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?

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

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

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?

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 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 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?

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.

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

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.

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

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

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

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?

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.

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

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?

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

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?

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

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.

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 few extra challenges set by some young NRICH members.

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

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?!

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".

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

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 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?

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?

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 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?

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?

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.

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?

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

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

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

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?

Solve this Sudoku puzzle whose clues are in the form of sums of the numbers which should appear in diagonal opposite cells.

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

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.

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

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

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?