  Using computer calculations and working with representatives of pretzel
tangles we established general adequacy criteria for different classes of knots
and links. Based on adequate graphs obtained from all Kauffman states of an
alternating link we defined a new numerical invariant: adequacy number, and
computed adequacy polynomial which is the invariant of alternating link
families. Adequacy polynomial distinguishes (up to mutation) all families of
alternating knots and links whose generating link has at most $n=12$ crossings.
