Before we do a sectional analysis, it is a good idea to show why we are clustering a whole chapter of Matthew with such small sections of Mark and Luke. This is a chapter that tries QM theorists' souls:

Matthew 18:1 At the same time came the disciples unto Jesus, saying, Who is the greatest in the kingdom of heaven? 2 And Jesus called a little child unto him, and set him in the midst of them, 3 And said, Verily I say unto you, Except ye be converted, and become as little children, ye shall not enter into the kingdom of heaven. 4 Whosoever therefore shall humble himself as this little child, the same is greatest in the kingdom of heaven. 5 And whoso shall receive one such little child in my name receiveth me. [parallels: Mark 9:33-37, Luke 9:46-48]

6 But whoso shall offend one of these little ones which believe in me, it were better for him that a millstone were hanged about his neck, and that he were drowned in the depth of the sea. [Mark 9:42, Luke 17:2]

7 Woe unto the world because of offences! for it must needs be that offences come; but woe to that man by whom the offence cometh! [Luke 17:1]

8 Wherefore if thy hand or thy foot offend thee, cut them off, and cast them from thee: it is better for thee to enter into life halt or maimed, rather than having two hands or two feet to be cast into everlasting fire. 9 And if thine eye offend thee, pluck it out, and cast it from thee: it is better for thee to enter into life with one eye, rather than having two eyes to be cast into hell fire. [Mark 9:43-48]

10 Take heed that ye despise not one of these little ones; for I say unto you, That in heaven their angels do always behold the face of my Father which is in heaven. 11 For the Son of man is come to save that which was lost. 12 How think ye? if a man have an hundred sheep, and one of them be gone astray, doth he not leave the ninety and nine, and goeth into the mountains, and seeketh that which is gone astray? 13 And if so be that he find it, verily I say unto you, he rejoiceth more of that sheep, than of the ninety and nine which went not astray. [Luke 15:3-7]

16 But if he will not hear thee, then take with thee one or two more, that in the mouth of two or three witnesses every word may be established. 17 And if he shall neglect to hear them, tell it unto the church: but if he neglect to hear the church, let him be unto thee as a heathen man and a publican. 18 Verily I say unto you, Whatsoever ye shall bind on earth shall be bound in heaven: and whatsoever ye shall loose on earth shall be loosed in heaven. 19 Again I say unto you, That if two of you shall agree on earth as touching any thing that they shall ask, it shall be done for them of my Father which is in heaven. 20 For where two or three are gathered together in my name, there am I in the midst of them. [no paralells]

21 Then came Peter to him, and said, Lord, how oft shall my brother sin against me, and I forgive him? till seven times? 22 Jesus saith unto him, I say not unto thee, Until seven times: but, Until seventy times seven. [Luke 17:3-4]

23 Therefore is the kingdom of heaven likened unto a certain king, which would take account of his servants. 24 And when he had begun to reckon, one was brought unto him, which owed him ten thousand talents...35 So likewise shall my heavenly Father do also unto you, if ye from your hearts forgive not every one his brother their trespasses. [no parallels]

The variations here in order have led some theorists to say that Q was not the common source, or that there were two editions of Q....whatever is needed to keep the theory going! Is there any way through this thicket? There is, but it requires wearing a thinking cap and abandoning presuppositions about Q and Marcan priority -- the very thing the theorists are loathe to do.

Let's start with a framework. Prior to this, Matthew has his unique story of the coin in the fish's mouth (17:24-27). Prior to this, Matthew has a story of Jesus predicting his death. Mark has this same story before 9:33, as does Luke before 9:46. Thereafter, the evangelists diverge wildly and, other than the parallel at Matthew 18:8-9, do not join again until the divorce issue in Matthew 19/Mark 10, and then Luke rejoins in the pericope following. How is this to be explained with a Q document? It can't be, which is why we have insane ideas of a second Q and more mystery documents. Let's try something simpler, shall we?

Sectional Analysis

As usual, we find Mark including details notable only from a Petrine memory (embracing the child, going in "the house") and each author introducing the pericope differently. We also see that the "lesser-greater" point is made by Mark and Luke, and that Luke makes it in a different order than Mark, while Matthew has reworded it to make it more intelligible within the pericope. Why? The most probable reason is that Luke's main source is Ur-Matthew, and that Greek Matthew has moved this teaching elsewhere (19:30/20:16) as part of his topical restructuring. Thus an Ur-Matthew reconstruction:

Came-in a reasoning among them (the) who might be greater of-them. (the) And Jesus having-seen the reasoning of-the heart of-them having-laid-hold-of child stood it beside himself and said to-them who ever receives this (the) child on the name of me, me receives. And who ever me receives receives the (one) having sent me. the For lesser among all you being this-one will-be great

And now we must switch gears, for here, Matthew drops out of the picture a bit, and Mark and Luke coordinate -- partially, in a way that gives Marcan prioritists fits!

