Having watched again "Heaven Sent" (Doctor Who) last night, I
  wanted to share the story: "The Shepherd Boy" by the brother's
  Grimm. After you read it, I'd like to see some interesting
  answers to some impossible questions. It engages a different
  style of logic than you may be accustomed to, unless you already
  are accustomed to this style of logic presentation. ==== THE
  SHEPHERD BOY.
  There was once on a time a shepherd boy whose fame spread far
  and wide because of the wise answers which he gave to every
  question. The King of the country heard of it likewise, but did
  not believe it, and sent for the boy. Then he said to him, "If
  thou canst give me an answer to three questions which I will ask
  thee, I will look on thee as my own child, and thou shalt dwell
  with me in my royal palace." The boy said, "What are the three
  questions?" The King said, "The first is, how many drops of
  water are there in the ocean?" The shepherd boy answered, "Lord
  King, if you will have all the rivers on earth dammed up so that
  not a single drop runs from them into the sea until I have
  counted it, I will tell you how many drops there are in the
  sea." The King said, "The next question is, how many stars are
  there in the sky?" The shepherd boy said, "Give me a great sheet
  of white paper," and then he made so many fine points on it with
  a pen that they could scarcely be seen, and it was all but
  impossible to count them; any one who looked at them would have
  lost his sight. Then he said, "There are as many stars in the
  sky as there are points on the paper; just count them." But no
  one was able to do it. The King said, "The third question is,
  how many seconds of time are there in eternity?" Then said the
  shepherd boy, "In Lower Pomerania is the Diamond Mountain, which
  is two miles and a half high, two miles and a half wide, and two
  miles and a half in depth; every hundred years a little bird
  comes and sharpens its beak on it, and when the whole mountain
  is worn away by this, then the first second of eternity will be
  over." The King said, "Thou hast answered the three questions
  like a wise man, and shalt henceforth dwell with me in my royal
  palace, and I will regard thee as my own child."