Many thanks to Vladimir V. Zelevinsky for this new "chapter" of the Holmes & Watson story!
"It appears," said Sherlock Holmes one evening, "that none of my poultry is an officer."
I dropped the book I was reading with a heavy thud.
"Holmes," I said, "I must again protest your deplorable habit of injecting yourself with experimental chemicals just to see how they affect your brain!"
Holmes laughed.
"This is not the case this time, Watson," he said. "I was merely recalling my conversation with my friend Lewis Carroll..."
"One moment," I said. "Such a person doesn't exist. Lewis Carroll is merely the pen name of Charles Dodgson, an Oxford professor of mathematics, who -"
"Lewis Carroll," said Holmes severely, "is exactly as real as you and I, Watson. But in one way you are correct: it is his research in mathematical logic that formed the topic of our discussion. After all, my deductive method is nothing but a chain of logical conclusions."
"I fail to see what this has to do with poultry," I remarked.
"Ah, that," said Holmes. "This comes from a logical challenge that Carroll had set before me. His term for it
is sorites."
"What are those?"
"Is, not are, Watson; the word is singular, not plural. Sorites is a logical problem that consists of a list of logical implications - similar to those from one of our recent adventures - that you must combine to arrive at a particular conclusion. I was thinking of one of Carroll's sorites that goes as follows."
No ducks waltz.
No officers ever decline to waltz.
All my poultry are ducks.
"To make the implications clear, Watson, we can rewrite these statements like this."
Of those who are ducks, none waltz.
Of those who are officers, all waltz.
Of those who are my poultry, all are ducks.
"What can you conclude from these statements?"
"I can conclude many things," I said. "For example, I can come up with a somewhat obvious statement that of your poultry, none waltz."
Holmes shook his head.
"While this is correct, Watson," he said, "this is not the proper solution of this particular sorites. The correct solution must utilize every single statement."
I stared at the three statements until my head was full of waltzing ducks.
"Well," I said eventually, "I guess I can agree with your initial statement.
Of those who are my poultry, none are officers."
"Or?" asked Holmes.
"Or...?" I repeated in confusion.
"Every logical implication can be flipped into its
contrapositive. For example, the first statement of the sorites
above is equivalent to Of those who waltz, none are ducks."
"In this case," I said, "Of those who are officers, none are my poultry."
"This is correct," said Holmes. "That, of course, was an elementary exercise with only three statements. Carroll has written some sorites that have up to twenty statements..."
"Twenty statements!" I exclaimed in horror. "I had enough trouble with three!"
"...so, naturally," continued Holmes, ignoring my interjection, "I've come up with some that have thirty.
Can you solve one of mine? Make sure to provide the answer that uses every single statement given in the puzzle
input. Please phrase your solution as a single sentence in the same format as the statements that make up the
sorites; you will notice that there are four different types. Both the logical conclusion and its
contrapositive will be accepted as valid answers. If you need more help, feel free to consult this
extremely educational analysis of Carroll's logical puzzles."
Here is a little example with only three statements:
input data:
Of those who do not eat apples, all like summer.
Of those who like summer, none make soup.
Of those who ride horses, none eat apples.
answer:
Of those who ride horses, none make soup.
alternative answer:
Of those who make soup, none ride horses.
And another one:
input data:
Of those who play tennis, none visit cafes.
Of those who do not collect books, none know your uncle.
Of those who do not play tennis, all know your uncle.
answer:
Of those who visit cafes, all collect books.
alternative answer:
Of those who do not collect books, none visit cafes.