
If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?
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?
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?
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
Find the next number in this pattern: 3, 7, 19, 55 ...
Use your logical reasoning to work out how many cows and how many sheep there are in each field.
How would you count the number of fingers in these pictures?
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?
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?
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?
This number has 903 digits. What is the sum of all 903 digits?
This task combines spatial awareness with addition and multiplication.
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?
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 November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
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 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?
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 combines addition, multiplication, perseverance and even proof.
If the answer's 2010, what could the question be?
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?
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
In this investigation, you are challenged to make mobile phone numbers which are easy to remember. What happens if you make a sequence adding 2 each time?
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.
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?
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?