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.

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

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

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

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. . . .

A few extra challenges set by some young NRICH members.

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

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

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?

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

Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

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?

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?

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?

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....?

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?

What happens when you round these three-digit numbers to the nearest 100?

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

How many solutions can you find to this sum? Each of the different letters stands for a different number.

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?"

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

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

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

What happens when you round these numbers to the nearest whole number?

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.

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?

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

In this matching game, you have to decide how long different events take.

My local DIY shop calculates the price of its windows according to the area of glass and the length of frame used. Can you work out how they arrived at these prices?

Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?

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?

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?

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

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

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

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?

Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?

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

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.

How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?

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

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.

How could you arrange at least two dice in a stack so that the total of the visible spots is 18?

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?

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

Can you work out some different ways to balance this equation?

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