Each clue in this Sudoku is the product of the two numbers in adjacent cells.
Bellringers have a special way to write down the patterns they ring. Learn about these patterns and draw some of your own.
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?
Find the values of the nine letters in the sum: FOOT + BALL = GAME
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?"
The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.
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?
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?
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.
This Sudoku, based on differences. Using the one clue number can you find the solution?
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?
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.
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.
You need to find the values of the stars before you can apply normal Sudoku rules.
Rather than using the numbers 1-9, this sudoku uses the nine different letters used to make the words "Advent Calendar".
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
An extra constraint means this Sudoku requires you to think in diagonals as well as horizontal and vertical lines and boxes of nine.
Given the products of adjacent cells, can you complete this Sudoku?
A pair of Sudoku puzzles that together lead to a complete solution.
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?
Use the differences to find the solution to this Sudoku.
The letters of the word ABACUS have been arranged in the shape of a triangle. How many different ways can you find to read the word ABACUS from this triangular pattern?
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?
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.
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.
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 few extra challenges set by some young NRICH members.
Four small numbers give the clue to the contents of the four surrounding cells.
Given the products of diagonally opposite cells - can you complete this Sudoku?
A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.
Can you use your powers of logic and deduction to work out the missing information in these sporty situations?
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
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?
Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.
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?
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?
You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.
Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.
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?
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
Just four procedures were used to produce a design. How was it done? Can you be systematic and elegant so that someone can follow your logic?
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
A challenging activity focusing on finding all possible ways of stacking rods.
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...
First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.
60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?