• Rav Zev Jacobson
DAF 6a
            The beraita [lines 15-20] discusses three different cases where a Jew comes into contact with the chametz of a nokhri (non-Jew) on Pesach:
1.  The nokhri walks into the courtyard of the Jew holding chametz.  There is no transgression of bal yera'eh and, therefore, no need for the Jew to dispose of the chametz.
2.  The nokhri deposits his chametz in the trusteeship of the Jew.  This chametz must be disposed of.
3.  The nokhri leaves his chametz in a designated corner in the house of the Jew.  There is no need to dispose of the chametz.
            The beraita explains its rationale based on the pasuk of "lo yimatzeh."  According to R. Pappa, this refers to case #2 and thus stresses -"chametz should not be found AT ALL in your houses."  According to R. Ashi this refers to case #3 rendering: "Chametz should not be found at all IN YOUR HOUSES" [as opposed to a corner set aside for the use of the nokhri].
ANALYSIS of the sugya:
            There are a number of inter-related points that require elucidation:
A.  Wherein lies the difference between case #2 and the other cases?
B.  What is the basis of the argument between R. Pappa and R. Ashi?
C.  Is it not possible that the pasuk explains both case #2 AND case #3?
D. Why is there no opinion that the pasuk explains case #1?
A.  According to the gemara on daf 5b, a Jew is not commanded to dispose of a nokhri's chametz if he did not accept responsibility over it.  Therefore, it seems clear that the beraita, which requires disposal of the chametz, is dealing  with a scenario where the Jew accepted responsibility over the chametz.  [It is unlikely that the beraita contradicts the conclusion of the gemara on 5b].
            Thus, it is this acceptance of responsibility that differentiates case #2 from cases #1 and #3.  A relationship is established between the Jew and the chametz making it imperative for him to dispose of it.  [See this week's Pesachim shiur for a full discussion on the exact nature of the relationship.]  Note: This is according to the opinion of Rashi, the majority of Rishonim explain that case #3 is also dealing with a scenario where the Jew accepted responsibility over the nokhri's chametz.
B & C.  There are two distinct ways of understanding the prohibition of "lo yimatzeh":
1.  It is forbidden to OWN chametz on Pesach.
2.  It is forbidden to POSSESS chametz on Pesach.
            The first option implies a much stronger connection between the Jew and the chametz than the second option.  One may be defined as POSSESSING chametz even if he does not OWN it.
I.  Rav Pappa
            It is possible that according to R. Pappa, "lo yimatzeh" necessitates OWNERSHIP.  However, there are different levels of ownership and it is sufficient for the Jew to accept full responsibility over the chametz (kabalat achrayut) for "lo yimatzeh" to apply.  Nevertheless, this is not a foregone conclusion.  Therefore, it is imperative for the beraita to state that the prohibition is indeed learnt from the Torah.  Thus, "lo yimatzeh" is quoted in connection with case #2.
            However, in case #3, the Jew has no connection with the nokhri's chametz - it is simply placed in a corner of his house.  There is no room whatsoever to claim that he OWNS the chametz.  Therefore, it is obvious that "lo yimatzeh" does not apply and the beraita has no need to support this exclusion by quoting the pasuk.  Thus, "lo yimatzeh" is not stated with regard to case #3.
II.  Rav Ashi
            It is possible that according to R. Ashi, "lo yimatzeh" only necessitates POSSESSION.  Once the Jew accepts full responsibility over the chametz, it is clear that he POSSESSES the chametz and that the prohibition applies.  Thus, it is unnecessary for the beraita to mention "lo yimatzeh" with regard to case #2.
            However, in case #3 it could be argued that the nokhri's chametz IS in the POSSESSION of the Jew.  After all, it is in his house.  Therefore, it is imperative for the beraita to negate such a conclusion by quoting the pasuk of "lo yimatzeh" - only chametz which is under your control is considered to be in you POSSESSION and is thus, forbidden.  Although the nokhri's chametz is in the domain of the Jew, this criterion is not fulfilled.  Thus, "lo yimatzeh" is mentioned specifically with  regards to case #3.
D.  In case #1 the Jew has no connection whatsoever with the chametz and it is unnecessary, according to both R. Pappa and R. Ashi, to utilize the pasuk of "lo yimatzeh."