The three-source hypothesis is a candidate solution to the synoptic problem. It combines aspects of the two-source hypothesis and the Farrer hypothesis. It states that the Gospel of Matthew and the Gospel of Luke used the Gospel of Mark and a sayings collection as primary sources, but that the Gospel of Luke also used Gospel of Matthew as a subsidiary source. The hypothesis is named after the three documents it posits as sources, namely the sayings collection, the Gospel of Mark, and the Gospel of Matthew.
The sayings collection may be identified with Q, or some (typically narrative-related) material normally assigned to Q may instead be attributed to Luke's use of Matthew.
This theory has been advocated by Heinrich Julius Holtzmann,  Eduard Simons,  Hans Hinrich Wendt,  Edward Y. Hincks,  Robert Morgenthaler,  and Robert H. Gundry.  It has also been invoked as a viable fall-back position by several contemporary scholars trying to defend the two-source hypothesis against criticism of its handling of the "minor agreements" of Matthew and Luke against Mark.
- H. J. Holtzmann, Zur synoptischen Frage, pp. 553–54 in "Jahrbücher für protestantische Theologie" 4 (1878)
- E. Simons, Hat der dritte Evangelist den kanonischen Matthäus benutzt? (Bonn: Carl Georgi 1880)
- H. H. Wendt, Die Lehre Jesu (Göttingen: Vandenhoeck & Ruprecht 1886)
- E. Y. Hincks, The Probable Use of the First Gospel by Luke, JBL Vol. 10 No. 2 (1891), pp. 92–106
- R. Morgenthaler, Statistische Synopse (Zürich: Gotthelf 1971)
- R.H.Gundry, Matthew, A Commentary on His Literary and Theological Art (Michigan: Eerdmans 1982)
- Mark Goodacre, The Case Against Q (Harrisburg, PA: Trinity Press International, 2002, p. 165)