I added together some of my neighbours' house numbers. Can you explain the patterns I noticed?
If you take a three by three square on a 1-10 addition square and multiply the diagonally opposite numbers together, what is the difference between these products. Why?
15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?
The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
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?
Replace the letters with numbers to make the addition work out correctly. R E A D + T H I S = P A G E
Find the values of the nine letters in the sum: FOOT + BALL = GAME
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.
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.
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?
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?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
This task encourages you to investigate the number of edging pieces and panes in different sized windows.
Try to solve this very difficult problem and then study our two suggested solutions. How would you use your knowledge to try to solve variants on the original problem?
Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?
You need to find the values of the stars before you can apply normal Sudoku rules.
Special clue numbers related to the difference between numbers in two adjacent cells and values of the stars in the "constellation" make this a doubly interesting problem.
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
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.
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?
Given the products of adjacent cells, can you complete this Sudoku?
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.
Find out about Magic Squares in this article written for students. Why are they magic?!
The clues for this Sudoku are the product of the numbers in adjacent squares.
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.
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 cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.
Bellringers have a special way to write down the patterns they ring. Learn about these patterns and draw some of your own.
You have twelve weights, one of which is different from the rest. Using just 3 weighings, can you identify which weight is the odd one out, and whether it is heavier or lighter than the rest?
Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.
Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.
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?"
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?
An extra constraint means this Sudoku requires you to think in diagonals as well as horizontal and vertical lines and boxes of nine.
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.
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?
Each clue in this Sudoku is the product of the two numbers in adjacent cells.
You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.
Use the clues about the shaded areas to help solve this sudoku
Each of the main diagonals of this sudoku must contain the numbers 1 to 9 and each rectangle width the numbers 1 to 4.
Four numbers on an intersection that need to be placed in the surrounding cells. That is all you need to know to solve this sudoku.
Charlie and Abi 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?
Take three whole numbers. The differences between them give you three new numbers. Find the differences between the new numbers and keep repeating this. What happens?
Have a go at this game which has been inspired by the Big Internet Math-Off 2019. Can you gain more columns of lily pads than your opponent?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?