Can You Solve the Train Riddle About the Engineer's Identity?

[Sartradjm]

On a train, Smith, Robinson, and Jones are the fireman, brakeman, and the engineer, but NOT respectively. Also aboard the train are three businessmen who have the same names: a Mr. Smith, a Mr. Robinson, and a Mr. Jones.

Mr. Robinson Lives in Detroit.

The brakeman lives exactly halfway between Chicago and Detroit

Mr. Jones earns exactly $20,000 per year.

The brakeman's nearest neighbor, one of the passengers, earns exactly three times as much as the brakeman.

Smith beats the fireman in billiards.

The passenger whose name is the same as the brakeman's lives in Chicago.

Who is the Engineer?

 

[ƒ(x)]

Spoiler

Smith

T:5

On second thought...is there enough info?
I need clarification, are Smith, Robinson, and Jones passengers, or are they running the train?

 

[Sartradjm]

Spoiler

Smith

T:5

On second thought...is there enough info?
I need clarification, are Smith, Robinson, and Jones passengers, or are they running the train?

Smith, Robinson, and Jones are running the train, Mr. Smith, Mr. Robinson, and Mr. Jones are passengers.
And yes, there is enough info.

 

[ƒ(x)]

In that case, it's the person I mentioned

 

[Sartradjm]

You are right.

 

[HawkLogic]

Note that "Smith beats the fireman in billiards." is redundant.

 

[Sartradjm]

Note that "Smith beats the fireman in billiards." is redundant.

I know what you meant. And you are right. Instead of "but NOT respectively" should be "but NOT necessarily respectively".

 

[davee123]

I remember this problem from years ago, and the thing that always bothered me was the salary bit. Technically speaking, it doesn't say that the brakeman earns an annual salary-- it just says he earns 1/3 of one of the passenger's salaries. So it's entirely possible that (say) he's paid once every 3 years. Or that (given our modern crazy technology) that his earnings aren't fully monetary, or are otherwise capable of being precisely 1/3 of a penny (different currency, perhaps?). Anyway, the mathematician in me says that it's got to be AMAZINGLY explicit in order to prevent 20,000 from being divisible by 3.

DaveE

 

[HawkLogic]

I remember this problem from years ago, and the thing that always bothered me was the salary bit. Technically speaking, it doesn't say that the brakeman earns an annual salary-- it just says he earns 1/3 of one of the passenger's salaries. So it's entirely possible that (say) he's paid once every 3 years. Or that (given our modern crazy technology) that his earnings aren't fully monetary, or are otherwise capable of being precisely 1/3 of a penny (different currency, perhaps?). Anyway, the mathematician in me says that it's got to be AMAZINGLY explicit in order to prevent 20,000 from being divisible by 3.

DaveE

Even in mathematics it is not possible to be as explicit as your rebuttal requires. Even mathematicians presume an understanding that everyone in the discussion is speaking the same language and using the same grammar and dictionary to do so.

 

[davee123]

Even in mathematics it is not possible to be as explicit as your rebuttal requires.

Rawr!

I'm not saying I think you did a poor job wording it, I'm just saying that's a problem I had with the original wording, which I didn't like back when I read it years ago.

Anyway, I think I'd be happy with:

"Mr. Jones earns exactly $20,000 USD per year."

and:

"The brakeman's nearest neighbor, one of the passengers, earns exactly three times as much per year as the brakeman does annually, who is completely paid in legal USD cash."

Going for the utterly absurd, you could expand "USD" into "United States of America Dollars", and explicitly specify that we're talking about Earth years. But that's going too far even for me.

But really, for the sake of elegance, if I were writing the problem I think I'd opt to choose a different criteria rather than money being divisible by 3. It's the same deal (to a lesser extent, I think) with the "Einstein" puzzle that keeps swinging around. The puzzle is constructed such that the common interpretation of the language is sufficiently clear, but it's susceptible to interpretations that can make the problem unsolvable or solvable with different conclusions.

DaveE

 

[HawkLogic]

Rawr!

But really, for the sake of elegance, if I were writing the problem I think I'd opt to choose a different criteria rather than money being divisible by 3. It's the same deal (to a lesser extent, I think) with the "Einstein" puzzle that keeps swinging around. The puzzle is constructed such that the common interpretation of the language is sufficiently clear, but it's susceptible to interpretations that can make the problem unsolvable or solvable with different conclusions.

DaveE

The problem is "sufficiently clear" but "unsolvable"? If you understand how to read puzzles then it is not ambiguous. There is no such thing as a puzzle which cannot be quibbled into complete incoherence. Using straightforward common sense and logic this problem leads to a single answer, which is a good definition of "unambiguous". You are confusing riddles with lateral thinking problems, which are generally solved by finding an intentional ambiguity.

 

[davee123]

The problem is "sufficiently clear" but "unsolvable"?

I didn't say that. I said it's sufficiently clear for common interpretation of the language. Effectively, that for some given percentage of people who read the problem (I don't know what that percentage would be), it's fine. But for that other percentage, it isn't.

