Design patterns are essential building blocks of computer programs. In the design of programs, patterns are selected and composed together. Pattern compositions may be of various kinds, among them: concatenation, inclusion (of one pattern in another), and interleaving (of two or more patterns). Pattern interleaving is the subtler composition. Yet, it is already required in early programming (e.g., the number of appearances of the max in a list, which requires the interleaving of counting and max computation). In this paper, we illuminate novices´ struggle with interleaved compositions. We present an empirical study of high-school CS students, which reveals several kinds of novice difficulties, including: "bypassing" of interleaved composition by concatenation, improper application of patterns, and design of malformed interleaved structures. We offer some didactic suggestions to teachers for coping with these difficulties.