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The letter of the law:
Only the five grains which are 1) wheat, 2) barley; 3) rye, 4) spelt, 5) oats, can become leavened and become Chametz. All other grains/flours, such as flour made from rice or millet and all other legumes [and starches], cannot ever leaven and become Chametz. Although these flours also rise when kneaded with water, this rising is not a leavening but rather a spoiling [i.e. Sirchon]. For example, if one were to take rice flour and the like and knead it with boiling water and then cover it with a cloth until it rises like dough that has leavened, in truth, this act of rising is not leavening but rather a spoiling of the dough. The dough thus remains permitted to be eaten on Pesach. From the letter of the law, it is likewise permitted to cook a dish of these legumes on Pesach.
The custom: The custom in these provinces [i.e. Ashkenazim] is not to eat a cooked dish of Kitniyos/legumes on Pesach, even on the last day of Yom Tov [even in the Diaspora]. This accustomed prohibition is a mere stringency. [Nevertheless, as a result of the custom, these foods are forbidden to be eaten by all Jews of Ashkenazi origin, and one may not swerve from this custom. The Maharil writes that one who goes against this custom transgresses the prohibition of Lo Sasur and is liable for death, as he has gone against a Rabbinical command. The above only applies to Ashkenazi Jewry, however the majority of Sephardim never accepted such a custom upon themselves and it therefore remains permitted for a Sephardic to eat Kitniyos on Pesach and so is their custom. However, there do exist Sephardic communities who likewise avoid Kitniyos, such as rice, and so is the custom of Moroccan Jewry, and the Yishuv Hayashan of Jerusalem Jewry. Every person should follow the custom of his origin. Those who are accustomed to eat legumes on Pesach must be careful to check the legumes for grains prior to cooking, as explained in Halacha 7C!]
It is forbidden, due to custom, for Ashkenazim to eat Kitniyos throughout the entire Pesach.
May one eat Kitniyos if there are no other foods available?
A community Rav may allow Kitniyos foods to be eaten in the event that other foods are not available during Pesach. In such a case, it is better to eat other legumes if available rather than rice or millet. One must check the legumes for grains prior to cooking.
May an ill person eat Kitniyos?
An ill person may eat Kitniyos on Pesach for medical reasons.
May an infant be fed Kitniyos?
Infants may be given Kitniyos to eat in a time of need, even if there is no danger involved. Thus, an infant who is accustomed to eating Kitniyos based formula, may be fed such formulas during Pesach. When doing so, it is proper to designate pots which will be used for the Kitniyos.
If an Ashkenazi woman married a Sefardi may she eat Kitniyos?
Yes. She is not required to perform Hataras Nedarim prior to doing so.
 Admur 453:1; Michaber 453:1; Pesachim 35a
Other opinions: The Talmud [Pesachim 35a] records the opinions of Rav Yochanan Ben Nury who holds that rice and millet are considered a grain and its leavening is actual Chametz for which one is liable for Kareis, just like the five grains. The Mishneh in Pesachim 2:5 rules that only the five grains can become Chametz, and the Gemara ibid establishes that this Mishneh does not follow the opinion of Rebbe Yochanon Ben Nury, and so is the final ruling of the Talmud, and all Rishonim and Achronim.
 Admur ibid; Chok Yaakov 453:4; Rambam 5:1
 Admur 453:3
 Admur 453:3; Rama 453:1 “Some Poskim prohibit it and so is the custom”; Darkei Moshe 453:2; Beis Yosef 453; Tur 453:1 in name of Yeish Osrin although concludes the custom is not like this; Terumos Hadeshen 113; Hagahos Maimanis 5:1 in name of Semak 222 and Rav Shmuel of Uroyah; Mordechai Remez 588; Peri Chadash 453:1 brings a proof for this custom from Pesachim 40b; See Kaf Hachaim 453:9-10
Other opinions: Some Poskim negate the custom of Ashkenazi Jewry, and rule it is to be nullified. [Rabbeinu Yerucham 5:3 p. 41 [brought in Beis Yosef 453] “It is a Minhag Shtus not to eat cooked Kitniyos unless they do it as a mere stringency, and I don’t know why”; Hagahos Maimanis 5:1 that Rav Yechiel and other Gedolim permitted Kitniyos; See Chasam Sofer 122 regarding a certain Ashkenazi community whose leaders permitted eating Kitniyos on Yom Tov of Pesach; Mor Uketzia 453, brought in Machazik Bracha 453:1 and Kaf Hachaim 453:10, writes his father the Chacham Tzevi protested against this custom, as it leaves people without food to eat and they end up baking a lot of Matzah of which if they are not careful, they can transgress an Issur Kareis. “Therefore, if I had the power I would abolish this custom”; See however Sheilas Yaavetz 2:146, brought in Shaareiy Teshuvah 453:1; Bashamayim Rosh 348 “It is a mistaken custom”; See Shaareiy Teshuvah ibid that some Sages desired to nullify this custom and the leaders of the generation stopped them.]
