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

A few extra challenges set by some young NRICH members.

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

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

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

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

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

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

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

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.

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

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 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?"

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?

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

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?

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

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.

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.

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.

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?

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

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?

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?

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.

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

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

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?

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.

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

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

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

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?

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.

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?

Can you help the children find the two triangles which have the lengths of two sides numerically equal to their areas?

Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?

Systematically explore the range of symmetric designs that can be created by shading parts of the motif below. Use normal square lattice paper to record your results.

This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?

The Vikings communicated in writing by making simple scratches on wood or stones called runes. Can you work out how their code works using the table of the alphabet?

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.

What is the date in February 2002 where the 8 digits are palindromic if the date is written in the British way?

Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99 How many ways can you do it?

Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.

George and Jim want to buy a chocolate bar. George needs 2p more and Jim need 50p more to buy it. How much is the chocolate bar?

I was in my car when I noticed a line of four cars on the lane next to me with number plates starting and ending with J, K, L and M. What order were they in?

Alice and Brian are snails who live on a wall and can only travel along the cracks. Alice wants to go to see Brian. How far is the shortest route along the cracks? Is there more than one way to go?