Q:

$1$ of $100$ Homes

On Crossfield Housing Estate, there are exactly $100$ homes numbered from $1$ to $100$. Rook is living in one of them. Kaito hasn't met with him for a long time and wants to pay a visit. Here is some transcripts of their call.

Rook : ".. Haha.. Yep, it's been a while.. You are welcomed to visit my home tomorrow."
Kaito : "Seriously? Alright I'll come tomorrow morning! But.. I guess I forgot which number is your house, ahaha."
Rook : "Well, in that case, let's play a puzzle!"  
Kaito : "Hmm.. Is the number more than $50$?"
Rook answers with either yes or no.
Kaito : "Is it a square number?"
Rook answers with either yes or no.
Kaito : "Hmm.. Is it an odd number?"
Rook answers with either yes or no. 
Kaito : "Is the number.."
Rook: "Hey, hey, enough, haha."
Kaito : "Huh? I'm still clueless Rook.."
Rook : "Haha, I thought you still remember that Freecell is also living in this estate and you know his number. All of these information will be perfect for you to figure out my number."
Kaito : "Oh! I remember now! I remember his home number and it must be greater than yours, right?"
Rook : "Haha, I know you will get it! See you, I'll prepare a nice breakfast for you if you want."
Kaito : "Yosh! Thanks and see you too!"

So on which number is the Rook's home?

A:

I think the answer is   

 Rook's home is number $64$

Reasoning

 If house # were less than $50$ there would have been no way for Kaito to figure it out from the following 2 questions - there are 4 odd squares ($1, 9, 25, 49$) and 3 even squares ($4, 16, 36$).

 So the house # is more than $50$. It also has to be a square. Once again it would have been impossible for Kaito to figure it out otherwise.

 That leaves Kaito with three choices ($64, 81, 100$).

 If the house # were odd, Kaito would not have asked any more questions, but he still was not sure. So the house # must be even.

 Then Kaito remembers that Freecell's house has a bigger number than Rook's house. This leaves $64$ as the only possible number.

A:

I think I found more possible solutions. All of them are compatible with the puzzle, though it wouldn't make a lot of sense for Kaito to ask for the number, yet.

 no, yes, yes, Kaito 1, Freecell 2-9
 no, yes, no, Kaito 4, Freecell 5-16
 no, no, yes, Kaito 1, Freecell 2 or 3
 no, no, no, Kaito 2, Freecell 3 or 4
 yes, yes, no, Kaito 64, Freecell 65-100
 yes, no, yes, Kaito 51, Freecell 52 or 53
 yes, no, no, Kaito 52, Freecell 53 or 54

