R. Yerachmiel Zelcer published his Ner Le-Me’ah, a collection of 100 answers to the Beis Yosef’s question...
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They divided the oil into eight parts and used one-eighth each night
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After they filled the menorah each night, the bottle of oil was miraculously refilled
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On each morning, they found the menorah refilled with oil
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Not all the oil burned the first day so a little would remain on the second, because a blessing/miracle can only impact an existent item
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One day of Chanukah celebrates the military victory
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The first day commemorates the rededication of the Temple by the Hasmoneans
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The eight days correspond to the eight days of circumcision, which the Greeks outlawed
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The receptacles used as a menorah were broken and could not contain a full day’s amount of oil but still miraculously burned for a full day
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The first day commemorates the dedication of the Second Temple when it was built – R. Yaakov Emden
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Finding the bottle of pure oil was in itself a miracle
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The Geonic work She’eiltos has a different version of the Talmudic passage (as it often does) which reads that they did not even have enough oil for one day
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There was only enough oil for the first night but the menorah must be lit all day also
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They were forbidden to extinguish the fire on the morning of the first day in order to conserve oil yet the oil continued burning through the eighth evening
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The eighth day is celebrated out of doubt, as all holidays are observed outside of Israel
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They planned on using multiple wicks dipped in the oil but the original wicks miraculously lasted all day
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They lit in the courtyard rather than the inner chamber. The greater wind created a need for more oil
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The month of Kislev was short that year but is now long (29 vs. 30 days). We still observe the holiday from 25 Kislev through 2 Teives even though it is now eight days rather than the original seven
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On the first day, after they found the bottle with only enough oil for one day, it miraculously became enough for eight days
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There was enough oil for lighting the menorah but not for relighting the western light in the morning, as it was each day
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They thinned the wicks so they would only use 1/8th of the oil. The miracle was that the flame was as strong as if they used full wicks
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The bottle only had enough for one light for one day but it lasted for all seven lights for eight days
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They lit the menorah before dark on the evening of 24 Kislev, so the miracle also applied to the end of the first day
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We are not allowed to make a replica of Temple utensils. We therefore celebrate for eight days so the menorah will have eight branches, rather than seven like the Temple menorah
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Eight days like Sukkos
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The miracle was not in the quantity of oil but the quality, that it burned eight times slower than normal, which also occurred on the first day

