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.

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

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

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?

Solve this Sudoku puzzle whose clues are in the form of sums of the numbers which should appear in diagonal opposite cells.

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.

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 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.

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.

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?"

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

A few extra challenges set by some young NRICH members.

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

Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?

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

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

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.

Arrange the digits 1, 1, 2, 2, 3 and 3 so that between the two 1's there is one digit, between the two 2's there are two digits, and between the two 3's there are three digits.

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

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

Here are four cubes joined together. How many other arrangements of four cubes can you find? Can you draw them on dotty paper?

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

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

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

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

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?

Each of the main diagonals of this sudoku must contain the numbers 1 to 9 and each rectangle width the numbers 1 to 4.

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.

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?

Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.

Each clue in this Sudoku is the product of the two numbers in adjacent cells.

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

In this Sudoku, there are three coloured "islands" in the 9x9 grid. Within each "island" EVERY group of nine cells that form a 3x3 square must contain the numbers 1 through 9.

In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?

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

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

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?

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

How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?

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?

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?

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?

Jack has nine tiles. He put them together to make a square so that two tiles of the same colour were not beside each other. Can you find another way to do it?

Arrange 3 red, 3 blue and 3 yellow counters into a three-by-three square grid, so that there is only one of each colour in every row and every column

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

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.