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
Partly by coming up with reasonable explanations for how they were finding things out. For example, when attacking axis vessels at sea they might send out a plane to “discover” the vessels’ location. The axis vessels would report they had been spotted by a plane, then attacked. The axis also mistakenly attributed at least some of the allied success at U-boat hunting to HFDF (high frequency direction finding), i.e. listening for U-boat radio transmissions to pinpoint their location.
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