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Topic: Where are the missing railroad trains? (Read 757 times) |
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fiziwig
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Where are the missing railroad trains?
« on: Dec 18th, 2006, 7:31pm » |
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This is an old riddle to me, but I searched the forum for relevant words and came up empty, so here goes:
From my front porch I can see a railroad track winding through the valley below. I noticed that whenever I sat out on the porch to enjoy a pipe after dinner I could see a northbound train, and wondered if southbound trains used the same track. To find out, I set my alarm clock for a different random time every day, and when it went off, day or night, I would step out onto the porch and wait for the first train to come by and mark down which direction it was traveling.
After a month or so I had counted 57 northbound trains and only 11 southbound ones. Being curious, I called the railroad and they assured me that there were exactly four northbound trains and four southbound trains using that track every day, and that both trains pulled the same number of standard-length cars.
Why did I see so few southbound trains?
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flamingdragon
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Re: Where are the missing railroad trains?
« Reply #1 on: Dec 18th, 2006, 7:42pm » |
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Pure chance is a good answer. 
Your alarm clock is broken? 
The riddle is a trick, as a railroad cannot answer the phone. 
The railroad company lied. 
Your going crazy and did not notice most of the southbound ones. 
You dont know how to count. 
Or of course for merely the purpose of this riddle u called up ur friend who was a couple miles northward and told him to tell u when he saw a southbound train, and if he did u went inside and did not notice the southbound ones, of course to make the riddle more challenging, u did stay there to notice a couple southbound trains. 
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| « Last Edit: Dec 18th, 2006, 7:43pm by flamingdragon » |
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fiziwig
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Re: Where are the missing railroad trains?
« Reply #2 on: Dec 18th, 2006, 7:59pm » |
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To clarify:
1. In the VERY long run I will see about 5 times as many N-bound as S-bound.
2. The alarm clock works fine.
3. No tricks, no lies, no insanity.
4. I got an A+ in fourth grade math, so counting is not a problem.
5. If I stay up 24 hours I will count exactly 4 N-bound and 4 S-bound trains.
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flamingdragon
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Re: Where are the missing railroad trains?
« Reply #3 on: Dec 18th, 2006, 8:16pm » |
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Leaving pure chance standing as an alternate answer.
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"The fool doth think he is wise, yet the wise man knoweth himself to be a fool"
"He who commands the past, commands the future. He who commands the future, commands the past."
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flamingdragon
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Re: Where are the missing railroad trains?
« Reply #4 on: Dec 18th, 2006, 8:20pm » |
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I would say they go southward in the middle of the day and northward when ur alarm goes off at night, however u said when ur alarm goes off, day or night, so I must assume that you go to sleep as soon as u see a train go by and randomly set ur alarm for any time of the day or night and wake up even if it goes off in a minute?
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| « Last Edit: Dec 18th, 2006, 8:21pm by flamingdragon » |
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"He who commands the past, commands the future. He who commands the future, commands the past."
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ThudnBlunder
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Re: Where are the missing railroad trains?
« Reply #5 on: Dec 18th, 2006, 8:28pm » |
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on Dec 18th, 2006, 8:16pm, flamingdragon wrote:| Leaving pure chance standing as an alternate answer. |
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I think he covered that.
How do cogs work?
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Icarus
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Re: Where are the missing railroad trains?
« Reply #6 on: Dec 18th, 2006, 8:43pm » |
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Of course, if he lived a few miles down the track, he'd better be seeing a side rail!
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flamingdragon
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Re: Where are the missing railroad trains?
« Reply #7 on: Dec 18th, 2006, 8:47pm » |
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Quote:| Leaving pure chance standing as an alternate answer. |
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on Dec 18th, 2006, 7:59pm, fiziwig wrote:To clarify:
1. In the VERY long run I will see about 5 times as many N-bound as S-bound.
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Quote:
Astronomical, yet still possible.
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Eigenray
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Re: Where are the missing railroad trains?
« Reply #8 on: Dec 19th, 2006, 12:05am » |
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Do you live near the end of the line?
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Grimbal
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Re: Where are the missing railroad trains?
