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?

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

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

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. . . .

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

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 few extra challenges set by some young NRICH members.

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

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

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?

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

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.

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.

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

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?

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.

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

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 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?

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

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

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?"

My cube 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?

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.

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. . . .

Can you use this information to work out Charlie's house number?

Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99 How many ways can you do it?

This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.

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

Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?

Suppose there is a train with 24 carriages which are going to be put together to make up some new trains. Can you find all the ways that this can be done?

Your challenge is to find the longest way through the network following this rule. You can start and finish anywhere, and with any shape, as long as you follow the correct order.

Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.

You have two egg timers. One takes 4 minutes exactly to empty and the other takes 7 minutes. What times in whole minutes can you measure and how?

Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?

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

In this matching game, you have to decide how long different events take.

There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?

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

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

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