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Posted: 9/24/2023 10:07:50 AM EST
I've posted this here before. It always leads to a fun time...in the same vein as "airplane on a treadmill".
A riddle: One morning a monk sets out at 8AM to climb a path up the mountain to reach the temple at the summit. He arrives at the temple at 8PM. He stays the night. The next day, he leaves the temple at 8AM to descend the mountain, traveling downhill, arriving at his starting point from the previous day at 8PM. The riddle: Is there a spot along the path that the monk will pass at precisely the same time of day on both trips? For the purposes of discussion: The monk does not leave the path either day. He may speed up, slow down, even stop to rest, but he doesn't leave the path. Also, "same spot" means same spot on the mountain path relative to the mountain; not space, so the Earth's rotation and path around the Sun don't affect anything for the purposes of discussion. Basically summarized: At any point on the second day, will the monk pass the same point at the exact same time that he did the previous day? View Quote I will be over in the corner, watching the festivities. 

Riddle me this, riddle me that.
I have a can of gasoline and a match. Who am I? 

Yes, guaranteed.
I was not so sure, thinking he could maybe walk different areas at different rates and avoid being in the same part of the path at the same time of day, but it all made sense when someone pointed this out: Imagine he’s walking down on the second day, and there is some kind of holographic recording of his previous day’s trip up being replayed at the same time. At some point on the way down, he will pass the recording going up. That’s the point where he’s at the same place at the same time. No matter what speeds or changes in speed he makes in either direction, he can’t avoid passing by the replay. That’s the time and place. 



Yes . . . assuming he leaves and arrives at the exact same time both days . . . then his first step on the path and his last step on the path


Yes.
If there is one path to travel upon down to up and up to down the monk has no other choice but to occupy one portion of that trail at the same time on each trip (up/down). The trip up is slower possibly on the way up rather than the way down, the monk might pause longer in one direction or the other, but the trail is constrained and the monk must cross all the same points down as up and therefore one of those points is going to be the same time up and down. 

Quoted: Yes, guaranteed. I was not so sure, thinking he could maybe walk different areas at different rates and avoid being in the same part of the path at the same time of day, but it all made sense when someone pointed this out: Imagine he's walking down on the second day, and there is some kind of holographic recording of his previous day's trip up being replayed at the same time. At some point, he will pass the recording going up. That's the point where he's at the same place at the same time. No matter what speeds or changes in speed he makes in either direction, he can't avoid passing by the replay. That's the time and place. View Quote View All Quotes View All Quotes Quoted: Yes, guaranteed. I was not so sure, thinking he could maybe walk different areas at different rates and avoid being in the same part of the path at the same time of day, but it all made sense when someone pointed this out: Imagine he's walking down on the second day, and there is some kind of holographic recording of his previous day's trip up being replayed at the same time. At some point, he will pass the recording going up. That's the point where he's at the same place at the same time. No matter what speeds or changes in speed he makes in either direction, he can't avoid passing by the replay. That's the time and place. Of course he'd cross his holographic self at some point along the trail, but at the exact same time of the day? Doubtful, unless this is a play on words when 'same time of day' doesn't mean the time shown on the clock... ... The riddle: Is there a spot along the path that the monk will pass at precisely the same time of day on both trips? ... 


Quoted: Yes . . . assuming he leaves and arrives at the exact same time both days . . . then his first step on the path and his last step on the path View Quote More probable than anywhere else along the path, but not guaranteed. Monk can slow walk the first step up the hill and/or speed walk the last step down the hill so as to not make that happen... 

Quoted: Of course he'd cross his holographic self at some point along the trail, but at the exact same time of the day? Doubtful, unless this is a play on words when 'same time of day' doesn't mean the time shown on the clock... View Quote Imagine two monks on the same trail, one climbing and the other descending. Will they ever meet on that one trail, be at the same place at the same time? Yes, there is only one trail. They are both on it heading in different directions. They will meet somewhere along the trail. That time is the same for both travelers  "they meet at the same time of day"  satisfying the riddle. OK now one monk leaves on Monday and the other on Tuesday it doesn't change the result. 