 The reason: The reason behind this custom is because in the later generations the population of uneducated Jews who are not expert in the laws of Issur Viheter [i.e. Kashrus] increased. Now, if they were to see people eating a cooked dish of Kitniyos on Pesach, they will mistakenly come to permit cooking [and eating] even grains [such as heat/spelt/rye/oats/barley]. The reason for this is because the entire year it is common to make legume dishes just as it is common to make grain dishes, and they will thus assume that they have an equal law regarding Pesach. For this reason, it became accustomed to forbid everything. [Admur ibid; 1st reason in Hagahos Maimanis ibid, Semak 222, Mordechai Remez 588, Beis Yosef 453; 1st reason in Chok Yaakov 453:5; Peri Chadash 453:1 based on Pesachim 40b; 1st reason in Perisha 453:3; M”B 453:6 omits this reason and states cooked legumes is forbidden due to Lo Pelug]
Other reasons mentioned in Poskim: Some Poskim write the reason behind this custom is because wheat grains tend to get mixed into Kitniyos, and hence people may come to stumble and eat Chametz grains during Pesach, when eating their Kitniyos dish. [Tur 453:1; 1st reason in Taz 453:1; 2nd reason in Chok Yaakov 453:5; 3rd reason in Hagahos Maimanis ibid and Beis Yosef 453; 1st reason in M”B 453:6] Alternatively, the reason is because it is possible to make flour/dough out of legumes and thus one may come to confuse it with Chametz flour/dough and come to allow even Chametz flour/dough. [2nd reason brought in Taz 453:1; 2nd reason in Hagahos Maimanis ibid, Semak 222, Mordechai Remez 588, Beis Yosef 453; Bach 453; 2nd reason in Perisha 453:3; 2nd reason in M”B 453:6; See also Biur Halacha 453:1 “Veyeish Osrin”]
The practical ramifications between the reasons: 1) May an Ashkenazi eat dry Kitniyos [Permitted according to reason of Admur, forbidden according to 2nd reason] 2) May an Ashkenazi eat cooked Kitniyos if it was checked for grains. [Permitted according to 1st reason, forbidden according to Admur, 3rd reason] [See Piskeiy Teshuvos 453:3 that the custom is to be stringent like all the reasons]
 Admur 253:5; Taz 453:1; Chok Yaakov 453:5; Tur 453:1; See Rabbeinu Yerucham ibid
 Beis Yosef ibid writes “Ashkenazim”; Chayeh Adam 127:1 writes it applies to all Ashkenaz and Poland; See Chasam Sofer 122 regarding a certain Ashkenazi community whose leaders permitted eating Kitniyos on Yom Tov of Pesach;
 Rama 453:1; Darkei Moshe ibid; Taz 453:1; Chok Yaakov 453:5; Levush 453; Bach 453; Maharil in next footnote; Chida in Shiyurei Bracha 453 and Tov Ayin ibid, brought in Shaareiy Teshuvah 453:1 and Kaf Hachaim 453:11; Chayeh Adam 127:1; See Admur 453:3-5 who uses the term “forbidden” regarding the custom, although does not write the wording of the Rama ibid.
 Drashos Maharil 5 Hilchos Machalos Assuros Bepesach, brought in Shaareiy Teshuvah 453:1 and Kaf Hachaim 453:11
 Michaber 453:1 “It is permitted to cook and eat it” Beis Yosef 453 “Only the Ashkenazim suspect for this matter”; Peri Chadash ibid; Chida in Tov Ayin 9:6; Tur 453:1 that the custom is not to prohibit Kitniyos; Rabbeinu Yerucham 5:3 p. 41 “It is a Minhag Shtus not to eat cooked Kitniyos unless they do it as a mere stringency, and I don’t know why”; Shaareiy Teshuvah 453:1 that it is similar to Takanas Rabbeinu Gershom not to marry two wives, which depends on country
 See Peri Chadash ibid “It is not our custom to avoid Kitniyos, with exception to rice, being that we once checked it three times and we still found a wheat kernel in it afterwards, and from that day and onwards we stopped eating rice on Pesach.” This refers to Jerusalem Jewry, of which the Peri Chadash was its Rabbinical leader. So writes also Chida in Tov Ayin ibid and Pekudas Eliezer 51, brought in Kaf Hachaim 453:10, that Jerusalem Jewry forbids rice/Kitniyos on Pesach. Kaf Hachaim ibid concludes that today Yerushalayim is made up of many communities and each group is to follow their custom.
 Shaareiy Teshuvah ibid; Kaf Hachaim 453:9-10
 Aruch Hashulchan 453:5; M”B 453:7
 M”B 453:7
 Piskeiy Teshuvos 453:9
 Tashbatz 3:179; Igros Moshe O.C. 1:155; Poskim in Nitei Gavriel 2 39:15