On the application of phase relationships to complex structures. XVII. When MULTAN fails

Two new multisolution direct-methods procedures are described: /b MAGIC/, which employs the magic-integer concept and /b YZARC/ which refines initially random sets of phases by a least-squares approach. Each procedure produces several sets of phases for a number of reflexions, usually in the range 35-100. These are then extended by the tangent formula but with the constraint that the basis phases are not allowed to change until the final cycle. It is shown that for difficult structures these methods, which deal simultaneously with many phase relationships, may have intrinsic advantages over the /b MULTAN/ procedure. Examples of their use are given.