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

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

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

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?

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.

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

Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.

A few extra challenges set by some young NRICH members.

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

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

Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?

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

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

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?

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.

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

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

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

You need to find the values of the stars before you can apply normal Sudoku rules.

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?

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

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.

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

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.

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.

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

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?"

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

Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

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?

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

Whenever a monkey has peaches, he always keeps a fraction of them each day, gives the rest away, and then eats one. How long could he make his peaches last for?

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?

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

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

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

Using the statements, can you work out how many of each type of rabbit there are in these pens?

If we had 16 light bars which digital numbers could we make? How will you know you've found them all?

Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

What is the smallest number of tiles needed to tile this patio? Can you investigate patios of different sizes?

These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.

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

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

When you throw two regular, six-faced dice you have more chance of getting one particular result than any other. What result would that be? Why is this?

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

Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?

Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.