Have you heard about Lewis Carroll's unsolvable riddle?
Yes, the riddle is proposed by the Mad Hatter during a tea party in the book.
Apparently Caroll had dozens of riddles throughout his life, he was a mathematician at Christ church College 
He was a very clever author. While initially the unsolvable riddle had no answer, in his updated version of the book he provided an answer to the riddle.
I think it was one of history's toughest riddles. If it took over 100 years to solve!
Many believe that the "raven" in Carroll's unsolvable riddle is actually an allusion to the Liddells' Ravensworth Estate, which served as Carroll's writing space while working on Alice in Wonderland.
Your referring to the line "a writing-desk"? Brilliant to incorporate  that into the story.
Yes, although it is only lore, I feel that it could be connected. Have you read the book before?
I've only seen the movie, but I know about Carroll's riddles. I'm somewhat of a mathematician at University, and Carroll was also a mathematician. 
Which movie adaptation have you seen? 
The Disney adaption with Johnny Depp. I saw it when I was younger. I think it was a pretty good adaption.