Quoted: Of course he'd cross his holographic self at some point along the trail, but at the exact same time of the day? Doubtful, unless this is a play on words when 'same time of day' doesn't mean the time shown on the clock... View Quote View All Quotes View All Quotes Quoted: Quoted: Yes, guaranteed. I was not so sure, thinking he could maybe walk different areas at different rates and avoid being in the same part of the path at the same time of day, but it all made sense when someone pointed this out: Imagine he's walking down on the second day, and there is some kind of holographic recording of his previous day's trip up being replayed at the same time. At some point, he will pass the recording going up. That's the point where he's at the same place at the same time. No matter what speeds or changes in speed he makes in either direction, he can't avoid passing by the replay. That's the time and place. Of course he'd cross his holographic self at some point along the trail, but at the exact same time of the day? Doubtful, unless this is a play on words when 'same time of day' doesn't mean the time shown on the clock... ... The riddle: Is there a spot along the path that the monk will pass at precisely the same time of day on both trips? ... Not a play on words. Literally the same time of day. If he passes the hologram at 1:30pm, then he’s at the same point at 1:30pm today that he was at 1:30pm yesterday. 

No he will never be at the same place at the same time of day.
(unless you want to count the middle of the path, but that would assume ascent and descent rates are the same. He also will be facing different directions) ETA: I see the trap now. Yes they will intersect at some point regardless of rate. 

If a monk shits in the woods is the bear Catholic? Does the Pope hear it?


Quoted: No he will never be at the same place at the same time of day. (unless you want to count the middle of the path, but that would assume ascent and descent rates are the same. He also will be facing different directions) View Quote If you want to get REALLY pedantic, then no, because the first monk has no doubt taken in food and/or water, and has sluffed of millions of skin cells during the trip, so can we really say that it's the "same" monk? 

Quoted: Yes, guaranteed. I was not so sure, thinking he could maybe walk different areas at different rates and avoid being in the same part of the path at the same time of day, but it all made sense when someone pointed this out: Imagine he’s walking down on the second day, and there is some kind of holographic recording of his previous day’s trip up being replayed at the same time. At some point on the way down, he will pass the recording going up. That’s the point where he’s at the same place at the same time. No matter what speeds or changes in speed he makes in either direction, he can’t avoid passing by the replay. That’s the time and place. View Quote Your answer is wrong. If he passed the hologram at its position at 1pm on the way up and noon on the way down its different times. 

Quoted:Your answer is wrong. If he passed the hologram at its position at 1pm on the way up and noon on the way down its different times. View Quote Imagine two monks on the same trail, one climbing and the other descending. Will they ever meet on that one trail, be at the same place at the same time? Yes, there is only one trail. They are both on it heading in different directions. They will meet somewhere along the trail. That time is the same for both travelers  "they meet at the same time of day"  satisfying the riddle. OK now one monk leaves on Monday and the other on Tuesday it doesn't change the result the time is the same. 

Quoted: Imagine two monks on the same trail, one climbing and the other descending. Will they ever meet on that one trail, be at the same place at the same time? Yes, there is only one trail. They are both on it heading in different directions. They will meet somewhere along the trail. That time is the same for both travelers  "they meet at the same time of day"  satisfying the riddle. OK now one monk leaves on Monday and the other on Tuesday it doesn't change the result. View Quote View All Quotes View All Quotes Quoted: Quoted: Of course he'd cross his holographic self at some point along the trail, but at the exact same time of the day? Doubtful, unless this is a play on words when 'same time of day' doesn't mean the time shown on the clock... Imagine two monks on the same trail, one climbing and the other descending. Will they ever meet on that one trail, be at the same place at the same time? Yes, there is only one trail. They are both on it heading in different directions. They will meet somewhere along the trail. That time is the same for both travelers  "they meet at the same time of day"  satisfying the riddle. OK now one monk leaves on Monday and the other on Tuesday it doesn't change the result. I get that, and it seems a bit yo obvious to be the correct answer/response and isn't how I construe the OP when he states 'same time of day'. To me, that means at the same time as shown on a clock. He would have to walk at exactly the same pace but up & down or lead/lag one way or the other while watching his clock to time it correctly. In your explanation, he absolutely crosses his own path. However, there is no guarantee that it is at the same clock time during the day... ...this riddle is intentionally stated to allow for varying ways to construe its intent. Very sneaky 

Only if his pace is such that he travels uphill at the same rate that he travels downhill.
Possible but likely no. 

