Department of Mathematics2024-11-0920050315-3681N/A2-s2.0-31144433384N/Ahttps://hdl.handle.net/20.500.14288/14763Let (X, B) be a λ-fold block design with block size four and define sets B(K) and E(K4\ K) as follows: for each block b ε B, remove a path of length two, obtain a kite (a triangle with a tail), and place the kites in B(K) and the paths of length 2 in E(K4\ K). If we can reassemble the edges belonging to E(K4\ K) into a collection of kites E(K) with leave L, then (X, B(K) ∪ E(K), L) is a packing of λK n with kites. If |L| is as small as possible, then (X, B(K) ∪ E(K), L) is called a metamorphosis of the λ-fold block design (X, B) into a maximum packing of λKn with kites. In this paper we give a complete solution of the metamorphosis problem for λ-fold block designs with block size four into a maximum packing of λKn with kites for all λ. That is, for each λ we determine the set of all n such that there exists a λ-fold block design of order n having a metamorphosis into a maximum packing of λKn with kites.MathematicsJournal Articlehttps://www.scopus.com/inward/record.uri?eid=2-s2.0-31144433384&partnerID=40&md5=c6585052b02f6b93e3353084d1ffc07f234383000015Q45029