Sunday, June 8, 2014

Impossible Things Before Breakfast

Literary works by Charles Lutwidge Dodgson (1832-1898, aka Lewis Carroll) are crammed with mentions of mathematics.   One of my favorites (found here with numerous others, including "Ambition, Distraction, Uglification, Derision") is this exchange from Carroll's Alice in Wonderland.

          "Alice laughed: "There's no use trying," she said; "one can't believe impossible things."
          "I daresay you haven't had much practice," said the Queen.  "When I was younger, I always did it for half an hour a day.  Why, sometimes I've believed as many as six impossible things before breakfast."

                                                                                       Alice in Wonderland 

     This morning, while browsing the collection Imaginary Numbers:  An Anthology of Marvelous Mathematical Stories, Diversions, Poems, and Musings edited by William Frucht (Wiley, 1999), I found this poem (by Anonymous) that also has fun with the impossible.

     Ten Weary, Footsore Travelers

      Ten weary, footsore travelers
          All in a woeful plight,
      Sought shelter at a wayside inn
          One dark and stormy night.

    "Nine rooms, no more," the landlord said
          "Have I to offer you.
     To each of eight a single bed,
          But the ninth must serve for two."

      A din arose. The troubled host
          Could only scratch his head,
     For of those tired men no two
          Would occupy one bed.

     The puzzled host was soon at ease --
          He was a clever man  
     And so to please his guests devised
          This most ingenious plan.

     In room marked A two men were placed,
          The third was lodged in B,
     The fourth to C was then assigned,
          The fifth retired to D.

     In E the sixth he tucked away,
          In F the seventh man.
     The eighth and ninth in G and H,
          And then to A he ran,

     Wherein the host, as I have said,
          Had laid two travelers by;
     Then taking one -- the tenth and last --
          He lodged him safe in I.

     Nine single rooms -- a room for each --
          Were made to serve for ten;
     And this it is that puzzles me
          And many wiser men.

In The Worlds of David Darling, we find reference to this puzzle as the "nine rooms paradox" and it is compared to the puzzle of the missing dollar.

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