The quantum speed up as advanced knowledge of the solution

With reference to a search in a database of size N , Grover states: ”What is the reason that one would expect that a quantum mechanical scheme could accomplish the search in O “√ N ” steps? It would be insightful to have a simple two line argument for this without having to describe the details of the search algorithm”. The answer provided in this work is: ”because any quantum algorithm takes the time taken by a classical algorithm that knows in advance 50% of the information that specifies the solution of the problem”. In database search, knowing in advance 50% of the n bits that specify the database location, brings the search from O (2 = N) to O “