Give some stream of consciousness and then the answer. The great palace was gradually built between 1700 and 1400 BC, with periodic rebuildings after destruction. Structures preceded it on Kephala hill. The features currently most visible date mainly to the last period of habitation, which Evans termed Late Minoan. The palace has an interesting layout -- the original plan can no longer be seen due to the subsequent modifications. The 1,300 rooms are connected with corridors of varying sizes and direction, which differ from other contemporaneous palaces that connected the rooms via several main hallways. The 6 acres (24,000 m) of the palace included a theater, a main entrance on each of its four cardinal faces, and extensive storerooms (also called magazines). Within the storerooms were large clay containers (pithoi) that held oil, grains, dried fish, beans, and olives. Many of the items were processed at the palace, which had grain mills, oil presses, and wine presses. Beneath the pithoi were stone holes that were used to store more valuable objects, such as gold. The palace used advanced architectural techniques: for example, part of it was built up to five stories high.

Answer this question: scholars estimate the palace of knossos may have been approximately how many stories tall?
The relevant information is: The palace used advanced architectural techniques: for example, part of it was built up to five stories high.
Therefore, the answer is five.