Relighting Chanukah lights that extinguish

Question

In light of this answer (no pun intended) which directs you to never pass your hand over a light without lighting it, what happens when the lights extinguish before you've lit fully.

There are several cases to consider (let's assume it's the eighth night):

1. Light candle 8, then 7, then candle 7 goes out before you light 6.
2. Light candle 8, then 7, then candle 8 goes out before you light 6.
3. Light candle 8, then it goes out before you light 7.
4. Light candles 8 through 6, then 7 goes out before you light 5.

(The primary reason for the last two cases is to see if there's a distinction between the first light and the remaining ones. Are there other variables that matter?)

Answer 1

The Shulchan Aruch (673:2) rules (based on the discussion in the Talmud Shabbat 21a-b) that if a Chanukkah candle goes out after lighting it, even on Friday before Shabbat starts, one need not relight it because the mitzva was already accomplished after lighting.

The Taz there (sk 10) recommends relighting it anyway (without a bracha) to 'complete the mitzva'. The Mishna Berura there (sk 27) concurs, and notes this applies especially on Friday before Shabbat starts when there are opinions that one must relight with a bracha.

The second Biur Halacha on that se'if suggests that if a candle goes out while still lighting, one must return and light it if one wants to accomplish the mehadrin min hamehadrin, the choice way of lighting which involves specific numbers of candles per night.

As for your concern about passing over candles, I'm not exactly sure what the problem is. Just never move your hand over an unlit candle without lighting it.