Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
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...
A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What size rectangle(s) contain(s) exactly 100 squares? Can you find them all?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
You have been given nine weights, one of which is slightly heavier than the rest. Can you work out which weight is heavier in just two weighings of the balance?
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.
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?
Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?
The NRICH team are always looking for new ways to engage teachers and pupils in problem solving. Here we explain the thinking behind maths trails.
Find a cuboid (with edges of integer values) that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?
Charlie and Lynne put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: x2 and -5. What do you think?
My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?
The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?
The clues for this Sudoku are the product of the numbers in adjacent squares.
Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?
How many different symmetrical shapes can you make by shading triangles or squares?
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
Bellringers have a special way to write down the patterns they ring. Learn about these patterns and draw some of your own.
Starting with four different triangles, imagine you have an unlimited number of each type. How many different tetrahedra can you make? Convince us you have found them all.
Given the products of diagonally opposite cells - can you complete this Sudoku?
Problem solving is at the heart of the NRICH site. All the problems give learners opportunities to learn, develop or use mathematical concepts and skills. Read here for more information.
A Latin square of order n is an array of n symbols in which each symbol occurs exactly once in each row and exactly once in each column.
The puzzle can be solved by finding the values of the unknown digits (all indicated by asterisks) in the squares of the $9\times9$ grid.
You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.
Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.
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. . . .
Whenever a monkey has peaches, he always keeps a fraction of them each day, gives the rest away, and then eats one. How long could he make his peaches last for?
This article for teachers describes several games, found on the site, all of which have a related structure that can be used to develop the skills of strategic planning.
Use the differences to find the solution to this Sudoku.
Use the interactivity to listen to the bells ringing a pattern. Now it's your turn! Play one of the bells yourself. How do you know when it is your turn to ring?
Given the products of adjacent cells, can you complete this Sudoku?
Use the interactivity to play two of the bells in a pattern. How do you know when it is your turn to ring, and how do you know which bell to ring?
The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?
How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?
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?"
Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.
An irregular tetrahedron is composed of four different triangles. Can such a tetrahedron be constructed where the side lengths are 4, 5, 6, 7, 8 and 9 units of length?
Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.
This Sudoku requires you to do some working backwards before working forwards.
Label this plum tree graph to make it totally magic!
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
A man has 5 coins in his pocket. Given the clues, can you work out what the coins are?
This is a variation of sudoku which contains a set of special clue-numbers. Each set of 4 small digits stands for the numbers in the four cells of the grid adjacent to this set.
Four friends must cross a bridge. How can they all cross it in just 17 minutes?
This Sudoku combines all four arithmetic operations.
This Sudoku, based on differences. Using the one clue number can you find the solution?
A package contains a set of resources designed to develop students’ mathematical thinking. This package places a particular emphasis on “being systematic” and is designed to meet. . . .