What were Alluka's first three wishes from Killua (after reunion)? It is stated that Alluka made 3 wishes, but I counted 4 of them. Which of the ones I counted is discarded? What are the 3 wishes exactly?

1) "Die."



2) "Wake up."



3) "Play Shiritori with me."



4) "Pat my head."



But they count the wishes as 3 only.
Remember that when Alluka requests something, she can't force it to happen. Like when they Alluka was a kid, and wanted something, she couldn't force the other person to do it. They simply fulfilled her request, whenever they could (except when Alluka's parents forbade them from doing so).

Killua and Alluka definitely played shiritori together, and when Alluka said "wake up," this was a request he fulfilled, since he was "sleeping". Lastly, we definitely saw Killua pat her head.

It seems that the family observed that Killua did not grant Alluka her request of, "Die." He simply said, "Okay, sure," pretended to die, and made her laugh in the process. But he did not actually do anything to harm himself. This allowed them to think that exactly three requests had been performed.





Note: In reality, the reason that the requests work this way is explained in a very convoluted and expository manner in episode 146.

From what I can understand, there is a difference between when Alluka makes a request and when Something makes a request. The two are different, and "wishes" can only be fulfilled by actualizing requests from Something. However, the initial "wish" we see Killua make is not a "wish", it's a "command", so it doesn't count as a wish. Confused? Good, me too.



So in reality, since Killua was with Alluka, he was not in any danger of receiving requests. (I feel like this contradicts earlier flashbacks, but that's just a matter of Togashi's writing being, er... poor.)

However, since the original question is about why the Zoldyck family thought it was three requests, the above answer remains true. (Edited a small bit to reflect this.)