The Palermo Stone is fifth dynasty and records events, etc back to the unification. See: [touregypt.net] It has quantitative records of the inundation going back something like 500 or 600 years. They had an infrastructure in place that could have recorded virtually anything they wanted.

It's a bit like 1421 - the Chinese could have done everything Menzies suggests. The guys who designed and built the Gizamids were part of a sequence of architectural development going back centuries and the Palermo Stone tells us that there must have been some sort of "archive" holding records going back centuries (we know that papyrus was around in the 1st dynasty).

But there's nothing to suggest that they got anything better than 365 days.

John