CLUE
This somewhat grim puzzle was created for us by Vladimir V. Zelevinsky - thanks a lot!
I've never seen Sherlock Holmes in such distress.
Pale, disheveled, and unshaved, he was pacing in circles around our living room, muttering, "But if Professor Plum... no. What if the conservatory... but then if the candlestick... no. No. No!"
"A difficult case, Holmes?" I asked, commiserating.
"This is the most uniquely challenging problem in my experience," he groaned.
"Sorry to hear this," I said. "Not enough clues?"
"The number of clues is exactly what makes this case absolutely and entirely unique!" he said. "But it's not that I don't have enough clues. I have too many!"
"Are they... unreliable?" I ventured a guess.
"No," said Holmes.
"Are they contradictory?"
"No," sighed Holmes, "that's not the difficulty, either. Perhaps I should describe this remarkable case to you in an orderly fashion."
I sat down and got ready to listen.
"A murder was committed," said Holmes. "There are six suspects. Here are their names."
Miss Scarlett
Mr. Green
Colonel Mustard
Professor Plum
Mrs. Peacock
Mrs. White
"This is straightforward so far," I said.
"That won't be the case for long," said Holmes darkly. "There are nine possible locations where the murder could have taken place."
ballroom
kitchen
conservatory
dining room
billiard room
library
hall
lounge
study
"Wait," I said, "how can it not be known where the murder occurred??"
Holmes waved his hand. "I don't think that is important, Watson. Perhaps the body was moved. Finally, there are six possible murder weapons."
candlestick
knife
lead pipe
revolver
rope
wrench
"But, Holmes!" I exclaimed. "I accepted your statement that the location of the murder might be unknown, but I cannot accept that there could be any confusion about the murder weapon! I'm an army doctor! A body, shot from a revolver, is very different from a body, strangled with a rope!"
Holmes glared at me with more than a touch of irritation. "Don't be nitpicky, Watson. Think of the body as being hideously mangled if that helps you sleep better. In any case, Scotland Yard sent Inspector Gregson to investigate. What Gregson lacks in imagination, he compensates for with his bulldog-like tenacity. He spent a week at the scene of the crime, gathering clues. He gathered 99 clues. Ninety-nine, Watson! I have enough knowledge of his dedication and professionalism to trust that each of his clues is correct. We also know that only a single culprit, a single location, and a single weapon were involved. Here're all the clues; take a look."
"One moment," I said, glancing at the somewhat daunting list of clues (your puzzle input). "Each one of these clues logically connects a suspect, a weapon, or a location with another suspect, weapon, or a location! These clues are extremely useful!"
"Are they, Watson?" asked Holmes, shrugging. "Perhaps an example is in order. Let's say, the clue is If the culprit is Colonel Mustard, then the weapon is the revolver. What would you deduce from this statement?"
"Well..." I said. "I would deduce... that if the culprit is Colonel Mustard... then the weapon is the revolver."
"A truly brilliant deduction, Watson," said Holmes bitterly. "And what if the culprit is not Colonel Mustard?"
"Then," I said, "the weapon is not the revolver. That is also useful information."
"No!" exclaimed Holmes. "No, a thousand times no! You cannot conclude that! A statement of the form If A, then B. is called a logical implication. Yes, if A is true, then B is also true. But if A is false, then you cannot make any conclusions regarding B. If the culprit is not Colonel Mustard, the weapon might be the revolver, or it might not be the revolver. The clue doesn't tell us either way."
"But..." I said weakly, "every single clue on this list is a logical implication. Each one requires the knowledge we don't have. This is all circular logic. Does this mean they are all useless?"
"Why do you think I've been pulling on my hair for hours!" said Holmes. "What am I supposed to make out of this clue?! And this clue! And..."
He froze in the middle of his sentence, staring at the list of clues. For five seconds, everything was silent at 221B, Baker Street.
Then Holmes unfroze. "Perhaps," he muttered, "these are not quite as useless as I thought."
His eyes flashed and he turned toward me with a grin.
"Thank you, Watson," he said. "Your help was invaluable."
"How... how did I help?" I stammered.
"Sometimes, the mere act of carefully explaining the problem focuses one's mind on the constraints," said Holmes. "Perhaps you could take another look at the clues and solve the mystery yourself? Naturally, since your brain isn't quite as, umm, efficient as mine, you should use your computation engine. Your solution should be expressed as a single English sentence of the form Culprit, in the location, with the weapon. Please use the correct capitalization and punctuation of the culprit's name (as given in the list above) and don't forget the commas and the trailing period."
Here are a few examples of correctly-phrased solutions:
Miss Scarlett, in the billiard room, with the wrench.
Professor Plum, in the dining room, with the candlestick.
Mrs. Peacock, in the lounge, with the lead pipe.