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One who forgot to check for Chametz on the night of the 14th:
Remembered on Erev Pesach, or on Yom Tov/Chol Hamoed: One who transgressed, or forgot, and did not check his home, or a certain area of his home, for Chametz on the night of the 14th, then he is obligated to check it for Chametz on the day of the 14th, or as soon as he remembers anytime during Pesach, whether day or night. This obligation applies even on Yom Tov and even on the last day of Pesach in the Diaspora; he must search for the Chametz on Yom Tov as soon as he remembers [although any found Chametz is simply to be covered until after Yom Tov, as will be explained]. However, on Shabbos one does not check at all [those areas that require light and rather checks immediately after Shabbos]. This obligation to check applies even if he already nullified his Chametz before Pesach, and he is thus no longer obligated to Biblically destroy it. [This obligation applies even if one sold his Chametz to a gentile before Pesach.]
Saying a blessing: If one did not check [at all] on the night of the 14th, then before beginning the search on the day of the 14th, one says the blessing of “Al Biur Chametz.” [However, if he already said a blessing and checked on the night of the 14th, and simply forgot to check a certain area, then a blessing is not recited.] Likewise, if he forgot to perform the Bedika on the day of the 14th, then prior to searching upon remembering during Pesach [Yom Tov/Chol Hamoed] he is obligated to say the blessing of “Al Biur Chametz.” This applies even if he already nullified his Chametz before Pesach, and he is thus no longer obligated to Biblically destroy it. [This, however, only applies if one did not sell his Chametz to a gentile through Mechiras Chametz. If, however, one performed Mechiras Chametz, then one is not to say a blessing prior to the search, if it is after the 6th hour on Erev Pesach.]
How to check-sunlight or candle: [Although when checking for Chametz prior to the night of the 14th, one may never check during the daytime, on the day of the 14th and onwards, when must check whenever he remembers, even during the day. The following will discuss if sunlight may be used for this checking.] When checking during the daytime, such as on Erev Pesach [the day of the 14th] he remembered that he did not check a certain area for Chametz, then all areas that are directly opposite sunlight [i.e. the sky], such as areas that are directly opposite an open window, or areas that are directly under an open roof, may be checked using sunlight. This applies even if the sky is cloudy, and the sun cannot be seen. However, all other areas that are not opposite or under sunlight, must be checked with a candle, just as is done on the night of the 14th.
What to do with the Chametz: If one found Chametz during his search [then if he did not sell his Chametz to a gentile, and it is Chol Hamoed] he is to immediately destroy the Chametz from the world as explained in Chapter 3 Halacha 6B]. [If one sold his Chametz to a gentile before Pesach, as is accustomed today for all Jewry to do through the Rav of their community, then they found Chametz is to be moved with a broom to an area sold to the gentile, as explained in Chapter 3 Halacha 9A.] If one found Chametz on [Shabbos or] Yom Tov, one may not move the Chametz [being that it is Muktzah] and is rather to cover it with a vessel until Yom Tov is over, and then immediately destroy it [or if he sold his Chametz, to move it with a broom to the area sold to the gentile].
Nullifying the Chametz: If one is performing the Bedika on the day of the 14th prior to the 6th hour of the day, then after the Bedika, one is to nullify his Chametz.
Forgot to check and it is now after Pesach: One who transgressed, or forgot, and did not check his home, or a certain area of his home, for Chametz, and it is now after Pesach, then [if he did not sell his Chametz to a gentile before Pesach] he needs to search for the Chametz after Pesach [as soon as he remembers]. One is to search for the Chametz with a candle, although no blessing is recited prior to the search. Any Chametz that is found is to be destroyed. [Accordingly, a Jew who becomes observant/Baal Teshuvah after Pesach, is to be instructed to search his home for any Chametz that was owned from before the previous Pesach, and have it destroyed.]
Summary of C-D:
Checking during daytime: Lechatchilah, one may never check during the day, unless it is past the night of the 14th and he did not check, in which case he checks on the day of the 14th. If one transgressed and checked during the day before the night of the 14th, then all areas which may not be checked with sunlight [i.e. all areas in a four-walled roofed room that are not opposite an open window] must be rechecked at night, even if he checked them with a candle in a dark room. However, when checking on the day of the 14th, or on Yom Tov or Chol Hamoed, all areas can be checked with a candle, and all areas that are opposite sunlight [under open roof, opposite open window] may be checked with the sunlight even on a cloudy day.
Forgot to check: One who did not check for Chametz on the night of the 14th must do so when he remembers, whether on Erev Pesach, Yom Tov or Chol Hamoed. On Shabbos, one waits to search until after Shabbos. On Yom Tov, any Chametz that is found is to be covered until after Yom Tov. If one did not sell his Chametz to a gentile, one recites a blessing prior to beginning the search. If one did not perform the search, and it is already after Pesach, the search is to be performed after Pesach without a blessing.
