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Diversion 1: combinatorics

The mathematics behind the Enigma Machine - how many ways could they encode messages?

 
158,962,555,217,826,360,000 (Enigma Machine) - Numberphile

 
 
  ... and what was the flaw that allowed Alan Turing to break the code:

 
Flaw in the Enigma Code - Numberphile

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