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

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

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

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.

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

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?

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?

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

Each clue in this Sudoku is the product of the two numbers in adjacent cells.

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?

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.

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

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

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

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

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?"

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.

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

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

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?

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?

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?

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

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?

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?

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

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?

Can you replace the letters with numbers? Is there only one solution in each case?

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

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.

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

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.

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

A few extra challenges set by some young NRICH members.

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

Number problems at primary level that require careful consideration.

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?

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

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

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.

What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.

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?

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

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.

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.