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?

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.

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?

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.

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 values of the nine letters in the sum: FOOT + BALL = GAME

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?

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

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

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?

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.

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

Two sudokus in one. Challenge yourself to make the necessary connections.

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 Sudoku that uses transformations as supporting clues.

Use the clues about the shaded areas to help solve this sudoku

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?

Four friends must cross a bridge. How can they all cross it in just 17 minutes?

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

Bellringers have a special way to write down the patterns they ring. Learn about these patterns and draw some of your own.

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

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

Two sudokus in one. Challenge yourself to make the necessary connections.

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 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?

How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?

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

This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?

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. . . .

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.

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

Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?

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?

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 requires you to have "double vision" - two Sudoku's for the price of one

A challenging activity focusing on finding all possible ways of stacking rods.

A pair of Sudokus with lots in common. In fact they are the same problem but rearranged. Can you find how they relate to solve them both?

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

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

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...

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

A few extra challenges set by some young NRICH members.

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.