There are several open questions in Grover's paper. Foremost among
these is how many times exactly should we iterate step 2 of Grover's
algorithm. Grover proves the existence of some
m 
O(
),
such that after m iterations of step 2 of the algorithm the
probability of finding the register in the marked state is greater
than 1/2. Since the amplitude of the desired state, and hence the
of probability of measuring the desired state, is not monotonic
increasing after m iterations, it is not enough to know know the
existence of m, it's value must be determined.