This month: Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5

16 Matches

Book Codes

Stage: 2 Challenge Level:

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?

Inspector Morse

Stage: 3 Challenge Level:

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 Secret World of Codes and Code Breaking

Stage: 2, 3 and 4

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.

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. . . .

Substitution Cipher and Frequency Analysis

Stage: 4 Challenge Level:

Investigate some text to find the frequency distribution for ordinary English and use that to help you crack the coded text below.

Double Time

Stage: 5 Challenge Level:

Crack this code which depends on taking pairs of letters and using two simultaneous relations and modulus arithmetic to encode the message.

Transposition Fix

Stage: 4 Challenge Level:

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. . . .

Code Breaker

Stage: 2 Challenge Level:

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?

The Knapsack Problem and Public Key Cryptography

Stage: 5

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.

Check Code Sensitivity

Stage: 4 Challenge Level:

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.

Knapsack

Stage: 4 Challenge Level:

You have worked out a secret code with a friend. Every letter in the alphabet can be represented by a binary value.

Pattern Recognition

Stage: 5 Challenge Level:

When does a pattern start to exhibit structure? Can you crack the code used by the computer?

Numbers and Notation - Ambiguities and Confusions

Stage: 1

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. . . .

History of Morse

Stage: 2, 3, 4 and 5

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.

Enrichment at NRICH

Stage:

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. . . .

Taking Chances Extended

Stage: 4 and 5

This article, for students and teachers, is mainly about probability, the mathematical way of looking at random chance.

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