Brain Teasers
Murder on the ABC Express
The ABC Express pulled out of the station late one night and began its winding journey up the coast to its destination under heavy darkness. Owing to the late hour, there were only a handful of passengers aboard the small train. At the stroke of midnight, the lights illuminating the interior of the two cars were suddenly extinguished. When they flicked back to life a few moments later, the passengers were alarmed to see one of their number lying on the ground motionless.
The conductor phoned the local police department, and though it was very late, the dispatcher assured the worried conductor that they were sending their very best detective. A bit of an eccentric, Detective Y had an usual methodology when it came to solving crimes. Knowing witnesses to be often be mistaken and contradictory, Y made a habit of asking his witnesses to state to him only one fact they remembered clearly and with absolute certainty from the moment the crime took place.
Y wasted no time upon arriving and, after taking a quick overview of the scene, asked each of the ten remaining passengers in turn to state one absolute fact from the moment right before lights went out in the two train cars. His interview notes are as follows:
Ms. S: I was dining with Mr. J.
Mr. G: There were the same number of men and women in my car.
Mr. J: Mr. K was not in the dining car.
Ms. L: Mr. Q had just entered my car.
Mr. F: Ms. W and Ms. P were talking to one another in hushed tones.
Mr. R: Mr. G was not in the passenger car.
Mr. Q: There were fewer women in my car than the other.
Ms. P: Ms. L was not in the same car as me.
Mr. K: Ms. P was in the passenger car.
Ms. W: Mr. F was avoiding Mr. R and hiding behind a newspaper in the opposite car.
The bewildered conductor watched as Detective Y completed his interviews, scribbled a few more lines in his notes, and turned to announce he had solved the case.
"But surely you can't have figured out the identity of a murderer simply from a list of seating arrangements?" the conductor protested. "You haven't even been told in which car the victim was seated!"
"To the contrary, my good man," the detective answered placidly. "It is the curse of a criminal that he must answer any question regarding the crime he has committed with a lie. The innocent tell only truths, but the lone murderer has been betrayed by his testimony."
Who did Detective Y arrest?
The conductor phoned the local police department, and though it was very late, the dispatcher assured the worried conductor that they were sending their very best detective. A bit of an eccentric, Detective Y had an usual methodology when it came to solving crimes. Knowing witnesses to be often be mistaken and contradictory, Y made a habit of asking his witnesses to state to him only one fact they remembered clearly and with absolute certainty from the moment the crime took place.
Y wasted no time upon arriving and, after taking a quick overview of the scene, asked each of the ten remaining passengers in turn to state one absolute fact from the moment right before lights went out in the two train cars. His interview notes are as follows:
Ms. S: I was dining with Mr. J.
Mr. G: There were the same number of men and women in my car.
Mr. J: Mr. K was not in the dining car.
Ms. L: Mr. Q had just entered my car.
Mr. F: Ms. W and Ms. P were talking to one another in hushed tones.
Mr. R: Mr. G was not in the passenger car.
Mr. Q: There were fewer women in my car than the other.
Ms. P: Ms. L was not in the same car as me.
Mr. K: Ms. P was in the passenger car.
Ms. W: Mr. F was avoiding Mr. R and hiding behind a newspaper in the opposite car.
The bewildered conductor watched as Detective Y completed his interviews, scribbled a few more lines in his notes, and turned to announce he had solved the case.
"But surely you can't have figured out the identity of a murderer simply from a list of seating arrangements?" the conductor protested. "You haven't even been told in which car the victim was seated!"
"To the contrary, my good man," the detective answered placidly. "It is the curse of a criminal that he must answer any question regarding the crime he has committed with a lie. The innocent tell only truths, but the lone murderer has been betrayed by his testimony."
Who did Detective Y arrest?
Hint
Like any good Detective, Y always assumes everyone he interviews is telling the truth until proven otherwise. He also knows the simplest explanation is always the best. He compares the witness statements until he discovers the scenario that is accurately described by nine truthful witnesses and arrests the liar.Answer
Y began by assuming everyone was telling the truth about each other's location and came up with the following arrangement: S J L Q G R (4 men, 2 women) in the dining car and K P W F (2 men, 2 women) in the passenger car. (R and F are interchangeable in this scenario, but as both are men, the precise position of each is irrelevant to this point.) This contradicted both G's statement that there were an equal number of men and women in his (the dining) car and Mr. Q's claim that fewer women were in one car than the other.Thus, the detective concluded both G and Q were telling the truth and someone was lying about the occupancy. Y reasoned that only one possible configuration could make both men's testimonies true: G, 2 other men, and 3 women in one car and Q, 2 other men, and 1 woman in the other.
Because G and Q had to have been in opposite cars, Y worked back up his witness list to find the lie that had placed Q in the wrong car. He first examined L's statement that she and Q shared the same car. If this alone was the lie, it would leave S J L G R (3 men, 2 women) in the dining car and put K P Q W F (3 men, 2 women) in the passenger car, meaning G and Q's statements still would be inaccurate.
Ms. L must be telling the truth then, and Y instead turned to P's claim, which had placed L (and Q by extension) in the other car. If P was lying, it would mean only S J G R (3 men, 1 woman) were in the dining car and K P L Q W F (3 men, 3 women) were in the passenger car. Again, neither G or Q's statements are met.
Detective Y, now certain Mr. G, Mr. Q, Ms. L, and Ms. P were all telling the truth, backtracked to Mr. K next, who had established P's position. Assuming K a liar, Y was able to place S J P G W R (3 men, 3 women) in the dining car and K L Q F (3 men, 1 woman) in the passenger car.
A prudent man, Y double checked his work by running each remaining statement against his reasoning and stiffened his resolve upon finding K to be the only possible person whose lone lie could make every other witness statement truthful.
Mr. K was arrested and led away to the relief (albeit, slight puzzlement) of the conductor and his passengers.
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