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Nearly every conceivable theory has been advanced as a solution to the synoptic problem.[1] The most notable theories are listed here:

Notable synoptic theories
Priority Theory[2] Diagram Notes
Marcan
priority
Two‑source
(Mark‑Q)
Most widely accepted theory. Matthew and Luke have independently used Q, taken to be a Greek document with sayings and narrative.
Farrer
(Mark-Matthew)
Double tradition explained entirely by Luke's use of Matthew.
Three‑source
(Mark‑Q/Matthew)
A hybrid of Two-source and Farrer. Q may be limited to sayings, may be in Aramaic, may be also a source for Mark.
Q+/Papias Hypothesis
(Mark‑Q/Matthew)
Each document drew from each of its predecessors, including Logoi (Q+) and Papias' Exposition.
Wilke
(Mark-Luke)
Double tradition explained entirely by Matthew's use of Luke.
Matthaean
priority
Two‑gospel
(Griesbach)
(Matthew‑Luke)
Mark primarily has collected what Matthew and Luke share in common (Marcan posteriority).
Augustinian
(Matthew‑Mark)
The oldest known view, still advocated by some. Mark's special place is neither priority nor posteriority, but as the intermediate between the other two gospels. Canonical order is based on this view having been assumed (at the time when New Testament Canon was finalized).
Lucan
priority
Jerusalem school
(Luke‑Q)
فائل:Synoptic Theory JSH ur.svg A Greek anthology (A), translated literally from a Hebrew original, was used by each gospel. Luke also drew from an earlier lost gospel, a reconstruction (R) of the life of Jesus reconciling the anthology with yet another narrative work. Matthew has not used Luke directly.
None Multi‑source Each gospel drew from a different combination of hypothetical earlier documents.
Proto‑gospel The gospels each independently derive from a common proto-gospel (Ur-Gospel), possibly in Hebrew or Aramaic.
Independence Each gospel is an independent and original composition based upon oral history.
  1. Carlson (September 2004)۔ "Synoptic Problem"۔ Hypotyposeis.org  Carlson lists over twenty of the major ones, with citations of the literature.
  2. Though eponymous and some haphazard structural names are prevalent in the literature, a systematic structural nomenclature is advocated by Carlson and Smith, and these names are also provided.