I notice that the blog post content appears to be incomplete. Only the title "AT, BAT, and CAT" and a brief introduction mentioning it was posted by Konstantin Knop on Facebook are provided, but the actual mathematical content of the puzzle and its solution are missing.
Could you share the full content of the blog post? Once I have the complete text, I'll be happy to write a clear and engaging 3-paragraph summary for mathopen.com.