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1)

(a) If a mouse took Chametz from a pile of Chametz and scampered off with it into one of two rooms that had already been searched for Chametz , but we don't know which - Rebbi Yehudah says that, as long as they both come to ask separately, they are both declared Tahor (because of the principle 'Safek Tum'ah bi'Reshus ha'Rabim, Tahor').

(b) Rava (or Rebbi Yochanan) says that if the two owners came to ask simultaneously, then even Rebbi Yehudah will agree that they will both be Tamei; if they came independently, then even Rebbi Yossi will agree that they are both Tahor - when do they argue, only when one of the two comes to ask on behalf of both himself and his friend: Rebbi Yossi compares it to when they ask simultaneously, Rebbi Yehudah to when they ask independently (because it is possible to answer him that he is Tahor, without actually saying that his friend is Tahor, too.

(c) If in winter, someone enters a valley where there is a corpse in one of the fields, but he does not know which field he entered, according to Rebbi Eliezer, he remains Tahor - because it is a double Safek (a S'fek Sefeika) maybe he did not enter the field, and, even if he did, maybe he did not touch or walk over, the corpse.

(d) The rule that he is Tamei - because it is a case of Safek Tum'ah bi'Reshus ha'Yachid (seeing as we are speaking in the winter, when the seeds have already begun to grow, and one does not have permission to enter the field. Nevertheless, in our case, they agree that the room does not require a second Bedikah, because Bedikas Chametz (once one has made Bitul Chametz) is only mi'de'Rabbanan, whereas in the case of the two paths, we are speaking about Tum'ah d'Oraysa.

(a) In a field containing one pile which is Tamei, and two which are Tahor (or vice-versa), if all three are searched, but no Tum'ah is found - according to the Chachamim, all three piles are now Tahor (since we assume that the Tum'ah was somehow removed).

(b) According to Rebbi Meir, all three piles are Tamei. Why? Because anything that has a Chezkas Tum'ah remains Tamei until the Tum'ah is discovered.

(c) If a mouse carries Chametz into a room, and the owner searched but found nothing, then even Rebbi Meir will agree that it is not necessary to search again, since Bedikas Chametz is only mi'de'Rabbanan (see Tosfos, DH 'Al', in whose opinion Bitul Chametz is nevertheless required).

(a) According to Raban Shimon ben Gamliel, even if one searched and found a piece of Chametz, we do not assume that that is the piece brought in by the mouse; Consequently, he is obligated to search the entire room.

(b) They argue in a case where they searched a field for a grave which they knew to be there, and in the course of the search, they did indeed find a grave. According to Rebbi, we assume the grave that they found to be the one that was lost, and it is not necessary to continue with the search; whereas according to Raban Shimon ben Gamliel, they are obligated to search the entire field, irrespective of what they find.

(c) Rebbi Says that if someone left *one* Manah of Ma'aser Sheni money, and when he returned, he found *two* - we assume the Manah to be the one that he placed, and someone added a second Manah to the original one (so both are Safek Ma'aser Sheni).

(d) According to the Chachamim - since he left one Manah and found two, we presume that this is not the same money that he left, but that it is all Chulin money. Similarly in our case, since the mouse carried *nine* pieces of Chametz into the room and he found *ten*, we will not assume them to be the same pieces that the mouse carried into the room, and he will be obligated to continue searching until he finds just *nine* pieces. Note: This Sugya speaks when both the money and the pieces of Chametz are tied together (see Tosfos DH 'Hini'ach' and Maharsha).

5)

(a) If someone leaves an ax in a specific spot in a room, and then finds it elsewhere, the Chachamim rule that everything in the room is Tamei - because someone must have entered the room and moved the ax. In the process, he is likely to have touched any of the objects in the room (and as far as a Chaver is concerned, unspecified people are assumed to be Tamei).

(b) Raban Shimon ben Gamliel says that everything in the room retains is Chezkas Taharah, because he probably lent the ax to someone or even moved it himself, and forgot about it.

(c) According to the Rabbanan, if someone leaves Chametz in one corner of a room that has already been searched, and finds it in another, he will be obligated to search for Chametz; according to Raban Shimon ben Gamliel, he will be Patur.

(a) It is not common for mice to leave crumbs. Consequently, if someone follows a mouse that carried Chametz into a room and finds crumbs on the floor, the owner will be obligated to search the room again - he must assume that the Chametz that was found is not the same Chametz that the mouse carried in.

(b) Children eating bread *do* tend to leave crumbs. Consequently, if he followe a child into a room and discovered crumbs, he should just collect them, but does not need to search the room again.

(a) If one sees a white mouse enter a room with a piece of Chametz in its mouth and a black mouse leaving it, also with a piece of Chametz in *its* mouth, the Gemara considers the possibility that the second mouse grabbed the Chametz from the first one, in which case, the owner will be exempt from a second Bedikah.

(b) The counter-argument is that mice do not grab from each other (honor among thieves), in which case, this is a second pipece of Chametz, and he will remain obligated to make Bedikas Chametz again.

(a) If we saw a mouse enter the room with Chametz in its mouth, and a weasel come out with Chametz in *its* mouth, we will not necessarily assume that the weasel took the Chametz from the mouse - because then it would have been more likely for the weasel to have been holding the mouse (which was in turn, still holding the Chametz) in its mouth. Consequently, it is more logical to assume that this is not the same piece of Chametz.

(b) We even have doubts - if the weasel comes out holding the mouse and the Chametz in its mouth, but separately. Do we now say that this is most certainly not the same mouse and Chametz as the one that entered, because, if it had been, why was the Chametz not still in the mouse's mouth? Or perhaps, when the mouse saw the weasel, it got a shock and dropped the Chametz, and the weasel then picked up first the one and then the other.

(a) If there is Chametz on a high beam, the Gemara asks whether one is obligated to find a ladder to fetch it in order to burn it (due to the possibility of the Chametz falling down on Pesach, in which case he may come to eat it), or whether (seeing as he will anyway make Bitul Chametz, and the Chametz is currently out of harm's way) the Chachamim did not obligate him to go to such lengths).

(b) If the Chametz is in a deep pit, and is therefore not subject to falling, the Chachamim may still have obligated him to climb down and destroy the Chametz - because he may possibly descend into the pit on Pesach, to do something there, find the Chametz there and eat it.

(a) The three time periods for Bedikas Chametz, according to Rebbi Yehudah are the eve of the fourteenth, the morning of the fourteenth and the sixth hour.

(b) The Rabbanan add from the sixth hour until night-fall (see Tosfos DH 've'Im' who interpret 'be'Soch ha'Mo'ed' to mean during Yom-Tov, and 'le'Achar ha'Mo'ed', even after Yom-Tov.

(c) The Chametz that remains after the Bedikah on the eve of the fourteenth should be placed out of reach of children and mice, who may otherwise take some of it, thereby creating problems.

(a) From Rebbi Yehudah's statement in a Beraisa 'Kol she'Lo Badak bi'Sheloshah Perakim Halalu, Shuv Eino Bodek' it is clear that the dispute between him and the Rabbanan concerns whether or not to search for Chametz *after* the three times specified by Rebbi Yehudah (and not the three periods themselves).

(b) Rebbi Yehudah forbids searching after the time of Bi'ur, for fear that he may come to eat any Chametz that he finds; whereas the Rabbanan maintain that, since he is busy searching for Chametz to *destroy it*, he is most unlikely to then go and *eat it*.