Jenny Murray describes how she developed her interest in making and breaking codes.
Codebreaking as a hook to help develop mathematical skills.
Look on the back of any modern book and you will find an ISBN code. Take this code and calculate this sum in the way shown. Can you see what the answers always have in common?
Can you follow the rule to decode the messages?
Learn about the maths you need to become a codebreaker!
Details are given of how check codes are constructed (using modulus arithmetic for passports, bank accounts, credit cards, ISBN book numbers, and so on. A list of codes is given and you have to check. . . .
Is the regularity shown in this encoded message noise or structure?
This article describes the underlying mathematical ideas and skills involved in the important mathematical application of coding.
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.
Can you crack these very difficult challenge ciphers? How might you systematise the cracking of unknown ciphers?
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?
teacher short articles
The active Stage 5 problems. Why not submit a solution or chat about things on the blogs?
Choose any whole number n, cube it, add 11n, and divide by 6. What do you notice?
The Enigma Project's James Grime has created a video code challenge. Watch it here!
Crack this code which depends on taking pairs of letters and using two simultaneous relations and modulus arithmetic to encode the message.
Suppose an operator types a US Bank check code into a machine and transposes two adjacent digits will the machine pick up every error of this type? Does the same apply to ISBN numbers; will a machine. . . .
Problems to provoke curiosity and questioning
This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?
List of recent guest editors and the articles they contributed.
These problems will make you say "I wonder what happens if...?"
You are given the method used for assigning certain check codes and you have to find out if an error in a single digit can be identified.
Calling all maths detectives! This feature focuses on lots of fun problems for children to solve.
You have worked out a secret code with a friend. Every letter in the alphabet can be represented by a binary value.
This article for Primary and Secondary teachers is all about the mathematics behind solving puzzles, unravelling mysteries and breaking codes.
Sometimes it's not easy to know how to start a problem. Try talking to friend about how to start, and what sort of plan you'll have to carry on.
When does a pattern start to exhibit structure? Can you crack the code used by the computer?
These articles, although written for upper primary and secondary students, are useful background for teachers.
While musing about the difficulties children face in comprehending number structure, notation, etc., it occured to the author that there is a vast array of occasions when numbers and signs are used. . . .
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.
These articles, written for primary teachers, focus on the overarching curriculum aims of problem solving, reasoning and fluency.
This article for teachers looks at some suggestions taken from the NRICH website that offer a broad view of data and ask some more probing questions about it.
Past Features for lower secondary students
At NRICH our work has always focused on problem solving and enrichment, and we have recently been considering in some depth what we mean by these two ideas and how they impinge on children’s. . . .
Here is a list of all the secondary problems connected with Factors and Multiples
How was the data for this problem compiled? A guided tour through the process.
This article, for students and teachers, is mainly about probability, the mathematical way of looking at random chance.
Here is a list of books recommended for young people who are interested in mathematics.