Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?

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?

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?

The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?

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.

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

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.

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.

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.

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

Can you recreate these designs? What are the basic units? What movement is required between each unit? Some elegant use of procedures will help - variables not essential.

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

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?

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

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

A few extra challenges set by some young NRICH members.

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?

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

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

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

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?

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

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

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

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

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.

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

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.

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

A Sudoku that uses transformations as supporting clues.

Whenever a monkey has peaches, he always keeps a fraction of them each day, gives the rest away, and then eats one. How long could he make his peaches last for?

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

A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

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.

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?

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

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

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?

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

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?

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

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

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