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

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

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.

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

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?

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?

Solve this Sudoku puzzle whose clues are in the form of sums of the numbers which should appear in diagonal opposite cells.

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

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

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

Take three whole numbers. The differences between them give you three new numbers. Find the differences between the new numbers and keep repeating this. What happens?

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

Special clue numbers related to the difference between numbers in two adjacent cells and values of the stars in the "constellation" make this a doubly interesting problem.

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 Sudoku, based on differences. Using the one clue number can you find the solution?

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.

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

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.

Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?

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.

Four small numbers give the clue to the contents of the four surrounding cells.

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?

Just four procedures were used to produce a design. How was it done? Can you be systematic and elegant so that someone can follow your logic?

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

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...

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

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

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?

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

A pair of Sudoku puzzles that together lead to a complete solution.

Find out about Magic Squares in this article written for students. Why are they magic?!

This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?

Time for a little mathemagic! Choose any five cards from a pack and show four of them to your partner. How can they work out the fifth?

A Latin square of order n is an array of n symbols in which each symbol occurs exactly once in each row and exactly once in each column.

60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?

The puzzle can be solved by finding the values of the unknown digits (all indicated by asterisks) in the squares of the $9\times9$ grid.

Try to solve this very difficult problem and then study our two suggested solutions. How would you use your knowledge to try to solve variants on the original problem?

We're excited about this new program for drawing beautiful mathematical designs. Can you work out how we made our first few pictures and, even better, share your most elegant solutions with us?

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?

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

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

In this article, the NRICH team describe the process of selecting solutions for publication on the site.

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

Can you use your powers of logic and deduction to work out the missing information in these sporty situations?

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

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.