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?
Can you work out what a ziffle is on the planet Zargon?
56 406 is the product of two consecutive numbers. What are these two numbers?
A 3 digit number is multiplied by a 2 digit number and the calculation is written out as shown with a digit in place of each of the *'s. Complete the whole multiplication sum.
Using the numbers 1, 2, 3, 4 and 5 once and only once, and the operations x and ÷ once and only once, what is the smallest whole number you can make?
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.
A game for 2 people using a pack of cards Turn over 2 cards and try to make an odd number or a multiple of 3.
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
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?
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
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?
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?
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?
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
Take the number 6 469 693 230 and divide it by the first ten prime numbers and you'll find the most beautiful, most magic of all numbers. What is 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?
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
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!
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.
If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?
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?
Number problems at primary level that may require resilience.
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?
Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?
What is happening at each box in these machines?
Using the statements, can you work out how many of each type of rabbit there are in these pens?
What is the largest number you can make using the three digits 2, 3 and 4 in any way you like, using any operations you like? You can only use each digit once.
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
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?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Given the products of adjacent cells, can you complete this Sudoku?
When I type a sequence of letters my calculator gives the product of all the numbers in the corresponding memories. What numbers should I store so that when I type 'ONE' it returns 1, and when I type. . . .
Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
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 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!
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?
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?
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?
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?
After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?
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?
Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?
What is the sum of all the three digit whole numbers?
Bernard Bagnall recommends some primary school problems which use numbers from the environment around us, from clocks to house numbers.
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received 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?
Four Go game for an adult and child. Will you be the first to have four numbers in a row on the number line?