Answer to Puzzler #1:
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First off, Nobu should probably chase after Killua first, since Killua is the
one nearest the staircase, meaning he can get away faster [from the stairs].
Also, had he decided it was better to chase Gon, he should've gone in and out
of each door to the room rather than from the holes that Gon created. This way,
Gon wouldn't have gone out through a door when Nobunaga was weaving in and out
of rooms.
Another possiblitiy: Nobunaga should've exited the building and then ignited
his en, so that no matter what, Gon and Killua can't get out of the
building even if they can create holes in walls to escape a single room.
Well, the truth is...I don't really know what the answer is. If you have a
better answer, email me at yorkshinauction@gmail.com