Quoted: Not a play on words. Literally the same time of day. If he passes the hologram at 1:30pm, then he’s at the same point at 1:30pm today that he was at 1:30pm yesterday. View Quote View All Quotes View All Quotes Quoted: Quoted: Quoted: Yes, guaranteed. I was not so sure, thinking he could maybe walk different areas at different rates and avoid being in the same part of the path at the same time of day, but it all made sense when someone pointed this out: Imagine he's walking down on the second day, and there is some kind of holographic recording of his previous day's trip up being replayed at the same time. At some point, he will pass the recording going up. That's the point where he's at the same place at the same time. No matter what speeds or changes in speed he makes in either direction, he can't avoid passing by the replay. That's the time and place. Of course he'd cross his holographic self at some point along the trail, but at the exact same time of the day? Doubtful, unless this is a play on words when 'same time of day' doesn't mean the time shown on the clock... ... The riddle: Is there a spot along the path that the monk will pass at precisely the same time of day on both trips? ... Not a play on words. Literally the same time of day. If he passes the hologram at 1:30pm, then he’s at the same point at 1:30pm today that he was at 1:30pm yesterday. Hmmm...assuming same pace up & down, monk will be up the trail 45.83333% of its distance & down the trail 46.83333% of its distance. They haven't met/crossed yet... ...once again, intentionally vaguely worded riddle is intentionally vaguely worded. That's how I see it 


Quoted: Yes, guaranteed. I was not so sure, thinking he could maybe walk different areas at different rates and avoid being in the same part of the path at the same time of day, but it all made sense when someone pointed this out: Imagine he’s walking down on the second day, and there is some kind of holographic recording of his previous day’s trip up being replayed at the same time. At some point on the way down, he will pass the recording going up. That’s the point where he’s at the same place at the same time. No matter what speeds or changes in speed he makes in either direction, he can’t avoid passing by the replay. That’s the time and place. View Quote That’s how I am visualizing it working. Voted yes 

no, it is extremely unlikely.
When he passes his point, the prior day the odds of the time being the same are nearly impossible. 

If it takes the monk the same time going down, he's doing it wrong.


What would Einstein say ?
Seems to my poor old and wore out gray matter he would be in the same place at opposite ends of the trail or close. 

Quoted: I get that, and it seems a bit yo obvious to be the correct answer/response and isn't how I construe the OP when he states 'same time of day'. To me, that means at the same time as shown on a clock. He would have to walk at exactly the same pace but up & down or lead/lag one way or the other while watching his clock to time it correctly. In your explanation, he absolutely crosses his own path. However, there is no guarantee that it is at the same clock time during the day... ...this riddle is intentionally stated to allow for varying ways to construe its intent. Very sneaky View Quote View All Quotes View All Quotes Quoted: Quoted: Quoted: Of course he'd cross his holographic self at some point along the trail, but at the exact same time of the day? Doubtful, unless this is a play on words when 'same time of day' doesn't mean the time shown on the clock... Imagine two monks on the same trail, one climbing and the other descending. Will they ever meet on that one trail, be at the same place at the same time? Yes, there is only one trail. They are both on it heading in different directions. They will meet somewhere along the trail. That time is the same for both travelers  "they meet at the same time of day"  satisfying the riddle. OK now one monk leaves on Monday and the other on Tuesday it doesn't change the result. I get that, and it seems a bit yo obvious to be the correct answer/response and isn't how I construe the OP when he states 'same time of day'. To me, that means at the same time as shown on a clock. He would have to walk at exactly the same pace but up & down or lead/lag one way or the other while watching his clock to time it correctly. In your explanation, he absolutely crosses his own path. However, there is no guarantee that it is at the same clock time during the day... ...this riddle is intentionally stated to allow for varying ways to construe its intent. Very sneaky Are you arguing that if 2 monks, let's call them A and B, are both on the trail, A going up and B going down, that when they meet each other on the trail it will not be the same time for both of them? 

If a Buddhist Monk didn't achieve advancement in life by climbing a mountain and was right back at exactly a place before he achieved the summit wouldn't that be kinda depressing?


