712,882,560

That’s the number of possible code settings in the Wehrmacht version of Enigma that really mattered.

And the code settings were set for each date like this:

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Rotor order: There were five rotors available, and three of them could be used in the Wehrmacht Enigma, in any order. This gives us 5x4x3=60 combinations.

Ring setting: You could rotate the rings of a rotor to an offset which would affect the turnover of the previous rotor, but the leftmost offset didn’t affect the other two. So here you get 26×26=676 combinations.

Daily setting: The rotors were then set to a daily three-letter code. There were 26x26x26=17576 combinations here.

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Plugboard settings: You could swap two letters using a cable on a plugboard that connected two letters into a pair. There were ten such cables, and they gave 150,000,000,000,000 combinations.

And if you multiply them together, you get more than ten to the power of 23 (100,000,000,000,000,000,000,000, or a hundred billion billion) combinations.

The Germans assumed that their enemies had stolen Enigma machines, picked them apart, and figured out how they work and how the wiring was done. So the machines themselves were not that secret, but the daily code settings were.

However, the plugboard settings were not that important. You could use the (known) rotor wiring (not the rotor setting, but the wiring) and the weakness that Enigma could not encode a letter to itself, to deduce most of the plugboard settings. The few remaining plugboard settings could often be deduced using knowledge of German of the partially decoded messages.

So it’s just almost 713 million (60x17576x676=712,882,560) Enigma settings that actually matter.

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