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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Comments
Excellent teaser.
I am curious, however, about your feelings concerning the fact that are so few comments and votes about your hard work in making this contribution.
I think the health of Braingle is in jeopardy and those of us who care enough should do something about it.
Your response?
LGM
I am curious, however, about your feelings concerning the fact that are so few comments and votes about your hard work in making this contribution.
I think the health of Braingle is in jeopardy and those of us who care enough should do something about it.
Your response?
LGM
The oldest teasers on this site have been here 15 years and counting. I wouldn't put too much stock in how any of them spent their first few days but rather hope to be judged on how my contributions, like their predecessors, stand the test of time. Whether it's today, tomorrow or ten years down the road, I do hope the Braingle community rebounds with vigor. I appreciate your words and hope others will build on them.
Loved it!! Thought I had it, but turns out I didn't double check every statement. Great teaser--I'm going to have to look at it again
This teaser was very interesting. It gave me a run for my money, but was not impossible to solve. Thank you, OP, for putting so much time into this teaser!
Nice one!
Dear tedger,
I am sorry to say your riddle is flawed and your solution is incorrect.
It seems that in your solution logic you considered only the 10 surviving passengers and forgot about the victim, who was also in one of the cars and could be either a man or a woman.
Taking this into account, there are 3 possible suspects (I won't tell who they are), each with a corresponding configuration of passengers and complying with the requirement that only the murderer is lying. I also assumed that the victim was in the same car as the murderer, otherwise there are more than 3 possible suspects.
But hey, it was fun anyway
I am sorry to say your riddle is flawed and your solution is incorrect.
It seems that in your solution logic you considered only the 10 surviving passengers and forgot about the victim, who was also in one of the cars and could be either a man or a woman.
Taking this into account, there are 3 possible suspects (I won't tell who they are), each with a corresponding configuration of passengers and complying with the requirement that only the murderer is lying. I also assumed that the victim was in the same car as the murderer, otherwise there are more than 3 possible suspects.
But hey, it was fun anyway
Yes, as shalmak says, I worked out the initial positions of everyone, and then noted that adding a female victim in the passenger car makes Q's statement true and leaves G as the murderer without moving any of the known passengers around. That does mean the murderer and victim are in opposite cars before the lights go out, though.
there is a huge mistake. read the first prara of answer careflly
As you probably know, I posted no less than FIVE logic teasers. You should totally check them out.
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