How did they get over the catch-22 that if they used the information that Nazis could guess it came from breaking the code but if they didn’t use the information there was no point in having it.
EDIT. I tagged this as mathematics because the movie suggests the use of mathematics, but does not explain how you use mathematics to do it (it’s a movie!). I am wondering for example if they made a slight tweak to random search patterns so that they still looked random but “coincidentally” found what we already knew was there. It would be extremely hard to detect the difference between a genuinely random pattern and then almost genuinely random pattern.
In: Mathematics
Adding to what others have said, the actual investigative abilities of the germans was pretty poor. The Gestapo while very feared, were essentially beaurocrats filtering through denunciations and heavily reliant on people denouncing each other.
The actual German military intelligence, the Abwher, was run by Admiral Canaris, who very much hated the Nazis and may or may not have been a British spy.
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