**How many different combinations can the German Enigma machine be set to?**

The Enigma machine, a cipher device used by Nazi Germany during World War II, was renowned for its complexity and the secrecy it provided. This electro-mechanical rotor machine was employed to encrypt and decrypt secret messages, making it a critical tool in the German military’s communication network. The Enigma machine’s intricate design and constant changes in encryption made it extremely challenging to break, contributing to the Germans’ belief that it was an unbreakable code.

The Enigma machine’s encryption process was based on a series of rotors and a plugboard, which provided multiple layers of scrambling. Each rotor had 26 starting positions, corresponding to the letters of the alphabet. When a letter was pressed, an electrical circuit was completed through the rotors and plugboard, changing the input letter to a different output letter. After each key press, the rotors would move, altering the circuit and ensuring that the same letter would never encrypt to the same letter consecutively. This continuous alteration of the electrical pathways is what made the Enigma’s encryption so formidable.

The total number of possible combinations the Enigma machine could be set to is astoundingly large. To determine the number of combinations, several factors must be considered. Firstly, the machine used three rotors selected from a set of five, which could be arranged in 60 different ways (5 x 4 x 3). Each rotor had 26 possible starting positions, resulting in 17,576 (26 x 26 x 26) combinations for the rotors alone. Additionally, the plugboard added another layer of complexity by allowing pairs of letters to be swapped. With 10 pairs of 26 letters, the plugboard settings added approximately 150 trillion combinations.

**When all these factors are multiplied together, the total number of possible settings for the Enigma machine is around 158 quintillion (158,962,555,217,826,360,000)**. This astronomical number underscores the machine’s complexity and the monumental challenge faced by Allied cryptanalysts in their efforts to break the Enigma code. The successful decryption of Enigma messages by the Allies, particularly through the efforts of Polish cryptographers and British codebreakers at Bletchley Park, is often credited with significantly shortening the war and saving countless lives.