There are actually 2 questions: how do we know castling is theoretically permissible [ie neither King nor Rook have yet moved] AND whether it's legal under the current conditions?
To answer the first question, it's assumed to be permissible unless it can be proven otherwise.
The second question: castling is legal if
- neither King nor Rook have previously moved
- the King is not currently in check
- the King will not pass through check
- the King does not end up in check
- there are no pieces of either side in between King and Rook
Note that nowhere is the Rook involved in the castling mentioned; it's irrelevant.
So, in the below position, castling [long] is legal because the KING does not pass through nor end up, on b1. The fact that the Rook had to pass through b1 is irrelevant.
Here's an analogy:
Let's say there's a guy who lives on Elm street at #1. Call him, I don't know, Mr. King.
There's another guy who lives on Acacia street at #1. Call him Mr. Rook.
In between the two streets are Beech, Cedar, and Dogwood.
Mr. King wants to get to Cedar and Mr. Rook wants to get to Dogwood.
Beech street is locked but Mr. Rook has a key so he can get through.
Mr. King does not have a key but it doesn't matter because he doesn't need to reach or pass Beech street.
That's why castling is legal in the puzzle.
There are actually 2 questions: how do we know castling is theoretically permissible [ie neither King nor Rook have yet moved] AND whether it's legal under the current conditions?
To answer the first question, it's assumed to be permissible unless it can be proven otherwise.
The second question: castling is legal if
Note that nowhere is the Rook involved in the castling mentioned; it's irrelevant.
So, in the below position, castling [long] is legal because the KING does not pass through nor end up, on b1. The fact that the Rook had to pass through b1 is irrelevant.
Here's an analogy:
Let's say there's a guy who lives on Elm street at #1. Call him, I don't know, Mr. King.
There's another guy who lives on Acacia street at #1. Call him Mr. Rook.
In between the two streets are Beech, Cedar, and Dogwood.
Mr. King wants to get to Cedar and Mr. Rook wants to get to Dogwood.
Beech street is locked but Mr. Rook has a key so he can get through.
Mr. King does not have a key but it doesn't matter because he doesn't need to reach or pass Beech street.
That's why castling is legal in the puzzle.