56 406 is the product of two consecutive numbers. What are these two numbers?
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
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?
Can you work out what a ziffle is on the planet Zargon?
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.
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
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?
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
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.
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
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?
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.
What is the least square number which commences with six two's?
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?
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?
What is the sum of all the three digit whole numbers?
After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?
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?
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 using a pack of cards Turn over 2 cards and try to make an odd number or a multiple of 3.
This task combines spatial awareness with addition and multiplication.
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?
Number problems at primary level that may require resilience.
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.
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
Use the information to work out how many gifts there are in each pile.
This number has 903 digits. What is the sum of all 903 digits?
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
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 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!
Chandrika was practising a long distance run. Can you work out how long the race was from the information?
Use your logical reasoning to work out how many cows and how many sheep there are in each field.
Using the statements, can you work out how many of each type of rabbit there are in these pens?
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!
When the number x 1 x x x is multiplied by 417 this gives the answer 9 x x x 0 5 7. Find the missing digits, each of which is represented by an "x" .
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?
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?
Given the products of adjacent cells, can you complete this Sudoku?
Can you find different ways of creating paths using these paving slabs?
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. . . .
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Number problems at primary level that require careful consideration.
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?
Use this information to work out whether the front or back wheel of this bicycle gets more wear and tear.
Grandma found her pie balanced on the scale with two weights and a quarter of a pie. So how heavy was each pie?
If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
What is happening at each box in these machines?