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 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.

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.

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

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.

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

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

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

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.

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?

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?

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?

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

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

Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.

A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?

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

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 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?

Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?

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

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

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?

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?

Find out what a "fault-free" rectangle is and try to make some of your own.

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

Can you find all the different ways of lining up these Cuisenaire rods?

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.

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....?

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. . . .

How many different triangles can you make on a circular pegboard that has nine pegs?

Seven friends went to a fun fair with lots of scary rides. They decided to pair up for rides until each friend had ridden once with each of the others. What was the total number rides?

Can you find all the different triangles on these peg boards, and find their angles?

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.

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

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

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

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

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.

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

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?

A few extra challenges set by some young NRICH members.

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

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.

In this game for two players, you throw two dice and find the product. How many shapes can you draw on the grid which have that area or perimeter?

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

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

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?