Matthew's only resemblance here is in 12:30, the "for or against" statement (see here on the difference, where he has transported it to a place it is not found in Mark or Luke -- more of Matthew's topical shifting. But note here that Luke lacks the "cup of cold water" phrase, which is one of Mark's few unparalleled teachings. Why? Likely because this is a Petrine reminisce -- and Ur-Matthew read only:

answering And the John said Master we-saw someone on the Name of you casting out the demons and stopped him because not he-follows with us. And said to them the Jesus Not do-stop, whoever for not is against us for us is.

Matthew removed this story of the man casting out demons in Jesus' name; why? It can only be guessed, but perhaps by the time Matthew wrote his Greek edition, so many pagans were using Jesus' name in exorcisms illicitly (rather than being "friendly" or neutral as this man seems to have been) that the lesson became anachronistic. The inclusion of this in Mark and Luke is a pointer towards their earlier date and agrees with Greek Matthew being written after them (but not Ur-Matthew).

Hawkins [Hawk.HS, 124] also offers the "boy these people were dumb" argument that Matt eliminated this section because he thought the words about no man doing a mighty work would be seen as contradictory to Matt. 7:22-3 ("Many will say to me in that day, Lord, Lord, have we not prophesied in thy name? and in thy name have cast out devils? and in thy name done many wonderful works? And then will I profess unto them, I never knew you: depart from me, ye that work iniquity."). How so? None of Matt's subjects speak evil of Jesus at all! This is an over-creative reading by Hawkins.

What a dilemma for Marcan prioritists! Luke completely displaces this saying; it is in his 17:2, miles away from the circumstances of Matt and Mark and in the middle of a block of teaching featured by Luke. The solution? We get some hints: 1) Only Luke and Matt refer to the millstone as that of an ass. 2) Luke refers to "little ones: even though no children are in sight; 3) Matthew's NEXT verse, 18:7 ("Woe unto the world because of offences! for it must needs be that offences come; but woe to that man by whom the offence cometh!") is ALSO miles away from its context in Luke, but is found there is 17:1, in reverse order. What this tells us is that Luke is doing for a change what Matthew is doing as a whole: moving teachings into a topical framework. The reversal of the teachings matches the sort of reversal also done later by apocryphal Gospels. Thus Matthew 18:6-7 were taken by Luke from Ur-Matthew and placed instead, in reverse order, in a topical place in his Gospel. Thus Ur-Matthew would have said:

who But ever offends one of little(ones) these (the) believing into me it-is-gain for-him that be-hung millstone of-an-ass on the neck of-him and he-be-sunk in the depth of the sea. Woe to-the world from the offenses; necessity for it-is to-come the offenses, yet woe the man that through whom the offense comes!

It is our conclusion that we continue to see here the progression of Ur-Matthew. Why is this not in Luke? Probably because he already offered an illustration of this in the story of Lazarus and the rich man. Meanwhile he also does more topical shifting, moving the salt saying to Luke 14:34 and adding an extra comment in 14:35 that was either in Ur-Matthew or else taken from further research (as indicated by the non-Markan parallel; the last statement in Mark, being more likely then a Petrine reminisce). Note that the differences between Mark and Matt here are an ideal reflection of oral tradition variations. It is likely that the separate treatment of hands and feet is original and that Matt has compressed these for space. Thus our reconstruction:

And if offend you the hand of-you cut-off it good for-you is-it maimed into the life to-enter than the two hands having to-go-away-into the gehenna into the fire unquenchable where the worm of them not has-an-end and the fire not is-quenched. And if the foot of-you causes-to-offend you, cut-off it good for-you is-it to-enter into the life lame than the two feet having to-be-thrown-into the gehenna into the fire unquenchable where the worm of them not has-an-end and the fire not is-quenched. And if the eye of-you causes-to-offend you, cast-out it good for-you is-it one-eyed to-enter into the kingdom the of-God than two eyes having to-be-thrown into the gehenna of fire where the worm of them not has-an-end and the fire not is-quenched. everyone For with fire will-be-salted and every sacrifice with salt will-be-salted. Good is salt if but the salt saltless becomes by what it will you season?

At this point Mark is no longer with us. The following between Matthew and Luke indicate common Ur-Matthew comments; that solely in Matthew is either Ur-Matthew material passed over by Luke, or new Matthean material. We will assume the latter. Matthew 18:10 finds no parallel anywhere. Matthew 18:11-14 is paralleled in Luke 15:3-7. There is no need for a full analysis; it is made very likely that Luke has displaced this from his Ur-Matthew source, for 1) he has already done this just prior; 2) he dos not have the contextual closing statement of Matthew 18:14 about "little ones" perishing; 3) he pairs it with a parables of similar nature (the lost coin and the prodigal son) that are not paralleled elsewhere.

Matthew 18:15-20 has no parallels. Then we have Matthew 18:21-22, Peter's question about forgiveness. This one is way out of the way in Luke 17:3-4. Once again it is likely Luke has made a move here on his own, since he already has moved 17:1 and 2 from this same part of Matthew. Matthean originality is evident here; it is more likely that Luke has depersonalized the teaching (in light of his "universality" theme) than that Matthew has personalized it. Finally Matthew 18:23-35 has no parallels.