### 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?

### Secret Transmissions

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

### Secondary Cipher Challenge Part 1

Here is the start of a six-part challenge. Can you get to the end and crack the final message?

# Substitution Cipher

### Why do this problem?

This problem offers a statistical activity that has immediate practical application. We have offered a spreadsheet toolkit so that students can concentrate on the analysis of the data without needing to waste time on computation.

### Possible approach

"Which letters do you think appear most often in the English language?"
"How could you find out?"

Allow some time for students to think about and share their answers. If they have books with them, perhaps suggest that they take a look to see which letters seem most common at first glance.

If a computer room is available, introduce students to the toolkit and give them time to perform a frequency analysis on some English text (Wikipedia articles are a great source for this). Share results from the frequency analysis. Does everybody find the same letters come out top, and bottom? There is opportunity here for some discussion about the benefits of using longer sample texts.

Then present students with the ciphertext in the problem (available as a text file here).

If a computer room is not available, the ciphertext is available as a worksheet here. Here is a second version of the worksheet with the ciphertext faint so that students can write over it as they go deciphering the message.

### Key questions

Can you spot the vowels?

Are there any short words? What might they be?

### Possible extension

Students could investigate the frequency of digraphs (pairs of letters such as th or sh) in the English language and consider whether this speeds up the deciphering process.

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

### Possible support

Students could be encouraged to work collaboratively on this problem. There are lots of suggestions to help them get started in the hint.

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.