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

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

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

The clues for this Sudoku are the product of the numbers in adjacent squares.

My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?

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. . . .

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.

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

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?

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

The NRICH team are always looking for new ways to engage teachers and pupils in problem solving. Here we explain the thinking behind maths trails.

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

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

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?"

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.

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?

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?

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

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

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

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

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.

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 mathematician goes into a supermarket and buys four items. Using a calculator she multiplies the cost instead of adding them. How can her answer be the same as the total at the till?

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

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

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

A few extra challenges set by some young NRICH members.

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?

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

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

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.

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?

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?

Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

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

What happens when you add three numbers together? Will your answer be odd or even? How do you know?

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

Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.

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

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.

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?

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

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

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....?

Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma and Emma passed a fifth of her counters to Ben. After this they all had the same number of counters.

Use the differences to find the solution to this Sudoku.

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?