Here's the sticky point: if you give this to a group of regular people, you probably won't get any rebuttals. BUT, if you give this to a group of people who are explicitly interested in picking apart word problems and finding creative solutions to them (FWIW, there are a bunch of those people on these forums), I think you may find that some of them don't like it.

I mean, besides my comment, you already commented on the fact that it explicitly states "but NOT respectively", when the author CLEARLY meant "but not necessarily respectively". Again, you could give this to MOST people, and they'd understand perfectly well what was intended, and they wouldn't quibble about such a petty detail when the intent of the writing was obvious. Supposing for a moment that the author had accidentally written the first sentence as:

"On a train, Smith, Robinson, and Jones are the brakeman, fireman, and the engineer, but NOT respectively."

Wouldn't it be painfully obvious to you (like it would be to me) that the author accidentally mistyped that first sentence? Common sense says to me that they meant "not necessarily respectively", but as an aside, I would acknowledge that it's really incorrect.

DaveE

 

[HawkLogic]

It seems here that "picking apart word problems" is the opposite of "finding creative solutions."
Anyway, you note that regular people don't offer rebuttals, so you exempt yourself from that group. And you didn't offer a solution so you exempt yourself from the group of creative problem solvers. You seem to place yourself right in the middle of the obtuse quibblers
But how hard is it to pick apart a word problem and offer a solution?
I'll gave it a try.
1. Sometimes the OP refers to characters with "Mr", and other times he doesn't.
How can we be sure which Smith he is talking about?
2. He identifies three businessmen and other passengers.
Why should we assume these are the same characters?
3. Smith beats the fireman in billiards?
So do they live in the same city or know each other?
4. Which Omaha and Detroit is the OP referring to and does it matter?
5. In "Who is the Engineer?" note that "Engineer" is capitalized. Maybe this is a clue to the true answer:
The Engineer is ... "The person who is driving the train."
6. And many others.
That took about 60 seconds.

 

[davee123]

It seems here that "picking apart word problems" is the opposite of "finding creative solutions."

How would those be opposite? That would imply somehow that those that pick apart word problems don't find creative solutions? I tend to find that the two are often closely related-- when you pick apart word problems, you're finding creative ways in which the problem is in error. Essentially, you're thinking outside the box by attempting to interpret the problem in many different ways. Often, that's the way towards obtaining a solution.

Anyway, you note that regular people don't offer rebuttals, so you exempt yourself from that group. And you didn't offer a solution so you exempt yourself from the group of creative problem solvers.

Wait, what? I understand the first point, and I agree. I frequently offer observances about word problems when I find them to be lacking. But I exempt myself from the group of creative problem solvers because I didn't offer you an answer to this particular problem? I've answered plenty of problems here-- sometimes creatively, sometimes as intended. I've also come up with my own original creative puzzles and offered them here. It's silly for you to proffer that assessment with just such a limited scope.

But how hard is it to pick apart a word problem and offer a solution?
I'll gave it a try.

You already did that. You decided to pick apart the problem by saying "Note that 'Smith beats the fireman in billiards.' is redundant. " And you similarly didn't offer a solution. I guess I'm just surprised you're being so hypocritical. You quibbled, I quibbled. And I fully admit that your initial critique is more noteworthy (because I think it's a problem in the restatement of the puzzle rather than with the underlying puzzle itself). But I don't see how me offering my recollection of the problem and a critique I noticed years ago ought to be any less applicable than your critique of the problem.

If you think that my critique crosses the line of being picky, then that's fine-- you could've just said so, and that'd be fine. But you went and told me that it was impossible to satisfy me, which was incorrect. And now you're just being defensive-- are you new to the internet?

DaveE

 

[HawkLogic]

How would those be opposite? That would imply somehow that those that pick apart word problems don't find creative solutions? I tend to find that the two are often closely related-- when you pick apart word problems, you're finding creative ways in which the problem is in error. Essentially, you're thinking outside the box by attempting to interpret the problem in many different ways. Often, that's the way towards obtaining a solution.
DaveE

The problem is not in error.
Your interpretations offered no alternatives to a problem which had a solution.
It would be creative to find a heretofore unknown solution within the box.

Wait, what? I understand the first point, and I agree. I frequently offer observances about word problems when I find them to be lacking. But I exempt myself from the group of creative problem solvers because I didn't offer you an answer to this particular problem? I've answered plenty of problems here-- sometimes creatively, sometimes as intended. I've also come up with my own original creative puzzles and offered them here. It's silly for you to proffer that assessment with just such a limited scope.
DaveE

I limited my scope of assessment to the limited scope of your analysis.

You already did that. You decided to pick apart the problem by saying "Note that 'Smith beats the fireman in billiards.' is redundant. " And you similarly didn't offer a solution. I guess I'm just surprised you're being so hypocritical. You quibbled, I quibbled. And I fully admit that your initial critique is more noteworthy (because I think it's a problem in the restatement of the puzzle rather than with the underlying puzzle itself). But I don't see how me offering my recollection of the problem and a critique I noticed years ago ought to be any less applicable than your critique of the problem.
DaveE

My point was merely informational, a point of interest. Your quibbling claims there is a issue which affects solvability.
Again, there is no error or ambiguity.

