Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.
How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?
In this problem we are looking at sets of parallel sticks that cross each other. What is the least number of crossings you can make? And the greatest?
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?
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.
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
An investigation that gives you the opportunity to make and justify predictions.
Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
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?
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?
Four of these clues are needed to find the chosen number on this grid and four are true but do nothing to help in finding the number. Can you sort out the clues and find the number?
Can you make square numbers by adding two prime numbers together?
Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...
Can you order the digits from 1-6 to make a number which is divisible by 6 so when the last digit is removed it becomes a 5-figure number divisible by 5, and so on?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
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?
Given the products of adjacent cells, can you complete this Sudoku?
How many different sets of numbers with at least four members can you find in the numbers in this box?
A game in which players take it in turns to choose a number. Can you block your opponent?
This article for teachers describes how number arrays can be a useful reprentation for many number concepts.
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle?
The discs for this game are kept in a flat square box with a square hole for each disc. Use the information to find out how many discs of each colour there are in the box.
What is the smallest number with exactly 14 divisors?
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
Follow the clues to find the mystery number.
Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?
Follow this recipe for sieving numbers and see what interesting patterns emerge.
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
Do you know a quick way to check if a number is a multiple of two? How about three, four or six?
Complete the magic square using the numbers 1 to 25 once each. Each row, column and diagonal adds up to 65.
48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?
This package contains a collection of problems from the NRICH website that could be suitable for students who have a good understanding of Factors and Multiples and who feel ready to take on some. . . .
Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma and Emma passed a fifth of her counters to Ben. After this they all had the same number of counters.
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
A student in a maths class was trying to get some information from her teacher. She was given some clues and then the teacher ended by saying, "Well, how old are they?"
Some 4 digit numbers can be written as the product of a 3 digit number and a 2 digit number using the digits 1 to 9 each once and only once. The number 4396 can be written as just such a product. Can. . . .
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
A mathematician goes into a supermarket and buys four items. Using a calculator she multiplies the cost instead of adding them. How can her answer be the same as the total at the till?
Can you find what the last two digits of the number $4^{1999}$ are?
I throw three dice and get 5, 3 and 2. Add the scores on the three dice. What do you get? Now multiply the scores. What do you notice?
56 406 is the product of two consecutive numbers. What are these two numbers?
In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?
The sum of the first 'n' natural numbers is a 3 digit number in which all the digits are the same. How many numbers have been summed?
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?
"Ip dip sky blue! Who's 'it'? It's you!" Where would you position yourself so that you are 'it' if there are two players? Three players ...?
Can you find a relationship between the number of dots on the circle and the number of steps that will ensure that all points are hit?
When Charlie asked his grandmother how old she is, he didn't get a straightforward reply! Can you work out how old she is?
There are ten children in Becky's group. Can you find a set of numbers for each of them? Are there any other sets?