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 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?"
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?
Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.
Find the values of the nine letters in the sum: FOOT + BALL = GAME
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
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?
Follow the clues to find the mystery number.
There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.
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 planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
Each clue in this Sudoku is the product of the two numbers in adjacent cells.
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?
Bellringers have a special way to write down the patterns they ring. Learn about these patterns and draw some of your own.
This Sudoku, based on differences. Using the one clue number can you find the solution?
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.
Rather than using the numbers 1-9, this sudoku uses the nine different letters used to make the words "Advent Calendar".
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?
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?
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.
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?
Given the products of adjacent cells, can you complete this Sudoku?
Can you help the children find the two triangles which have the lengths of two sides numerically equal to their areas?
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.
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?
Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?
Find out about Magic Squares in this article written for students. Why are they magic?!
Can you coach your rowing eight to win?
Four small numbers give the clue to the contents of the four surrounding cells.
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
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?
You need to find the values of the stars before you can apply normal Sudoku rules.
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.
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?
Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?
This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!
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?
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?
Using the statements, can you work out how many of each type of rabbit there are in these pens?
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
A merchant brings four bars of gold to a jeweller. How can the jeweller use the scales just twice to identify the lighter, fake bar?
Stuart's watch loses two minutes every hour. Adam's watch gains one minute every hour. Use the information to work out what time (the real time) they arrived at the airport.
Investigate the different ways you could split up these rooms so that you have double the number.
Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.