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

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

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

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

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.

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.

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

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?

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?

Use the clues about the symmetrical properties of these letters to place them on the grid.

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

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

A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.

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?

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

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?

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

A few extra challenges set by some young NRICH members.

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

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

Systematically explore the range of symmetric designs that can be created by shading parts of the motif below. Use normal square lattice paper to record your results.

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

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.

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

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

Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.

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

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

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

How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?

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.

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

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

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....?

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?

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.

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.

These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.

Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

Try out the lottery that is played in a far-away land. What is the chance of winning?

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

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

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

Hover your mouse over the counters to see which ones will be removed. Click to remover them. The winner is the last one to remove a counter. How you can make sure you win?

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.