I added together some of my neighbours' house numbers. Can you explain the patterns I noticed?

A little mouse called Delia lives in a hole in the bottom of a tree.....How many days will it be before Delia has to take the same route again?

What happens when you add three numbers together? Will your answer be odd or even? How do you know?

Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.

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

Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

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

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

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.

This article for teachers describes several games, found on the site, all of which have a related structure that can be used to develop the skills of strategic planning.

60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?

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?"

Can you find a cuboid that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

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

My dice has inky marks on each face. Can you find the route it has taken? What does each face look like?

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?

This Sudoku requires you to do some working backwards before working forwards.

An investigation that gives you the opportunity to make and justify predictions.

In the planet system of Octa the planets are arranged in the shape of an octahedron. How many different routes could be taken to get from Planet A to Planet Zargon?

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

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.

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.

Replace the letters with numbers to make the addition work out correctly. R E A D + T H I S = P A G E

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.

Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?

Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?

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?

Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?

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

A monkey with peaches, keeps a fraction of them each day, gives the rest away, and then eats one. How long can his peaches last?

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 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What size rectangle(s) contain(s) exactly 100 squares? Can you find them all?

You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?

Four numbers on an intersection that need to be placed in the surrounding cells. That is all you need to know to solve this sudoku.

This task encourages you to investigate the number of edging pieces and panes in different sized windows.

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?

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.

I like to walk along the cracks of the paving stones, but not the outside edge of the path itself. How many different routes can you find for me to take?

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

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

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?

Alice and Brian are snails who live on a wall and can only travel along the cracks. Alice wants to go to see Brian. How far is the shortest route along the cracks? Is there more than one way to go?

Throughout these challenges, the touching faces of any adjacent dice must have the same number. Can you find a way of making the total on the top come to each number from 11 to 18 inclusive?