If Hillel and Shammai (as individuals) disagreed on only a few cases (which way to light is NOT one of them), then they must have agreed on this issue. One lights candles each year. How is possible that Beit Hillel and Beit Shammai disagreed on this issue? Are we talking about a disagreement that took place many generations after Hillel and Shammai died so that the people didn't actually see for themselves which way Hillel and Shammai lit? What about a very short term Mesorah?
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1Welcome to Mi Yodeya, Lazer. Do you have a reason that this is any different than, say, an argument about when to read Megillah? I am just trying to understand if you have a specific question on Chanukah lighting, or this was just your example. – Y e z Feb 3 '15 at 1:02
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Hillel and Shammai themselves very rarely argue - in fact, the Mishnah already compiled every such case into Eduyos chapter 1. So I’m unclear on why you think this case is unique in that Hillel and Shammai agree but their students didn’t. – DonielF Dec 12 '17 at 10:04
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Highly related (not sure if it counts as a dupe): judaism.stackexchange.com/q/48478 – DonielF Dec 12 '17 at 10:05
The basic halacha is that one only needs to light one candle per family, which is what people may have been accustomed to doing. Beis Hillel and Beis Shamai are disagreeing over what is the ultimate way to fulfill the mitzvah (mehadrin min hamehadrin). It is quite likely people had not lit in the ultimate fashion for years - or perhaps, never since the Chanukah miracle itself.
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because there was no clearly established minhag that everyone would know? It's likely candles were not as cheap back then as they are now. – CashCow Feb 3 '15 at 11:22
