  This work considers a generalization of Grover's search problem, viz., to
find any one element in a set of acceptable choices which constitute a fraction
f of the total number of choices in an unsorted data base. An infinite family
of sure-success quantum algorithms are introduced here to solve this problem,
each member for a different range of f. The nth member of this family involves
n queries of the data base, and so the lowest few members of this family should
be very convenient algorithms within their ranges of validity. The even member
{A}_{2n} of the family covers ever larger range of f for larger n, which is
expected to become the full range 0 <= f <= 1 in the limit n -->infinity.