And now you're just being defensive-- are you new to the internet?
DaveE

The connection you make between defending an opinion and inexperience on the internet implies that the internet is a place to expect andor accept offending comments.
My experience goes back to before it was called the internet.

 

[davee123]

Your interpretations offered no alternatives to a problem which had a solution.
It would be creative to find a heretofore unknown solution within the box.

I still don't get it-- you're attacking me for not having been creative? What's the big deal if I wasn't creative? Should your point about redundancy have been required to be creative in order to warrant posting?

My point was merely informational, a point of interest. Your quibbling claims there is a issue which affects solvability.

I beg to differ. My point was a point of interest, which I agree is probably of less interest. My point happened to involve whether or not the problem was solvable, yours didn't.

My point was basically that when I read the problem, I noted that there were only two clues dealing with money, and given their nature, the implication was that 20,000 is not divisible by 3. As a picky sort of person, I saw what the intention was, but I didn't like the implication that a real number wasn't divisible by another real number.

There are ways around it-- like using the word "evenly" (as in "is 20,000 evenly divisible by 3?") which is an accepted means of stipulating an integer-based quotient. Similarly, explicitly stating that integers are required would work equally well.

In the problem, I agree that such a requirement is difficult to work into the problem elegantly, so I'm left with a nagging annoyance in my mind that the problem isn't as clear as I'd like it to be. So I stated that I didn't like the way it was worded. If I had had an elegant way of rephrasing the problem, I probably would have suggested it. I can think of a few other ways of making the stipulation so that it doesn't leave that splinter of annoyance in my mind-- I even proffered one when seemingly prompted to-- but I haven't hit on one that's similarly as elegant as the problem intends.

Anyway, I don't think that the fact that such an interpretation would make the problem unsolvable makes the observation inapplicable or not suitable for posting.

But I think what disappointed me most is that you seemingly were telling me that it was impossible to satisfy me. You could have said that I was being too picky (which is a perfectly valid rebuttal), or that what I said was too minor of a detail to warrant posting (which is an issue for the moderators, I suppose). That would've been fine. But then, shortly thereafter, you implied that I didn't understand how to read puzzles, and that I wasn't creative! I have to say I honestly was surprised at the outcome of such a seemingly innocuous comment!

The connection you make between defending an opinion and inexperience on the internet implies that the internet is a place to expect andor accept offending comments.

I've been a part of internet discussions for the past 11 years or so, and I've tended to find that people who are overly defensive are often new to the medium. Maybe not new to the internet specifically so much as new to public internet discussion, perhaps. For starters, with just text-based interaction, it's difficult to tell what someone's tone is. Further, being able to post anonymously frequently encourages people to post more aggressively because there's less of a tangible outcome. So, yes, the internet IS a place where you should expect a higher level of offending comments. However, as such, you should also be able take the comments you read with a grain of salt-- if you want to call that "accepting", I suppose that could fit. But generally speaking, you want to resist being offended.

I expect if we had been sitting in a room and I made the observation, you probably would've seen the mild tone with which I offered it, and taken it in stride-- or you wouldn't have been as aggressive in your response. But for whatever reason, it struck a nerve with you, and here we are. Anyway, I DO like discussing such matters (as you can probably tell), but I'm sorry if I offended you.

DaveE

 

[HawkLogic]

The good thing about the internet is that you can't really offend someone unless you actually know who you are talking to.
"Games Magazine" has a section called "Eureka" for "better, more elegant, or more complete solutions." In "Scientific American" Martin Gardner would occasionally present newly discovered solutions or cooks to classic puzzles. These are the kinds of enhancements I look for in a challenge to a puzzle. To me if a challenge does not improve the quality of the puzzle or the solution then it interferes with the enjoyment of the puzzle.
Some puzzles are presented ambiguously, sloppily, copied with typos, unsolvable, with trivial solutions, etc. The salary thing...nah.

 

[CaptRyan]

I came across this puzzle some 45 years ago and I could never solve it. I under stand the solution below, but in the (my) original puzzle the 4th clue was different. the words "one of the passengers" was not included. Can this puzzle be solved without that phrase?

On a train, Smith, Robinson, and Jones are the fireman, brakeman, and the engineer, but NOT respectively. Also aboard the train are three businessmen who have the same names: a Mr. Smith, a Mr. Robinson, and a Mr. Jones.

Mr. Robinson Lives in Detroit.

The brakeman lives exactly halfway between Chicago and Detroit

Mr. Jones earns exactly $20,000 per year.

The brakeman's nearest neighbor, one of the passengers, earns exactly three times as much as the brakeman.

Smith beats the fireman in billiards.

The passenger whose name is the same as the brakeman's lives in Chicago.

Who is the Engineer?