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?
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?
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
What is the sum of all the three digit whole numbers?
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?
Mr. Sunshine tells the children they will have 2 hours of homework. After several calculations, Harry says he hasn't got time to do this homework. Can you see where his reasoning is wrong?
If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
This number has 903 digits. What is the sum of all 903 digits?
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?
How would you count the number of fingers in these pictures?
If the answer's 2010, what could the question be?
Find the next number in this pattern: 3, 7, 19, 55 ...
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.
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?
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.
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?
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.
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.
Number problems at primary level that require careful consideration.
Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.
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?
Go through the maze, collecting and losing your money as you go. Which route gives you the highest return? And the lowest?
What is happening at each box in these machines?
Use this information to work out whether the front or back wheel of this bicycle gets more wear and tear.
Use your logical reasoning to work out how many cows and how many sheep there are in each field.
Number problems at primary level that may require resilience.
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?
During the third hour after midnight the hands on a clock point in the same direction (so one hand is over the top of the other). At what time, to the nearest second, does this happen?
Chandrika was practising a long distance run. Can you work out how long the race was from the information?
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 a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?
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?
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?
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!
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
This article for teachers suggests ideas for activities built around 10 and 2010.
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
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.
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?
Grandma found her pie balanced on the scale with two weights and a quarter of a pie. So how heavy was each pie?
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
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?
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?
Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?