Maybe it wasn't there when you played, but rule 6 states kings cannot attack each other; chess kings can move one square in any direction. Without this rule the puzzle isn't solvable by logic, only trial and error.

Ah this rule is mentioned under “Kings cannot attack each other” (in the chess sense, two Kings cannot be diagonal from one another). I’ve updated the rule to make this a little clearer

I agree, I had the same problem.