An answer to the well known question of the Beis Yosef.
The Beis Yosef asked that since the oil that they found was enough to last one day, there was no miracle when they lit the menorah on the first day. So why do we celebrate the miracle of Chanukah for eight days? Surely the miracle was only for seven days!
I saw that the sefer Toldos Ya'akov Yosef wrote that maybe we could answer this question with what the Beis Yosef asked further, which was why did the Rabbis not establish Chanukah for nine days, adding a day like they did for all the festivals because of the doubt as to which day is Rosh Chodesh? Surely we can say that one question is answered by the other question - that really Chanukah should have been only seven days, but they established eight days because of the doubt of the day.
But he afterwards refuted this answer, because if it was because of the doubt of the day that they established eight days, then they should have fixed Chanukah to start from the second day, when the miracle started, that is, the 26th of Kislev, and then continue one more day at the end because of the doubt of the day. This would be like all the festivals, with Pesach starting on the 15th of Nisan and Succos on the 15th of Tishrei. But we never start a day earlier because of doubt of the day. See there for more.
I further saw a certain sefer on the Torah which brings in the name of R.A. in the glosses on the Semag a different answer to the question of the Beis Yosef. That presumably on the first night they put all the oil into the menorah in order that it will remain lit the required time, and they did not concern themselves about the next day, because every mitzvah which comes along should certainly be performed completely. If so, they would have almost certainly discarded the empty flask in some place out of the way, and if so, how did they find on the second day oil in that flask? Because who would have thought to look in that flask, and to think that perhaps a miracle occurred? It is not our way to rely on miracles. Perforce, it must be that on the first day when they poured the oil in the flask into the menorah, immediately a miracle happened and the flask refilled whilst it was still in the hand of the Kohen. So it emerges that even on the first day a miracle occurred.
But the sefer who brings his words queried this answer, because if so, there was no miracle on the eighth day, since on each day a miracle occurred for the sake of next day. Thus, the seventh day prepared for the eighth day, but on the eighth day no miracle was needed for the following day, since they already had new oil. (See there further that he suggests that perhaps they did not need that the flask would refill immediately except on the first day, but not on subsequent days. He discusses the matter further, but it is not needed for our own discussion, so I did not quote his words).
But it seems to me that we now have a fitting answer to the question of the Beis Yosef. Because even though each of these two suggested answers by themselves were refuted, nevertheless, by combining the two answers together the question of the Beis Yosef can be resolved. That really events happened like R.A. described, and thus every day starting from the 25th of Kislev there was a miracle, and the only problem is the eighth day when there was no miracle. For this we can use the answer of the Toldos Ya'akov Yosef, that the eighth day was added because of the doubt of the day. (Although there is still a problem, because if so, on the eighth day we should light only seven candles since there is a doubt that it might be the seventh day).