You have already used Magic Squares, now meet an Anti-Magic Square. Its properties are slightly different, but can you still solve it...
You may have seen magic squares before, but can you work out the missing numbers on this magic star?
This magic square has only been partially completed. Can you still solve it...
Four wiggles equal three woggles. Two woggles equal five waggles. Six waggles equal one wuggle. Using these, can you work out which of four values is the smallest?
The Queen of Hearts has lost her tarts! She asks each knave if he has eaten them, but how many of them are honest...
Given three concentric circles, shade in the annulus formed by the smaller two. What percentage of the larger circle is now shaded?
Imagine cutting out a circle which is just contained inside a semicircle. What fraction of the semi-circle will remain?
Can you fill in the empty boxes in the grid with the right shape
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
Someone at the top of a hill sends a message in semaphore to a
friend in the valley. A person in the valley behind also sees the
same message. What is it?
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?
What is the missing symbol? Can you decode this in a similar way?
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
I was looking at the number plate of a car parked outside. Using my special code S208VBJ adds to 65. Can you crack my code and use it to find out what both of these number plates add up to?
Semaphore is a way to signal the alphabet using two flags. You
might want to send a message that contains more than just letters.
How many other symbols could you send using this code?
You may like to read the article on Morse code before attempting
this question. Morse's letter analysis was done over 150 years ago,
so might there be a better allocation of symbols today?
The machine I use to produce Braille messages is faulty and one of the pins that makes a raised dot is not working. I typed a short message in Braille. Can you work out what it really says?
Mr Smith and Mr Jones are two maths teachers. By asking questions, the answers to which may be right or wrong, Mr Jones is able to find the number of the house Mr Smith lives in... Or not!
You have worked out a secret code with a friend. Every letter in the alphabet can be represented by a binary value.
Ask a friend to choose a number between 1 and 63. By identifying which of the six cards contains the number they are thinking of it is easy to tell them what the number is.
Decipher a simple code based on the rule C=7P+17 (mod 26) where C is the code for the letter P from the alphabet. Rearrange the formula and use the inverse to decipher automatically.
Crack this code which depends on taking pairs of letters and using
two simultaneous relations and modulus arithmetic to encode the
Find 180 to the power 59 (mod 391) to crack the code. To find the
secret number with a calculator we work with small numbers like 59
and 391 but very big numbers are used in the real world for this.
Ruth from Swanborne House School describes some unusual shapes very clearly.
The diagrams that Adam and Sam from Perton Middle School sent in help to explain this problem.
Thank you Hannah for this well argued, well presented, solution.
The problem was not as difficult as a first glance suggested.
Here's a clearly explained solution for the problem which starts 'Take three unit circles...' What would happen if the problem asked you to take
four or five or more unit circles?
When you think of spies and secret agents, you probably wouldn’t think of mathematics. Some of the most famous code breakers in history have been mathematicians.
A game for 2 people that everybody knows. You can play with a
friend or online. If you play correctly you never lose!
This short article gives an outline of the origins of Morse code and its inventor and how the frequency of letters is reflected in the code they were given.
A game for 2 players that can be played online. Players take it in turns to select a word from the 9 words given. The aim is to select all the occurrences of the same letter.
An example of a simple Public Key code, called the Knapsack Code is
described in this article, alongside some information on its
origins. A knowledge of modular arithmetic is useful.
Can you spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.
An introduction to the ideas of public key cryptography using small
numbers to explain the process. In practice the numbers used are
too large to factorise in a reasonable time.
To avoid losing think of another very well known game where the
patterns of play are similar.