The Egyptians begrudgingly accepted the Ptolemies as the successors to the pharaohs of independent Egypt, though the kingdom went through several native revolts. The Ptolemies took on the traditions of the Egyptian Pharaohs, such as marrying their siblings (Ptolemy II was the first to adopt this custom), having themselves portrayed on public monuments in Egyptian style and dress, and participating in Egyptian religious life. The Ptolemaic ruler cult portrayed the Ptolemies as gods, and temples to the Ptolemies were erected throughout the kingdom. Ptolemy I even created a new god, Serapis, who was combination of two Egyptian gods: Apis and Osiris, with attributes of Greek gods. Ptolemaic administration was, like the Ancient Egyptian bureaucracy, highly centralized and focused on squeezing as much revenue out of the population as possible though tariffs, excise duties, fines, taxes and so forth. A whole class of petty officials, tax farmers, clerks and overseers made this possible. The Egyptian countryside was directly administered by this royal bureaucracy. External possessions such as Cyprus and Cyrene were run by strategoi, military commanders appointed by the crown.
Is there an answer to this question (If it cannot be answered, say "unanswerable"): Whose tradition did Ptolemy take on as leader of Egypt?
Egyptian Pharaohs