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Lewis Carroll: 18 puzzles worth knowing

18 puzzles from Lewis Carroll, each explained in a minute and credited to the original work. Free on Savvy.

• Why logic can never fully force you to accept its own conclusion

  Lewis Carroll imagined the Tortoise refusing to accept a simple logical conclusion from Achilles unless Achilles also wrote down the rule that lets you draw it — and then refusing …

  — Lewis Carroll, What the Tortoise Said to Achilles

• Three barbers and the impossible if-then

  Three barbers, Allen, Brown, and Carr, share a shop that always has at least one of them minding it. Allen is so nervous he never leaves without Brown coming too. A logician tells …

  — Lewis Carroll (Charles Lutwidge Dodgson), A Logical Paradox

• Turn CAT into DOG, one letter at a time, always landing on a real word

  Change one letter at a time — never rearranging, adding or removing letters — so that every intermediate step is itself a real word, until CAT becomes DOG. What's the shortest chai…

  — Lewis Carroll, Doublets: A Word-Puzzle

• A bag, one hidden counter, and a draw that changes the odds

  A bag contains a single counter, known to be either black or white with equal probability. You add one white counter, shake the bag, and draw out a counter at random — it's white. …

  — Lewis Carroll, Curiosa Mathematica, Part II: Pillow Problems

• Three offhand facts about kittens hide one inevitable logical conclusion

  Lewis Carroll loved building chains of odd-sounding premises, called sorites, that hide one inevitable conclusion. Take just three of his: no kitten that loves fish is unteachable;…

  — Lewis Carroll (Charles Lutwidge Dodgson), Symbolic Logic

• Lewis Carroll's Monkey on a Rope

  A rope runs over a frictionless pulley. A weight hangs from one end; a monkey hangs from the other, exactly balancing it. The monkey starts climbing the rope. What happens to the w…

  — Lewis Carroll, The Diaries of Lewis Carroll

• Carroll's Tangled Tale: Two Travelers and a Hill

  In Lewis Carroll's 'A Tangled Tale,' two travelers leave at 3 o'clock and get home at 9, walking a level road, up a hill, and down again. On the level they walk 4 miles an hour, up…

  — Lewis Carroll, A Tangled Tale

• Achilles wins the race easily. Can he ever force the tortoise to admit he's right?

  In Lewis Carroll's 1895 dialogue, Achilles gets the tortoise to accept two premises: 'A: things equal to the same are equal to each other' and 'B: the two sides of this triangle ar…

  — Lewis Carroll, What the Tortoise Said to Achilles

• Why is a raven like a writing desk?

  In Chapter 7 of Alice's Adventures in Wonderland, the Mad Hatter asks Alice this riddle at the tea party — and never gives an answer. Alice guesses, gives up, and the story simply …

  — Lewis Carroll, Alice's Adventures in Wonderland

• Lewis Carroll's chronology puzzle: how old is the lady, exactly?

  In one of Lewis Carroll's puzzle stories, a lady is asked her age. She replies that eight years ago, her age was three times what her son's age would be six years from now, and her…

  — Lewis Carroll, A Tangled Tale

• A bag holds two counters, black or white — Carroll claimed you could find their colors

  Lewis Carroll's final and most argued-over 'pillow problem': a bag contains two counters, each independently either black or white, with no other information given. Carroll offered…

  — Lewis Carroll (Charles Dodgson), Pillow Problems

• Carroll's Cats-and-Rats Trap

  If 6 cats can kill 6 rats in 6 minutes, how many cats does it take to kill 100 rats in 50 minutes? Most people blurt out '100' — Lewis Carroll built this word problem specifically …

  — Lewis Carroll, A Tangled Tale

• A ship sails around the world westward — does it gain a day or lose one?

  In Lewis Carroll's 'A Tangled Tale', a ship's captain explains a puzzle of dates to his passengers: a vessel that circumnavigates the globe travelling west keeps setting its clocks…

  — Lewis Carroll, A Tangled Tale

• Three offhand claims about babies and crocodiles force one inescapable conclusion

  Lewis Carroll offers three statements to accept as true: all babies are illogical; nobody who can manage a crocodile is despised; and all illogical people are despised. Taking all …

  — Lewis Carroll (Charles Lutwidge Dodgson), Symbolic Logic

• Two rivals race opposite ways around a circular railway

  In Lewis Carroll's 'A Tangled Tale,' an aunt and her niece each board a train circling the same loop line in opposite directions — one direction takes 3 hours to complete the circu…

  — Lewis Carroll, A Tangled Tale

• A stopped clock vs. one losing a minute a day — which is right more often?

  You're offered two broken clocks. One has stopped completely and never moves at all. The other still runs, but loses exactly one minute every day. If what matters is how often a cl…

  — Lewis Carroll (Charles Lutwidge Dodgson), The Rectory Umbrella

• A dinner party guest list that only makes sense with one guest

  A man wants to host 'a very small dinner party' and invites his father's brother-in-law, his brother's father-in-law, his father-in-law's brother, and his brother-in-law's father. …

  — Lewis Carroll, A Tangled Tale

• Scatter Three Random Points — Is the Triangle Obtuse?

  Lewis Carroll posed this one while lying awake at night: scatter three points completely at random on an infinite flat plane. What is the chance that the triangle they form is obtu…

  — Lewis Carroll (Charles Lutwidge Dodgson), Pillow Problems

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