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.

Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.

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?

This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?

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

Two sudokus in one. Challenge yourself to make the necessary connections.

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.

A Sudoku with clues given as sums of entries.

Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possibilities that could come up?

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

This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.

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?

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.

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.

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?

This sudoku requires you to have "double vision" - two Sudoku's for the price of one

Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?

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

A Sudoku that uses transformations as supporting clues.

Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?

What could the half time scores have been in these Olympic hockey matches?

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

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

Two sudokus in one. Challenge yourself to make the necessary connections.

Can you find all the ways to get 15 at the top of this triangle of numbers?

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

In this article, the NRICH team describe the process of selecting solutions for publication on the site.

Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.

Use the interactivity to listen to the bells ringing a pattern. Now it's your turn! Play one of the bells yourself. How do you know when it is your turn to ring?

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

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

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

This Sudoku puzzle can be solved with the help of small clue-numbers on the border lines between pairs of neighbouring squares of the grid.

Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?

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?

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

Using the statements, can you work out how many of each type of rabbit there are in these pens?

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.

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?

Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?

This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!

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

Add the sum of the squares of four numbers between 10 and 20 to the sum of the squares of three numbers less than 6 to make the square of another, larger, number.

Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?

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