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 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?"

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

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 package contains a collection of problems from the NRICH website that could be suitable for students who have a good understanding of Factors and Multiples and who feel ready to take on some. . . .

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

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?

Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.

A few extra challenges set by some young NRICH members.

The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?

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?

A package contains a set of resources designed to develop students’ mathematical thinking. This package places a particular emphasis on “being systematic” and is designed to meet. . . .

Can you use the information to find out which cards I have used?

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

How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?

Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?

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

This challenge extends the Plants investigation so now four or more children are involved.

Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?

Use the differences to find the solution to this Sudoku.

Seven friends went to a fun fair with lots of scary rides. They decided to pair up for rides until each friend had ridden once with each of the others. What was the total number rides?

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

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

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.

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

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

Given the products of adjacent cells, can you complete this Sudoku?

This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.

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

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

Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?

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

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?

My local DIY shop calculates the price of its windows according to the area of glass and the length of frame used. Can you work out how they arrived at these prices?

How could you arrange at least two dice in a stack so that the total of the visible spots is 18?

Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.

Can you use your powers of logic and deduction to work out the missing information in these sporty situations?

Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?

If these elves wear a different outfit every day for as many days as possible, how many days can their fun last?

Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?

Have a go at balancing this equation. Can you find different ways of doing it?

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?

Can you work out some different ways to balance this equation?

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?

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

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

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

Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.