I hope that you can explain the ruling on not staying overnight in Mina during the Days of Tashreeq. If the answer is that (the one who does not stay in Mina) is obliged to offer a sacrifice, then should he offer a sheep for each night or is one sufficient?
Praise be to Allaah.
Staying overnight in Mina during the Days of Tashreeq is obligatory according to the majority of fuqahaa'; the one who fails to do that with no excuse is obliged to offer a sacrifice. According to the majority of scholars one should stay there for most of the night.
(al-Mawsoo'ah al-Fiqhiyyah, part 17, p. 58).
Not staying overnight in Mina during the Days of Tashreeq may be one of the following cases:
The first case: when a person does not stay overnight in Mina because he has an excuse.
Shaykh Ibn Baaz was asked about the ruling on a person who does not stay overnight in Mina during the Days of Tashreeq. He said: He is not obliged to offer any sacrifice because Allaah says (interpretation of the meaning): So keep your duty to Allaah and fear Him as much as you can' [al-Taghaabun 64:16] - whether he did not stay overnight at Mina because of sickness or because there was no room, of for some similar legitimate excuse such as those who bring water to the pilgrims and those who tend sheep, and whatever else comes under the same rulings.
The second case: when a person does not stay overnight (in Mina) during the days of Tahsreeq with no excuse.
The Shaykh (may Allaah have mercy on him) said:
Whoever does not stay overnight in Mina during the Days of Tashreeq with no excuse has failed to do something which was prescribed by the Messenger of Allaah SAWS (peace and blessings of Allaah be upon him) in both word and deed, and by the fact that he made a concession for some of those who have excuses such as shepherds and those who bring water to the pilgrims. Concessions can only be made when there is something which has to be done. Hence staying overnight in Mina during the Days of Tashreeq is considered to be one of the obligatory duties of Hajj, according to the more correct of the two scholarly views, and whoever does not do that and has no legitimate excuse has to offer a sacrifice, because it was reported that Ibn Abbaas (may Allaah be pleased with them both) said: Whoever fails to do one of the rituals [of Hajj] or forgets it, let him offer a sacrifice. It is sufficient to offer one sacrifice for not staying overnight in Mina during the days of Tashreeq.
(Majmoo' Fataawa al-Shaykh Ibn Baaz - may Allaah have mercy on him - vol. 5, p. 182)
He should offer the sacrifice and share out its meat among the poor in the Haram, and he should not eat any of it. And Allaah knows best.