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AC: Let's Go To The Wiki Serena
Serena is a spirit who appears out of your town fountain (gained after donating 500,000 bells to your town). Answering her questions correctly can get you a Silver or Gold Axe. A brief guide is below, which you should follow in order to have a chance of receiving a Silver or Gold Axe. This is currently very rough, and her exact questions may be slightly different.
A question with a letter and a ) before it signifies a question within a question.
a) Serena: What kind of axe did you throw in?
Your reply: Normal
Serena: Do you hate me?
Your reply: Yes
a) Serena: WHAT!?! Did I do something to make me hate you?
Your reply: Yeah, you did!
b) Serena: So how much do you hate me then?
Your reply: (A little bar will show. Keep this at exactly midway, then press continue.)
c) Serena: What? You...you don't know what you're talking about, goddesses are supposed to be revered and such...maybe I should resign being a goddess...
Your reply: Don't do that!
(There's another thing after this. I don't remember what it was, but just answer with a positive remark.)
d) Serena: Do you think you'll be able to like me more?
Your reply: Yeah!
(They missed another one... She'll say "Ok, maybe you're not so bad after all. I'll give you something special. Just pick a Hand" Now you pick Left or Right. I picked Right, but your answer may not give you it. Just pick whichever you think will give you what you want.)
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You may not get the above conversation, as it appears visiting her regularly builds up a friendship, increasing your chances of getting the Gold Axe. The conversation lines below may appear instead.
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b) Serena: Do I look different?
Your reply: Yes (You may not have the option to say Yes, in which case you cannot obtain a Silver or Gold Axe at this time, and your axe will be lost.)
c) Serena: What kind of axe do you want?
Your reply: (Still unknown) but the options are Gold Axe, Silver Axe. Regular Axe, or Nothing. I do know saying nothing or regular will just get your normal axe back and if your lucky a gold or silver one. If you press Gold axe she will say "You really think I will give you that?" Then a bar will appear; up is yes, down is no. The Silver Axe option still needs input.
This can be done once per day. Be careful, sometimes she might not have either a Golden Axe or a Silver Axe. Fortunately, she will give you back your regular axe.
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The possibility that you have to befriend serina may be why it's difficult to get the axes. Good luck fellow rare Axe Hunters. XD
(I'm still working on mine too...)