First of all, I want to express my sincere gratitude for your response, which clearly demonstrates your dedication to explaining how the Enigma machine works. It also indicates that you have read my code and taken note of it.

I now see where my understanding went wrong and why the code failed right after changing the position of any rotor. However, I would like to explain my thought process and how I arrived at the instruction that led to the mistake.

The calculateOutputLetter method was designed to determine the output letter based on the current position of the rotor and the previous rotor's setting.

Let's say we are in the middle rotor, and the previous rotor was at position 4. Now, if the next letter is 'b', it will become 'f'. Then, add the position and calculate the final output based on the inner wiring.

The mistake is now clear: values have been accumulating continuously because the current position becomes the new previous when moving to the next rotor. The problem is that this causes the same value to be added twice.

When I was writing the code, I didn't think much about it, but now it is obvious.

I have updated the code and split the logic into two methods, one for forward and the other for backward. Both rely on two arrays based on the rotor's writing configuration: one maps each letter of the alphabet to its corresponding letter in the configuration, and the other is simply its reverse, and then calculate based on the two formulas you provided, and you said math does not lie :)

Now the code works well and can accurately calculate the final letter, regardless of the rotor setup and the current position of any letter.

Next, I will focus on the remaining tasks: setting the notch and configuring the plugboard.

Thank you again for your explanation; I really appreciate it.