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

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.

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

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

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?

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?

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

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?

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

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

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?

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

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

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

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

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

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

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.

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?"

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?

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?

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

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

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

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

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?

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

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. . . .

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....?

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

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?

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.

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.

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

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?

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

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.

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. . . .

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...

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?

Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?