Monday Maths: Crypto-puzzles

Cryptography is the practice and study of techniques for secure communication in the presence of third parties. — Wikipedia

Or, for those of us who try to use words Brownies can understand, secret codes.  Secret codes are a lot of fun, especially when you start inventing your own!  You can pass messages to other people, without anyone else knowing what you’re saying.

Secret codes are part of the Brownie Number Fun badge.  They range from the simple:

Brownies are the best –> 2-18-15-23-14-9-5-19  1-18-5  20-8-5  2-5-19-20

to the more complex:

Brownies are the best –> 3-10-4-20-2-17-9-12  1-10-9  14-15-9  3-9-12-14

(By the way, there are virtual cookies for anyone who can explain that one in the comments.  I will upgrade you to real cookies if you live within five miles of me.  You know who you are.)

Not all codes include numbers of course, but ultimately breaking codes is all about maths and language skills.  We’ll stick to straight substitution codes for now – that is, each letter in the word is replaced by one (and only one) other letter, number, or symbol.

There are several key starting points to breaking a substitution code:

  • Know which letters are most common in your language.  You can get a table from Wikipedia, and if you create a frequency table for the sample you are trying to translate you can make some good guesses.  The symbol that occurs most often in your sample is probably an “e”.  Of course, this works better if you have a large sample to work from!
  • Know which letter combinations are common, for example “the” appears more often than “ghy”.  A three letter/symbol word at the start of several sentences is likely to be “the”, so now you know three letters.
  • Know which letters are allowed to appear on their own – in English, that would be “a” and “I”.

The other things that might help with breaking the code are knowing who sent it and what they are likely to be talking about.  If you have a message that was written by the Pixies, for example, which is being decoded by the Imps, it is almost inevitable that the translation will be something along the lines of “Pixies are better than Imps”!

Or is that too cynical?

So, on to the activities.

Number Wheels

This is a good intro to number codes, for younger girls.  Each person will need two circles, one larger than the other.  On one circle, you write the numbers from 1 to 26, and on the other the letters from A to Z.  If you want, you can include punctuation too – just remember to include extra numbers.

It’s very important that the numbers and letters are evenly spaced around the wheels.

Now, punch a hole through the middle and connect the two wheels with a split-pin.  The top wheel should rotate.  To use your wheel, line up the “A” with any number.  Simply read off the numbers which correspond to the letters in your message.

All your co-conspirator needs to know is what number your “A” was, and then they can line up their wheel the same way and read off the message.

Symbol Codes

The same system can be used to translate between letters and symbols, or you can challenge the girls to make up a code of their own.  Try Pigpen or Grid, from this website.

Wide Games

Everyone loves wide games.  For this activity you’ll need to have explained basic codes beforehand, otherwise it will take a very long time!

Set up a trail of clues, in code – you can use all one code or several different ones, depending on the age of your children.  For example, clue one might be a random string of symbols which translate to “Look under the doormat”, and the next clue is under the doormat.

Set the last clue to point back at the first clue, and then you can set several teams off at the same time, starting from different places.

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4 thoughts on “Monday Maths: Crypto-puzzles

  1. Ooh great tips on breaking a code. I’d never thought of just giving a coded message without also giving the clues to code-break!

    My girls are also very into morse code and/or braille letters (well, the dot symbols of braille) as the base of codes, both of which work well.

  2. 2nd code – Split the alphabet into 2 sections starting with A and N. First section is odd numbers 1-3-5-7… Second section is even numbers 2-4-6-8…

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