How to really crack the Enigma codes.

Because it is a puzzle I will use the SPOILER tags to give you progressively more hints. The puzzle is not really hard or difficult. Specially when you compare it with cracking the real Enigma.
If you do not care about the puzzle and you are just looking for the codes: See the Solution in the "All codes solved" section.
This first part of the guide is about how to find the secret key to the enigma puzzle.

Where can I find the secret key?
The secret key can be found in the game. Keep your eyes open.

I knew that. But, how does it look like, does it flash like loot?
It does not flash. It is part of the enviroment. Written on a wall, a black board, a piece of paper, or a computer screen etc.

Can you be more specific?
It has to do with math

I thought so, but what exactly?
It is an equation / fomula using basic math.

I ran through the game umpteen times but could not find enything. Where should I look?
The formula is all over the game. But here is an example whis really easy to spot:
Chapter 4: Eisenwald Prison. (Remember the actual prison is only one part of this chapter)

Once again. Can you be more specific?
Maybe. Did you know what the Secret Police does?

No?
Detaining and interrogating freedom fighters, smoking, making funny phone calls, and cryptography.

What?
At the secrets police's HQ there is a room full of crypto stuff. And two black boards. See it?

No!

Now?

In this part of the puzzle guide we will use the secret key to set the Enigma rotors to the correct position. Once again I will use the SPOILER tags to give you progressively more hints.

As we know from the first part it is a math equation / formula
we just have to apply it.

How?

It is more an example equation than a formula. You may deduct the actual formula when you look at the other examples in the game.

Can you give some more examples from the game?
Sure.



And more...



Really, I do not get it.
A: The fomula is: Number times number, if the result is bigger then nine add the first digit with the second digit of the result. If the result is still higher then 9 keep going with adding the digits and you will get a single digit number eventually

O.k. but what are the numbers I have to use.
A: What numbers, can you see?


Which ones to you mean?
A: The row number and the fixed tumbler number

Can you do a more specific example.
A: O.k. here is how you solve the first, left most, digit of the first row of Code 1.
Row number is 1 and tumbler number is also 1. Multiplying gives : 1 x 1 = 1. The result is already a one digit number. So we enter 1.
(Use W and S key or the little arrows over the box)

And the next ones?
A: Row number is still 1, tumbler number is 2, so. 1 x 2 = 2,
1 x 3 = 3 and so forth.

Hurray. I got the first line. But I am struggeling with the next row,
A: You are using 2 as row number, right?

Hell, how did you know?
A: Because it is the wrong number.

But which is the right one?
A: Look at the four different Enigma code puzzles. What does change, what is different?

I am blind. I do not see any difference!
A: The row number changes. Maybe you should try 8 as row number for the second row of the first puzzle.

I still hang, can you show how to calculate any of the codes?
A: See next section of this guide. All codes are solved there.

First row:

1x1=1
1x2=2
1x3=3
1x4=4
1x5=5
1x6=6
1x7=7
1x8=8
1x9=9
Solution: 01 02 03 04 05 06 07 08 09
Second row:

8x1=8
8x2=16, 1+6=7
8x3=24, 2+4=6
8x4=32, 3+2=5
8x5=40, 4+0=4
8x6=48, 4+8=12, 1+2=3
8x7=56, 5+6=11, 1+1=2
8x8=64, 6+4=10, 1+0=1
8x9=72, 7+2=9
Solution: 08 07 06 05 04 03 02 01 09

First row:

2x1=2
2x2=4
2x3=6
2x4=8
2x5=10, 1+0=1
2x6=12, 1+2=3
2x7=14, 1+4=5
2x8=16, 1+6=7
2x9=18, 1+8=9
Solution: 02 04 06 08 01 03 05 07 09

Second row:

7x1=7
7x2=14, 1+4=5
7x3=21, 2+1=3
7x4=28, 2+8=10, 1+0=1
7x5=35, 3+5=8
7x6=42, 4+2=6
7x7=49, 4+9=13, 1+3=4
7x8=56, 5+6=11, 1+1=2
7x9=63, 6+3=9
Solution: 07 05 03 01 08 06 04 02 09

First row:

3x1=3
3x2=6
3x3=9
3x4=12, 1+2=3
3x5=15, 1+5=6
3x6=18, 1+8=9
3x7=21, 2+1=3
3x8=24, 2+4=6
3x9=27, 2+7=9
Solution: 03 06 09 03 06 09 03 06 09

Second row:

6x1=6
6x2=12, 1+2=3
6x3=18, 1+8=9
6x4=24, 2+4=6
6x5=30, 3+0=3
6x6=36, 3+6=9
6x7=42, 4+2=6
6x8=48, 4+8=12, 1+2=3
6x9=54, 5+4=9
Solution: 06 03 09 06 03 09 06 03 09

First row:

4x1=4
4x2=8
4x3=12, 1+2=3
4x4=16, 1+6=7
4x5=20, 2+0=2
4x6=24, 2+4=6
4x7=28, 2+8=10, 1+0=1
4x8=32, 3+2=5
4x9=36, 3+6=9
Solution: 04 08 03 07 02 06 01 05 09

Second row:

5x1=5
5x2=10, 1+0=1
5x3=15, 1+5=6
5x4=20, 2+0=2
5x5=25, 2+5=7
5x6=30, 3+0=3
5x7=35, 3+5=8
5x8=40, 4+0=4
5x9=45, 4+5=9
Solution: 05 01 06 02 07 03 08 04 09

In this last part I will talk about an insteresting mathematical property of the solution.
This is not knowledge that you need to solve the puzzle and you may simply skip this.
But, if you read some of discussions about cracking the Wolfenstein Enigma Code you will see an emerging discussion. One side says you have to multiply, the other says you have to add repeatedly. But who is right and who is wrong?

Let us look into this and settle it once for all:

First a question: What is the difference of 7 + 7 + 7 + 7 + 7 and 5 * 7?
Answer: The first is repeatedly adding, the second is multiplying. At the end both give the same result.

As said in the previos section, the solution of the Enigma puzzle is: Row number times tumbler number, if the result is bigger then nine add the first digit with the second digit of the result. If the result is still higher then 9 keep going with adding the digits and you will get a single digit number eventually.

The part where we add the digits of the result until we get a single digit is known as the
digital root[en.wikipedia.org]. Let us denote the digital root as the function dr( ).

This allows us to write the solution in mathematical form: dr(Row Number x Tumbler number). Or just: dr(R * T).

The digital root has a linear like properties. For example dr(a + b) is equal to dr( dr(a) + dr(b)). The same goes for multiplication thus, dr(a * b) is equal to dr( dr(a) * dr(b)).

When we calculate the code segments from one tumbler to the next we can use this property to save us some multiplications. How, you may ask. Simple, dr(R * T) = dr(R + R * (T-1)) = dr( dr(R) + dr(R *(T-1)), and because R < 10 we can simply write dr(R + dr(R *(T-1)). But dr(R * (T-1)) is the code segment from the previous tumbler. For the first code segement we get the very simple solution R.

In words: The code segment of the first tumbler is R. To caluculate the next code segment take the code segment for the previous tumbler, add R to it. If the result is larger than 9 add the first digit of the result to the second.

Conclussion: Which is the right and correct way to calculate the codes? Both.
But, the second way only works because the tumblers are numbered 1, 2, 3, 4 etc. if they were scrambled like 4, 2, 7, 1, 8, 5, 3, 6 it would not work.