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Havdalah on Motzei Yom Tov:
*In those years that Motzei Yom Tov is also Motzei Shabbos then the order of Havdalah follows the same order as Motzei Shabbos.
On Motzei Yom Tov, whether it is Motzei Yom Tov to a weekday or Motzei Yom Tov to Chol Hamoed, one is required to recite Havdalah over a cup of wine just like on Motzei Shabbos. However, when Motzei Yom Tov falls on Friday night it is not recited.
Haeish: During Havdalah of Motzei Yom Tov, we do not say a blessing over fire.
Besamim: During Havdalah of Motzei Yom Tov, we do not say a blessing over Besamim.
Nussach: The Nussach of Havdalah on Motzei Yom Tov that falls on a weekday also contains the words “Bein Yom Hashevi’i Lesheishes Yimei Hamaaseh”, even though it is now in middle of the week [and it thus seems irrelevant to mention this statement]. [Thus, it follows the same Nussach as any Motzei Shabbos.]
Are the Pesukim of Hinei Keil Yeshuasi recited on Motzei Yom Tov?
May one who did not say Havdalah on Motzei Yom Tov say it the next day?
One who did not say Havdalah on Motzei Yom Tov is to say Havdalah the next day [until sunset], and is not to eat or drink anything, besides for water, until he does so. If one did not say Havdalah the next day [prior to sunset] then he may no longer say Havdalah, and may thus continue eating and drinking as usual.
Is Vayiten Lecha recited on Motzei Yom Tov?
Is Vayiten Lecha recited on Motzei Shabbos Chol Hamoed?
 Admur 491:1; 602:2 [Regarding Motzei R”H]
 Admur 491:4; Havdalah is not recited either in prayer or over a cup of wine. Hence, Veatah Chonantanu is omitted in Shemoneh Esrei of Friday night, and one does not say Yaknahaz by Kiddush.
The reason: The reason for this is because the holiness of Shabbos is greater than that of the holiness of Yom Tov. [Admur ibid]
 The reason: As the blessing over a flame was only instituted to be said on Motzei Shabbos and Motzei Yom Kippur, in which case fire was prohibited for the entire day and it now returns to be permitted, as explained in 298/1-2. However, on Yom Tov, fire was not prohibited from being used for a need on the Holiday. [Admur ibid]
 The reason: One is only required to say a blessing over Besamim on Motzei Shabbos, as the soul is pained by the leave of the extra soul it received on Shabbos and has now exited from it on Motzei Shabbos, and needs to be comforted. However, on Yom Tov, there is no extra soul given at all. [Admur ibid]
Background and analysis:
Admur in 491/1 adds the words “There is no extra soul given at all at all”. This follows the ruling of Tosafos Pesachim 102a; Rashba 3/290; Radbaz 2/620 that there is no extra soul on Yom Tov. However, the Rashbam Pesachim 102b rules there is an extra soul on Yom Tov, and so is the ruling of the Zohar. Vetzaruch Iyun how the above Poskim can go against the Zohar. Perhaps in truth there are many levels of an extra soul, and on Shabbos one receives a higher level than on Yom Tov. However, Tzaruch Iyun from Admur which states “on Yom Tov there is no extra soul at all”. In truth, in the source of Admur from the Magen Avraham and Levush these words “at all” are omitted. Furthermore, in certain prints of the Shulchan Aruch of Admur this entire Halacha is missing. It most probably then is the case that Admur did not write this word and it was written by the copier. [Shaar Hakolel 17/22; Likkutei Sichos 31 Ki Sisa] However, the Rebbe in Likkutei Sichos 31 Ki Sisa footnote 15 explains that based on Nigleh there is no extra soul at all on Yom Tov, and it is only based on Kabala that there is an extra soul, hence Admur wrote in his Shulchan Aruch, which follows the rulings of Nigleh, that there is no extra soul “at all”.
Another reason: Regarding the second reason mentioned by the Bach for smelling Besamim, due to the return of the fire of Gehenom, the Mordechai [Pesachim 105] rules that on Yom Tov Gehenom is not subdued, and thus there is no need for Besamim on Motzei Yom Tov. However, Tosafos [Beitza 33b] rules that Gehenom is subdued on Yom Tov and hence the reason for the omission of Besamim is because there is no extra soul.
 Admur 491/2
 As explained in 296 [ibid; Vetzaruch Iyun as in 296 no mention of this is made. See also 473/9]
 The reason: As one is simply stating the order of Havdalos that are written in the Torah “Bein Kodesh Lechol, Bein Or Lechoshech, Bein Yisrael Leamim etc”. [ibid; See also 599 regarding Vetodieinu for a similar ruling]
 Peri Megadim 491 M”Z 1; and so is the custom of the Rebbe as was witnessed in public.
 Mateh Ephraim 601/10; 624/5
 For list of opinions on this question see Sdei Chemed Asifas Dinim Mareches Heim 15; Kaf Hachaim 299/24
 So rules Kol Bo 59; Rav Akiva Eiger 299/6; Beis Ephraim; Mishneh Berurah 299/15; Piskeiy Teshuvos 299/4; SSH”K and so infers Sdei Chemed [Asifas Dinim Mareches Heim 15] from Admur 299/8 who allows saying Havdalah of Shabbos the next day even if one purposely skipped Havdalah at night, thus proving that the next say is not a Din Tashlumin, but rather a continuation of the obligation.
Other Poskim: Some Poskim rule one may not say Havdalah even the next day, as Safek Brachos Lehakel. [Many Poskim listed in Sdei Chemed ibid and so he rules; Chida in Birkeiy Yosef 491/1; Machazik Bracha 491/1; Chesed Leavraham 491/2; Ben Ish Chaiy Vayeitzei 23]
 However, past sunset, he is to no longer say Havdalah as it is now a question whether or not the next day has begun, and many Poskim hold that Havdalah on Motzei Yom Tov may not be made up even the next day. Thus, after sunset one is to be stringent. [So also rules Piskeiy Teshuvos 299/10]
 299/8 regarding Havdalah after Shabbos, and the same rule applies to Motzei Yom Tov
 So is understood from all the Poskim mentioned in the first footnote who only extend the allowance for the next day.
Other Opinions: The Beis Yehuda 2/28, and other Poskim [brought in Sdei Chemed ibid] rule that one may say Havdalah the entire week. We do not rule like this opinion, as brought in Chachma Umusur [see Sdei Chemed] that all the Poskim argued on his ruling. Likewise, the Chida [Bircheiy Yosef 491/1; Machazikei Bracha 491/1] argues against his ruling.
 P”M 295 M”Z 3; Beir Heiytiv 491:1
 Elya Raba 491:2; Aruch Hashulchan 295:3
 The reason: As Chol Hamoed is forbidden in Melacha, and it is hence a belittling of Chol Hamoed to bless the weeks Melacha.
 Hayom Yom 19th Nissan; see also Sefer Haminhagim p. 118 [English]; Otzer Minhagei Chabad p. 142
Original Chabad custom: In the earlier prints of Hayom Yom p. 46 it stated that one does not say Vayiten Lecha at all on Motzei Shabbos Chol Hamoed. This was based on an explicit directive of the Rebbe Rayatz that one is not to say it and that so was the custom of the Rebbe Rashab and the Rebbe Maharash, although there were some years in which they said it. [Reshimos 4:12 and 22]