Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
This big box multiplies anything that goes inside it by the same number. If you know the numbers that come out, what multiplication might be going on in the box?
56 406 is the product of two consecutive numbers. What are these two numbers?
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?
Here is a picnic that Chris and Michael are going to share equally. Can you tell us what each of them will have?
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 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.
A game that tests your understanding of remainders.
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.
Imagine you were given the chance to win some money... and imagine you had nothing to lose...
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
6! = 6 x 5 x 4 x 3 x 2 x 1. The highest power of 2 that divides exactly into 6! is 4 since (6!) / (2^4 ) = 45. What is the highest power of two that divides exactly into 100!?
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?
Grandma found her pie balanced on the scale with two weights and a quarter of a pie. So how heavy was each pie?
Find the highest power of 11 that will divide into 1000! exactly.
What is the least square number which commences with six two's?
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.
Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.
Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.
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" .
On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?
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. . . .
Ben’s class were making cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Find the number which has 8 divisors, such that the product of the divisors is 331776.
The number 8888...88M9999...99 is divisible by 7 and it starts with the digit 8 repeated 50 times and ends with the digit 9 repeated 50 times. What is the value of the digit M?
What is the smallest number of answers you need to reveal in order to work out the missing headers?
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?
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?
Using the digits 1, 2, 3, 4, 5, 6, 7 and 8, mulitply a two two digit numbers are multiplied to give a four digit number, so that the expression is correct. How many different solutions can you find?
Investigate $1^n + 19^n + 20^n + 51^n + 57^n + 80^n + 82^n $ and $2^n + 12^n + 31^n + 40^n + 69^n + 71^n + 85^n$ for different values of n.
The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?
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?
Can you find what the last two digits of the number $4^{1999}$ are?
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 complete this jigsaw of the multiplication square?
This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?
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?
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?
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?
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
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?
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?
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
Look at different ways of dividing things. What do they mean? How might you show them in a picture, with things, with numbers and symbols?
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
Resources to support understanding of multiplication and division through playing with number.