Quoted: Your answer is wrong. If he passed the hologram at its position at 1pm on the way up and noon on the way down its different times. View Quote View All Quotes View All Quotes Quoted: Quoted: Yes, guaranteed. I was not so sure, thinking he could maybe walk different areas at different rates and avoid being in the same part of the path at the same time of day, but it all made sense when someone pointed this out: Imagine he’s walking down on the second day, and there is some kind of holographic recording of his previous day’s trip up being replayed at the same time. At some point on the way down, he will pass the recording going up. That’s the point where he’s at the same place at the same time. No matter what speeds or changes in speed he makes in either direction, he can’t avoid passing by the replay. That’s the time and place. Your answer is wrong. If he passed the hologram at its position at 1pm on the way up and noon on the way down its different times. If he was at a specific spot at 1pm on the way up and at that same spot at noon on the way down, then that’s not the spot where they passed each other. 

Quoted: Are you arguing that if 2 monks, let's call them A and B, are both on the trail, A going up and B going down, that when they meet each other on the trail it will not be the same time for both of them? View Quote View All Quotes View All Quotes Quoted: Quoted: Quoted: Quoted: Of course he'd cross his holographic self at some point along the trail, but at the exact same time of the day? Doubtful, unless this is a play on words when 'same time of day' doesn't mean the time shown on the clock... Imagine two monks on the same trail, one climbing and the other descending. Will they ever meet on that one trail, be at the same place at the same time? Yes, there is only one trail. They are both on it heading in different directions. They will meet somewhere along the trail. That time is the same for both travelers  "they meet at the same time of day"  satisfying the riddle. OK now one monk leaves on Monday and the other on Tuesday it doesn't change the result. I get that, and it seems a bit yo obvious to be the correct answer/response and isn't how I construe the OP when he states 'same time of day'. To me, that means at the same time as shown on a clock. He would have to walk at exactly the same pace but up & down or lead/lag one way or the other while watching his clock to time it correctly. In your explanation, he absolutely crosses his own path. However, there is no guarantee that it is at the same clock time during the day... ...this riddle is intentionally stated to allow for varying ways to construe its intent. Very sneaky Are you arguing that if 2 monks, let's call them A and B, are both on the trail, A going up and B going down, that when they meet each other on the trail it will not be the same time for both of them? Same time of day, as shown on the clock. They both leave at 8am and will surely cross paths along the way... ...hold up, wait a minute. This scenario gets different results in my head when thinking about (2) people on the sane day walking different directions vs the same guy walking both directions on different days 

The answer is, of course, yes.
The real riddle is when and where. 


The EXACT same spot? No. He'll be in a sligtly different spot, even if by only a thousandth of an inch.


Quoted: Yes, guaranteed. I was not so sure, thinking he could maybe walk different areas at different rates and avoid being in the same part of the path at the same time of day, but it all made sense when someone pointed this out: Imagine he’s walking down on the second day, and there is some kind of holographic recording of his previous day’s trip up being replayed at the same time. At some point on the way down, he will pass the recording going up. That’s the point where he’s at the same place at the same time. No matter what speeds or changes in speed he makes in either direction, he can’t avoid passing by the replay. That’s the time and place. View Quote This, and I don't really understand why people are arguing otherwise. 



Quoted: Yes, guaranteed. I was not so sure, thinking he could maybe walk different areas at different rates and avoid being in the same part of the path at the same time of day, but it all made sense when someone pointed this out: Imagine he's walking down on the second day, and there is some kind of holographic recording of his previous day's trip up being replayed at the same time. At some point on the way down, he will pass the recording going up. That's the point where he's at the same place at the same time. No matter what speeds or changes in speed he makes in either direction, he can't avoid passing by the replay. That's the time and place. View Quote 

Assuming his pace to be equal in both directions, he will pass the halfway point at the same time of day in both directions.




You didn't specify *on the planet*, so the answer is no. Our planet/solar system/galaxy are always moving, so even the Earth won't be at the exact same spot.


Not interested in monks.
Now, Monkees is a different story. The Monkees Hey Hey We're The Monkees. 

He can’t help it, it’s a random crossing in two trips…now tell him to repeat it day after day and get the exact same spot, same time and it changes.


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