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
Replace the letters with numbers to make the addition work out correctly. R E A D + T H I S = P A G E
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.
Given the products of adjacent cells, can you complete this Sudoku?
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.
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?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
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?"
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?
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?
I added together some of my neighbours' house numbers. Can you explain the patterns I noticed?
Each clue in this Sudoku is the product of the two numbers in adjacent cells.
Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?
This task encourages you to investigate the number of edging pieces and panes in different sized windows.
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.
Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.
The items in the shopping basket add and multiply to give the same amount. What could their prices be?
Bellringers have a special way to write down the patterns they ring. Learn about these patterns and draw some of your own.
Given the products of diagonally opposite cells - can you complete this Sudoku?
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?
This Sudoku puzzle can be solved with the help of small clue-numbers on the border lines between pairs of neighbouring squares of the grid.
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?
Find out about Magic Squares in this article written for students. Why are they magic?!
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.
Different combinations of the weights available allow you to make different totals. Which totals can you make?
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.
An extra constraint means this Sudoku requires you to think in diagonals as well as horizontal and vertical lines and boxes of nine.
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...
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
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.
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.
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.
A man has 5 coins in his pocket. Given the clues, can you work out what the coins are?
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
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?
Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.
Four friends must cross a bridge. How can they all cross it in just 17 minutes?
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?
Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?
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.
A Sudoku with a twist.
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.
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. . . .
A Sudoku with clues given as sums of entries.