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.

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?

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?

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.

Replace the letters with numbers to make the addition work out correctly. R E A D + T H I S = P A G E

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?"

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

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

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?

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...

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?

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

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

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

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

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

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

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?

I added together some of my neighbours' house numbers. Can you explain the patterns I noticed?

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

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

This task encourages you to investigate the number of edging pieces and panes in different sized windows.

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?

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

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

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

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

You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.

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 puzzle can be solved with the help of small clue-numbers on the border lines between pairs of neighbouring squares of the grid.

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

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

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

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.

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

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

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?

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

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

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?

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

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.

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?

Each of the main diagonals of this sudoku must contain the numbers 1 to 9 and each rectangle width the numbers 1 to 4.

The puzzle can be solved with the help of small clue-numbers which are either placed on the border lines between selected pairs of neighbouring squares of the grid or placed after slash marks on. . . .

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.

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

In this Sudoku, there are three coloured "islands" in the 9x9 grid. Within each "island" EVERY group of nine cells that form a 3x3 square must contain the numbers 1 through 9.

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?