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

How many different symmetrical shapes can you make by shading triangles or squares?

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?

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

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

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.

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?

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. . . .

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?

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

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

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.

Use the differences to find the solution to this Sudoku.

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

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

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?

A few extra challenges set by some young NRICH members.

Problem solving is at the heart of the NRICH site. All the problems give learners opportunities to learn, develop or use mathematical concepts and skills. Read here for more information.

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

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

Find out about Magic Squares in this article written for students. Why are they magic?!

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

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

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?

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?

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

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

Starting with four different triangles, imagine you have an unlimited number of each type. How many different tetrahedra can you make? Convince us you have found them all.

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.

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. . . .

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?

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?

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

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

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

The NRICH team are always looking for new ways to engage teachers and pupils in problem solving. Here we explain the thinking behind maths trails.

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

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

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

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

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

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?

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.

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

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