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

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

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

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

Can you make square numbers by adding two prime numbers together?

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?

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.

Using all ten cards from 0 to 9, rearrange them to make five prime numbers. Can you find any other ways of doing it?

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

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

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

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

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?

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 numbers and symbols to make this number sentence correct. How many different ways can you find?

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

Different combinations of the weights available allow you to make different totals. Which totals can you make?

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

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.

Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?

Complete the magic square using the numbers 1 to 25 once each. Each row, column and diagonal adds up to 65.

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

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?

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.

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

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?

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?

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

Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

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

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

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

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

This task encourages you to investigate the number of edging pieces and panes in different sized windows.

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

Cut differently-sized square corners from a square piece of paper to make boxes without lids. Do they all have the same volume?

A few extra challenges set by some young NRICH members.

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

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

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?

Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?

Can you draw a square in which the perimeter is numerically equal to the area?

How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?

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!

There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.

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?