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

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 challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.

How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?

How many different symmetrical shapes can you make by shading triangles or squares?

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.

Use the clues about the symmetrical properties of these letters to place them on the grid.

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?

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?

Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?

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

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?

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

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

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?

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

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?

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?

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

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?"

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.

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.

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

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. . . .

This package contains a collection of problems from the NRICH website that could be suitable for students who have a good understanding of Factors and Multiples and who feel ready to take on some. . . .

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

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 ways of lining up these Cuisenaire rods?

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

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

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

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....?

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

A few extra challenges set by some young NRICH members.

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

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?

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?

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

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

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?

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

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

Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...

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

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

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

In how many ways can you stack these rods, following the rules?