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?"

Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.

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?

The clues for this Sudoku are the product of the numbers in adjacent squares.

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 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 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.

Each clue in this Sudoku is the product of the two numbers in adjacent cells.

Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.

You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the 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?

A few extra challenges set by some young NRICH members.

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 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.

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

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?

You need to find the values of the stars before you can apply normal Sudoku rules.

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.

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?

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.

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...

Rather than using the numbers 1-9, this sudoku uses the nine different letters used to make the words "Advent Calendar".

An extra constraint means this Sudoku requires you to think in diagonals as well as horizontal and vertical lines and boxes of nine.

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.

Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

Given the products of diagonally opposite cells - can you complete this Sudoku?

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?

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?

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?

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?

This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.

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?

The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?

Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?

This Sudoku, based on differences. Using the one clue number can you find the solution?

Different combinations of the weights available allow you to make different totals. Which totals can you make?

A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.

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.

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?

A Sudoku that uses transformations as supporting clues.

How many solutions can you find to this sum? Each of the different letters stands for a different number.

A man has 5 coins in his pocket. Given the clues, can you work out what the coins are?

A pair of Sudoku puzzles that together lead to a complete solution.

Four small numbers give the clue to the contents of the four surrounding cells.