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Yes now with help I found flaw in my calculations. The answer is Jule 16. Bernard has to pairs on months with similar numbers:
  1. May July
  2. July August
When Bernard got information from Albert that he 100% should know the answer we take pair with unique number (May July), and it can't be May. So the answer is July 16
That's what I was leaning towards, but I still don't totally see it. More coffee.
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At some point there's an option with 15 may or 15 august, but as Bernard final statement "I didn't know but now know", he shoude choose from month with to numbers this month is July.
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