Class Openers

Class Opener – Day 51 – Codebreaking Continues.

Yesterday, a team of students managed to win Jolly Ranchers off of me in my cryptogram challenge. I don’t feel nearly as generous with today’s cryptography challenge:


How many words is that? How did you code it? What do I do?

This is definitely a much trickier challenge than yesterday. The only hint I offered is that the original message was two words, 12 letters total, and that some extra information would be coming later in class.

This extra information came when we began our notes on matrices, where we talked about the constant need in math to “undo” an operation. So if we multiply matrices to obtain a product, we can use an inverse matrix to undo the operation.  Slyly, I then offered that if I were to (hypothetically) convert a message into numbers, arrange it into a matrix, then multiply it by a secret matrix, then a cunning student could undo my work by considering the inverse.

Clearly this isn’t much of a hint, as there are an infinite number of coding matrices to consider. But take a look at that original photo again….what’s that matrix lingering in the darkness?  To code my message, this matrix method (called the Hill Cipher) was used, and my coding matrix was provided all along.  This still provides a challenge to students who are new to inverse matrices, but before we departed I did show my class a Hill Cipher applet which I used to code my message, and which verifies the original message.


Tomorrow we’ll take another look at this cipher method, and try some of our own with a puzzle I have created.  By the end of the week, expect the Enigma to make an appearance for a final challenge!


By Bob Lochel

HS Math Teacher. Hatboro-Horsham School District, Horsham, PA.

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