The northern border of the Old Kingdom of Egypt was not clearly defined, as it was constantly in flux due to political and military factors.

However, we can say that during the Old Kingdom, the northern border generally extended to the Mediterranean Sea.

Here's a breakdown:

* The Delta: The northernmost regions of Egypt, known as the Delta, were under the control of the Old Kingdom. This area was vital for agriculture and trade.

* The Levant: While the Old Kingdom may have exerted some influence in the Levant, it was not considered part of the formal borders.

* The Sinai Peninsula: This peninsula was strategically important for access to trade routes and resources, and the Old Kingdom likely held control over parts of it.

Important to note: Defining a precise northern border for the Old Kingdom is challenging, as it changed over time and differed depending on the specific pharaoh's rule.