### The Best Card Trick?

Time for a little mathemagic! Choose any five cards from a pack and show four of them to your partner. How can they work out the fifth?

### Substitution Cipher

Find the frequency distribution for ordinary English, and use it to help you crack the code.

### Secret Transmissions

How can Agent X transmit data on a faulty line and be sure that her message will get through?

# Transposition Cipher

### Why do this problem?

This problem makes use of students' knowledge about factors and multiples, presented in an intriguing context using the 'hook' of codebreaking.

### Possible approach

This problem could follow on from Substitution Cipher where students are introduced to frequency analysis.

Start by performing a frequency analysis on this text:

ttanopnshonstpdeendoaiherltsmnemaihuogrebkedmhsdbendeeetiadenrlottin
tsfbhupltefeonpyolaalnettflveedhhblewlsaieirefutnfnynodakogdtrdlarde
sseibeoetoncoswprmleuhnwaeyhteweiwdasfhlgaodtoalhywnoutx


It is available here as a text file.

Invite the class to comment on what they notice. As they realise that the distribution of letters matches that of ordinary English, invite suggestions as to how the text might have been encoded if not by substitution.

Show the "Peter Rabbit" example from the problem, showing how to encode text using a transposition cipher. This set of PowerPoint slides describes each step of the encryption and decryption process.

Then hand out this worksheet with the text above, and invite students to decode it.

Students could then create their own transposition ciphers and challenge the rest of the class to decipher them.

If computers are available, students might want to use our Cipher Challenge Toolkit which contains a transposition solver.

### Key questions

Why might you choose a 48 character message rather than a 44 character one?

### Possible extension

The Secondary Cipher Challenge and Substitution Transposed offer challenging extensions for students who have worked on this problem and the problem Substitution Cipher.

### Possible support

Encourage students to work collaboratively. Working on squared paper is really helpful.

If your students have enjoyed working on this problem, you may be interested in booking a visit from the Millennium Maths Project's Enigma project.

The Enigma Project is a presentation about the history and mathematics of codes and code breaking, from ancient Greece to the present, including a demonstration of a genuine WWII enigma machine.