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I have read some theories that maybe it wasn't actually Arya, that it was Jaqen using her face somehow to see if the Waif would do as she was told, but I really can't see the show doing all that, it would probably confuse quite a bit of people.

 

This was something that came to my mind. Jaqen told the Waif she could kill Arya but not make her suffer. So Jaqen puts on Arya's face and strolls around like there's nothing wrong and the Waif finds her and stabs her. It a test for the Waif, not Arya. Arya wouldn't be that clueless and as you said, where was Needle? Jaqen didn't know about Needle so he wouldn't have been able to somehow have a similar sword or at least the illusion of one.


In the end the Waif failed the test. It will be interesting to see what the punishment will be and what all of this means for Arya.

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