Living Museum of Learning

Where real moments become exhibits

Ethan and the Enigma

Situation

During our Enigma investigation, Leo created a ciphertext based on two famous sentences from Charles Dickens's A Tale of Two Cities:

IT WAS THE BEST OF TIMES
IT WAS THE WORST OF TIMES

Ethan recognized the quotation immediately. Interestingly, he hadn't read the original novel. He had encountered the famous sentences in another book.

He then worked on recovering the original message from Leo's ciphertext.

Turning Point

Ethan initially made a counting mistake. After correcting his approach, he began looking for a mathematical relationship between the encrypted and original letter combinations.

His key observation was that the difference between two two-letter combinations could be expressed in base 26.

For example:

BIM → BHZ

Using W as position zero, he calculated:

IM − HZ = 39

Or, more explicitly:

(12 − 11) × 26 + (16 − 3) = 39

A promising result!

Emergence

But there was one hidden assumption.

Ethan's calculation treated W as position zero for both rotors.

We already had experimental evidence that W represented zero on the rightmost rotor. But did that mean the middle rotor used the same zero?

I wasn't convinced.

So I challenged one part of his calculation.

Instead of assuming that the two positions were 12 and 11, we could express their relationship more generally:

n − (n − 1) = 1

Ethan nodded.

The arithmetic was fine. The question was whether the starting position he had assigned to the middle rotor was actually correct.

Learning

This is where decoding became an investigation.

A mathematical calculation can be perfectly correct while relying on an assumption that has not been verified.

Ethan had successfully connected letter positions, base-26 arithmetic, and the length of the message. But one question remained unanswered:

Which letter represents position zero on the middle Enigma rotor?

Theme

Don't just check your calculations. Check your assumptions.

Doors

The investigation continues!

Can Ethan, Enning, and the other kids discover the middle rotor's zero?

No hints. No shortcuts. Just curiosity, experimentation, and a little patience.

After all, as Ethan observed at the end of class:

"It should be easy but a lot of labor..." 😁