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 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?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Given the products of adjacent cells, can you complete this Sudoku?
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?
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?
Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.
Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.
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 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.
Bellringers have a special way to write down the patterns they ring. Learn about these patterns and draw some of your own.
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.
Each clue in this Sudoku is the product of the two numbers in adjacent cells.
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?
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?
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?
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.
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.
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.
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.
This Sudoku, based on differences. Using the one clue number can you find the solution?
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?
A few extra challenges set by some young NRICH members.
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?
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?
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?
Rather than using the numbers 1-9, this sudoku uses the nine different letters used to make the words "Advent Calendar".
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...
You need to find the values of the stars before you can apply normal Sudoku rules.
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?
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.
Given the products of diagonally opposite cells - can you complete 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?
The clues for this Sudoku are the product of the numbers in adjacent squares.
Find out about Magic Squares in this article written for students. Why are they magic?!
An extra constraint means this Sudoku requires you to think in diagonals as well as horizontal and vertical lines and boxes of nine.
Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?
Find the values of the nine letters in the sum: FOOT + BALL = GAME
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?
Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.
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?
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.
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 letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
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.
You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.