« Reply #9 on: Dec 19th, 2006, 12:37am » |
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Or the only train driver lives in the south and works some 8h per day?
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towr
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Re: Where are the missing railroad trains?
« Reply #10 on: Dec 19th, 2006, 1:20am » |
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The southbound trains are distributed in 4 hours, the northbound in the other 20. So if you wait till the first train comes along, there's a five times bigger chance of catching a northnound one.
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Wikipedia, Google, Mathworld, Integer sequence DB
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Miles
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Re: Where are the missing railroad trains?
« Reply #11 on: Dec 19th, 2006, 2:25am » |
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A periodic solution would be to divide the day up into 6 hour slots, with a Northbound train passing 5 hours in, and the Southbound train passing an hour after that. If you randomly pick a time in the 6 hours, it is five times more likely that you see a Northbound (because the only way to see a Southbound is to start observing in that final hour of the slot).
Question: assuming the trains move at the same constant speed, how does the ratio N:S vary for observers along the track?
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jollytall
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Re: Where are the missing railroad trains?
« Reply #12 on: Dec 19th, 2006, 3:43am » |
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Assuming that every train leaves the terminus exactly in every 6 hours from both ends (but not necessarily at the same time), every train will meet with n trains from the opposite direction (where n can be 0 and upwards) at fixed points. Even if n=0 you can generate virtual meeting points by extending the lines beyond the terminals. Now for every point along the line you can measure the distance to the two nearest meeting points. The ratio of the two will give you the spotting probabilities.
If the trains not work the punctual then it can be more messy.
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fiziwig
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Re: Where are the missing railroad trains?
« Reply #13 on: Dec 19th, 2006, 7:54am » |
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The intended answer is the one provided by jollytall, although the one by Miles works just as well. The original answer I heard was that the N-bound trains passed every 6 hours and the S-bound trains passed 1 hour later.
Other people at other locations along the track might observe the exact opposite frequency.
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ThudnBlunder
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Re: Where are the missing railroad trains?
« Reply #14 on: Dec 19th, 2006, 8:32am » |
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on Dec 19th, 2006, 7:54am, fiziwig wrote:The intended answer is the one provided by jollytall, although the one by Miles works just as well. The original answer I heard was that the N-bound trains passed every 6 hours and the S-bound trains passed 1 hour later.
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Seems they run like clockwork (cogs) then.
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flamingdragon
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Re: Where are the missing railroad trains?
« Reply #15 on: Dec 19th, 2006, 5:04pm » |
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I still say pure chance is a good alternate answer.
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"The fool doth think he is wise, yet the wise man knoweth himself to be a fool"
"He who commands the past, commands the future. He who commands the future, commands the past."
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ThudnBlunder
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Re: Where are the missing railroad trains?
« Reply #16 on: Dec 19th, 2006, 8:39pm » |
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on Dec 19th, 2006, 5:04pm, flamingdragon wrote:| I still say pure chance is a good alternate answer. |
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One-tailed p-value
= [(57 - 34) +/- 0.5]/sqrt[(68*(1/2)*(1/2)]
~ 23.0/sqrt(17)
= 5.58
Taking both tails we get about 1 in 100 million.
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| « Last Edit: Dec 19th, 2006, 8:51pm by ThudnBlunder » |
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flamingdragon
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Re: Where are the missing railroad trains?
« Reply #17 on: Dec 19th, 2006, 10:03pm » |
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As I said earlier, astronomical is still possible.
And did u just make those #s up, lol, I can't make any sense of them.
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"The fool doth think he is wise, yet the wise man knoweth himself to be a fool"
"He who commands the past, commands the future. He who commands the future, commands the past."
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ThudnBlunder
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Re: Where are the missing railroad trains?  Normal.gif
« Reply #18 on: Dec 20th, 2006, 3:15am » |
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on Dec 19th, 2006, 10:03pm, flamingdragon wrote:| And did u just make those #s up, lol, I can't make any sense of them. |
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I calculated the black bit in the diagram below of the Normal distribution.
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| « Last Edit: Dec 20th, 2006, 3:15am by ThudnBlunder » |
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THE MEEK SHALL INHERIT THE EARTH.....................................................................er, if that's all right with the rest of you.
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