 Admur 433:1 and 435:1 regarding the 14th; 435:2-3 regarding the rest of Pesach
 Admur 435:2-3
Other opinions: Some Poskim rule one is not to search at all for the Chametz on Yom Tov, and should rather wait to do so at night. [Opinion in M”B 435:3]
 Admur 435:3
The reason: The reason for this is because one needs to check with candle light, and on Shabbos it is forbidden to carry around a candle. [Admur ibid]
Other opinions: Some Poskim rule that if one remembered on Shabbos then one should search for the Chametz on Shabbos, and he may have a gentile carry a candle for him into the rooms that need to be checked. [Piskeiy Teshuvos 444:1]
Areas that have sunlight or electricity: Those areas which may be checked with sunlight, as well as those areas that have electric lights that are on, should be checked on Shabbos, as soon as one remembers. [Piskeiy Teshuvos 444:1]
 The reason: Although since we suspect for coming to eat it, ideally once Pesach has arrived we should specifically not allow one to search for Chametz even if he did not do so beforehand, due to concern that he may find Chametz and eat it. Nevertheless, we require him to search, as during the time that one is searching for the Chametz we do not suspect that one will forget and come to eat it, as his entire purpose in searching for it is to destroy from the world, so how will one forget about the prohibition and come to eat it. [Admur 435:2]
 Piskeiy Teshuvos 435; As it is forbidden to allow even a gentiles Chametz to remain openly visible in one’s home, lest one accidently come to eat it. See Chapter 5 Halacha 5!
 Admur 435:1
 Admur 446:1-2
 Vetzaruch Iyun if one did not remember to check until the last day of Yom Tov, and thus must do the search on Yom Tov, if a blessing should be said before the search, even though the burning of the found Chametz will only be done after Yom Tov.
If one forgot to check only one area: Whenever one checked his home before Pesach and simply forgot to check one area, then if it is a room in which one commonly eats Chametz in, and it was not cleaned at all before Pesach, and there is thus a chance that it contains a Kezayis of Chametz, then a blessing may be said if one did not sell his Chametz before Pesach. [See Admur 432:5; 446:3]
 Admur 435:2
The reason: The reason for why the blessing is required is because nevertheless [even after nullifying the Chametz] one still remains Rabbinically obligated to check and search after it and destroy it completely from the world in order to prevent him from finding Chametz on Pesach and forgetting and coming to eat it. [Admur ibid] Now, although we never say a blessing when the reason for why we need to destroy a food is due to suspicion that one may come to eat it, nevertheless here a blessing is said as there is a Rabbinical prohibition of Baal Yiraeh and Tashbisu on a Kezayis of Chametz or more even if it was nullified, and thus one is required to destroy the Chametz in it of itself and not just because one may come to eat, (although the reason for why the sages decreed that there is a Rabbinical prohibition of Baal Yiraeh is because one may come to eat it.)] [See Admur 435:4; 446:1-3; Kuntrus Acharon 1]
 Piskeiy Teshuvos 435:1; Pashut, as the Chametz belongs to a gentile and there is no such Mitzvah to destroy his Chametz. Nonetheless, one is still to search for the Chametz in order to have it placed behind a Mechitza.
 Admur 433:4
Areas opposite a closed glass window: A glass window is considered an interval between the sky and the area of the room, and hence areas opposite a glass window, or glass sunroof cannot be checked with sunlight. [Admur 433:3 regarding sunroof and 433:4 regarding window] However, some suggest that our windows today are very clear and hence one may check using sunlight in areas that opposite a clear glass window. [Daas Torah 433; Piskeiy Teshuvah 433]
A three-walled room: A room which has only three walls, even if it is roofed, [and the area of the fourth wall is open to the sun outside], may be checked even Lechatchilah using sunlight [on the day of the 14th, if he forgot to do so the night before] being that it has a lot of sunlight in the room. This type of room is called an Achsadra. One may use the sunlight to check even on a cloudy day. [Admur 433:2]
A room with many windows: A room which has many open windows, and thus has much light, as is common in Shuls, then if one transgressed and did not check the shul on the night of the 14th, it may be entirely checked on the day of the 14th using sunlight, as its considered like an “Achsadra” which may be checked with sunlight. [Admur 433:37]
 Admur 433:3
 Admur 435:1
 Admur 433:3 regarding under an open roof; Admur 433:4 regarding opposite a window
 Admur 433:1, 3
The reason: As the light of a candle is good for checking and searching in hidden places and holes and cracks [Admur 433:1] while the sunlight that enters the room is [minute as] it only enters through the windows and holes of the room. [Admur 433:2]
 Admur 435:3
 The reason: In order so the Chametz be hidden from ones sight and he thereby not come to eat from it. [Admur ibid]
 Admur 435:1
 Admur 435:4
 The reason: The reason one must search and destroy all Chametz found even after Pesach is because any Chametz which was owned during Pesach is prohibited in benefit, as explained in chapter 448, [and thus we require one to check and search for it] as we suspect that if one were not to check and search for it in order to destroy it, then perhaps he will find it on its own [without searching for it] and he may forget and come to eat it. [Admur ibid]
 The reason: The reason for this is because how can one bless G-d for commanding him to destroy Chametz if he is now eating Chametz. Although one is Rabbinically commanded and obligated to destroy this Chametz that was owned over Pesach this is only in order to prevent him from coming to stumble upon a transgression of eating the Chametz. Meaning, one does not transgress on this Chametz any owning prohibition of Baal Yiraeh, not even a Rabbinical prohibition. Thus, one does not say a blessing on this destruction of the Chametz, just like no blessing is said when one kills birds which have been trampled [and are treifas] even though they are forbidden to be owned because one may come to eat them, as explained in Yorah Deah chapter 57. [Admur ibid]