8 Days of Chanuka #1

The Beit Yosef has a famous kashya: We celebrate 8 days of Chanuka in remembranc eof the 8 days the Menorah remained lit. Yet the miracle was only for 7 days; there was enough oil for the 1st day as the Gemara in Shabbos (21b) tells us. So why do we celebrate the 1st day as well? The Sefer Yemei Shmonah brings down 500 teirutzim to this question, so hopefully I'll post a few by the time Chanuka gets here.

The Beit Yosef himslef offers 3 explanations:

1. The people at that time divided up the oil that they had into 8 portions. Every night they put in one portion and they saw that it lasted until the following day. So they saw that every night, even the 1st night, was a miracle.
2. On the 1st night they poured in all the oil but the jug miraculously remained full, so even on the 1st night they recognized the miracle.
3. On the 1st night they poured in all the oil, and saw the following day that the candles remined full of oil. And so it was every night.

(Yemei Shmonah p.19- Mahut HaKushya)