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Romance and the Railroad

Question

A man has two girlfriends, reachable only by train. One lives to the North, the other to the South. Being a man, he is incapable of deciding which to marry. Since a train leaves his station each hour to the North, and another leaves each hour to the South, he decides to leave his amorous visits to chance. Let Fate decide.

Being a clever person, he creates a device that sounds an alarm at a random time of the day. Each day, promptly after the alarm sounds, he takes the 5-minute walk to his station and boards the next train to arrive: Northbound or Southbound. After a year has passed, he finds he has visited one of the girlfriends [turns out it was the one to the South] more than 300 times, and so he marries her.

Assuming his random time-of-day device was working properly, how could this have happened?

What times did the trains leave the station?

The trains to the North left the station on the hour; the trains to the South left at ten minutes after the hour. Each hour there was a 10-minute window for the Northbound train, and a 50-minute window for the Southbound train. After more than 360 days, 300 Southbound trips would be expected.

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Surely being a man he would have just married the Girlfriend with the biggest Breasts

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Spoiler 2: The trains to the North left the station on the hour; the trains to the South left at ten minutes after the hour. Each hour there was a 10-minute window for the Northbound train, and a 50-minute window for the Southbound train. After more than 360 days, 300 Southbound trips would be expected.

The solution given appears to have a mistake. If the Northbound train leaves on the hour and the Southbound train leaves ten minutes after the hour, the Northbound train would actually have the fifty minute window. Let's say the Northbound train arrives at 9:00AM and 10:00AM, the Southbound train arrives at 9:10AM and 10:10AM. Then if the man arrives between 9:11AM and 10:00AM, a fifty minute window, he would catch the Northbound train. He would only catch the Southbound train if he arrived between 9:01AM and 9:10AM.

Either the trains should be swapped or the time for the Southbound train should be changed to ten minutes before the hour.

To normdeplume: While your answer is amusing, there are actually many other physical and personality traits that different men would prefer. MAybe one of the ladies is a really good cook. Maybe one of them is rich. Who knows. However, since he is obviously having difficulty choosing between the two, I believe it is safe to say that their individual traits must be in fair balance, at least to the man in question.

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That is actually funny because based on your reply I assumed you were a woman implying that all men are pigs with one track minds. Regardless, as stated before, if this guy's interests were the same as yours, the two ladies in question must be of similar ampleness in order for him to need the random train experiment to help him decide between the two. OF course, if he has gotten away with this for a year, I am not sure why he would feel pressured to make a decision now.

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The trains to the North left the station on the hour; the trains to the South left at ten minutes after the hour. Each hour there was a 10-minute window for the Northbound train, and a 50-minute window for the Southbound train. After more than 360 days, 300 Southbound trips would be expected.

This answer is not exactly right. The ten-minute window explanation explains why this result is likely. But, because the alarm sounds randomly, the 10-minute window does not make this result necessary. That is, because the alarm sounds at a a random time, any solution is possible. Theoretically, it could sound at noon everyday. Since it's random, you have an expected distribution, but not a guaranteed one.

Also, even if your process were correct, you actually invert the answer. The train going South has to be 10 minutes before the one going North, not the other way around.

The question also leaves out an important piece of information: does he only take one train ride every day? Another possible explanation is that he rode each train approximately the same number of times, e.g., approximately 300 each, since the question doesn't limit him to one visit per day.

Edited by sunshipballoons

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This answer is not exactly right. The ten-minute window explanation explains why this result is likely. But, because the alarm sounds randomly, the 10-minute window does not make this result necessary. That is, because the alarm sounds at a a random time, any solution is possible. Theoretically, it could sound at noon everyday. Since it's random, you have an expected distribution, but not a guaranteed one.

Also, even if your process were correct, you actually invert the answer. The train going South has to be 10 minutes before the one going North, not the other way around.

The question also leaves out an important piece of information: does he only take one train ride every day? Another possible explanation is that he rode each train approximately the same number of times, e.g., approximately 300 each, since the question doesn't limit him to one visit per day.

Actually, you have made a few mistakes in your assumptions...

1. Any device which creates an artificial random will have an even distribution over a length of time, despite the term "Random". Even with all our sophisticated methods, there is still a distribution pattern. (ask those MIT kids to explain it to you).

2. You are right he inverted it, but then again, it still explained the answer for everyone.

3. The question does NOT leave out important information, your reading comprehension is lacking. "Being a clever person, he creates a device that sounds an alarm at a random time of the day." the key there is "A" random time, not multiple random times, not randomly throughout the day, It says specifically "A random time of the day"

I wish people would stop trying to over analysis someone's post and simply look at the riddle as a riddle and not some scientific experiment.

It was a great riddle, and one which I instinctively knew the answer to, however, as with most that I see here, I will definately ask my kids tonight over dinner....

Thanks for the good riddle!

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Surely being a man he would have just married the Girlfriend with the biggest Breasts

ha ha ha very true. :D

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the northbound train could have stopped operating and/or just skipped that station after a certain number of days only leaving 1 to catch?! this is what i think anyway...

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Could be a crazy rail system, where southbound trains come 5 times more often than northbound ones. That's the only other plausible suggestion I can give.

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The vagueness of the "over 300 times" resolves any probability issues to most extent. Since the answer could be any # of trips greater than 300, then the simplest answer is the North train leaves after the South train by less than 10 minutes. If it left 1 minute later than he has >98% chance of catching the South train (59 of 60 mins) and would have visited his Southern Girl 357 times!

One piece that is left to assumption is how long the trains remain in the station which gives him the option to decide or randomly board. The probability seems to require that there is only one train at the station and if he arrives after the North train leaves, the station is empty and he waits for the next train to arrive.

If he's allowed to choose a train (if both are in the station), he probably headed South since it's warmer and his girl wears less clothing...

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The vagueness of the "over 300 times" resolves any probability issues to most extent. Since the answer could be any # of trips greater than 300, then the simplest answer is the North train leaves after the South train by less than 10 minutes. If it left 1 minute later than he has >98% chance of catching the South train (59 of 60 mins) and would have visited his Southern Girl 357 times!

One piece that is left to assumption is how long the trains remain in the station which gives him the option to decide or randomly board. The probability seems to require that there is only one train at the station and if he arrives after the North train leaves, the station is empty and he waits for the next train to arrive.

If he's allowed to choose a train (if both are in the station), he probably headed South since it's warmer and his girl wears less clothing...

You have it. Good points, all. ;)

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Obviously the answer given works, but what if the trains arrive at the same time every day?

Since North bound trains are generally on the Eastern side of side-by-side tracks, the South bound train would be on the Western side of the tracks. If both trains arrive at the same time, the first train the man will come to will be the South bound train (he would have to go around the South bound train to catch the North bound train).

My answer would be that the man lived to the West of the train station, therefore making it easier to catch the South bound train.

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Coming from someone who's married and wife is probably never going to read this...

if he was truly clever, he'd never gotten married in the first place and kept being a playing the field with a multiple girlfriends...

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