The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
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?
Find the values of the nine letters in the sum: FOOT + BALL = GAME
I added together some of my neighbours' house numbers. Can you explain the patterns I noticed?
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.
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?
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?
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.
Replace the letters with numbers to make the addition work out correctly. R E A D + T H I S = P A G E
Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?
In this Sudoku, there are three coloured "islands" in the 9x9 grid. Within each "island" EVERY group of nine cells that form a 3x3 square must contain the numbers 1 through 9.
The items in the shopping basket add and multiply to give the same amount. What could their prices be?
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.
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?
Given the products of diagonally opposite cells - can you complete 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.
Each clue in this Sudoku is the product of the two numbers in adjacent cells.
Given the products of adjacent cells, can you complete this Sudoku?
You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.
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.
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
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.
This Sudoku combines all four arithmetic operations.
Four small numbers give the clue to the contents of the four surrounding cells.
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.
The puzzle can be solved with the help of small clue-numbers which are either placed on the border lines between selected pairs of neighbouring squares of the grid or placed after slash marks on. . . .
There is a long tradition of creating mazes throughout history and across the world. This article gives details of mazes you can visit and those that you can tackle on paper.
An extra constraint means this Sudoku requires you to think in diagonals as well as horizontal and vertical lines and boxes of nine.
You need to find the values of the stars before you can apply normal Sudoku rules.
Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.
A man has 5 coins in his pocket. Given the clues, can you work out what the coins are?
Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.
Four friends must cross a bridge. How can they all cross it in just 17 minutes?
This task encourages you to investigate the number of edging pieces and panes in different sized windows.
Countries from across the world competed in a sports tournament. Can you devise an efficient strategy to work out the order in which they finished?
This Sudoku, based on differences. Using the one clue number can you find the solution?
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.
Two sudokus in one. Challenge yourself to make the necessary connections.
A Sudoku with a twist.
Find out about Magic Squares in this article written for students. Why are they magic?!
Label this plum tree graph to make it totally magic!
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
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?
A Sudoku with a twist.
Solve the equations to identify the clue numbers in this Sudoku problem.