[Mikev]

The Monk ​

A monk talks during supper. As penance, he has to climb a mountain.
He leaves at 9 o'clock in the morning and reaches the top of the mountain at midday. He rests for a night under the stars and sets out again the next morning at 9 o'clock. Taking the same path down, he gets to the bottom at 11 o'clock.

Is there any place on the path that he passes through at the same time on both days?
How can the existence or nonexistence of such a place be demonstrated?


I will post the answer below later.

 

[Mikev]

Spoiler

Answer:
Yes, for example if the two monks both leave at 9 o’clock, one from the bottom of the mountain and the other from the top. Since they are on the same path, there is a place where they meet.

 

[Wandiwa]

Spoiler

I'll dispute your answer because the monk has to be at the same place at the same time going up and going down. I drew it as two time lines and I believe there is no common point for location AND time.
If you can show me I'm wrong, I'd love to see your logic. @Mikev

 

[Abby22]

Spoiler

Perhaps it could be due to human interference with DAYLIGHT SAVING which makes the time dierential and that would explain place on the path that he passes through at the same time on both days?

 

[Wandiwa]

Spoiler

Spoiler

Perhaps it could be due to human interference with DAYLIGHT SAVING which makes the time dierential and that would explain place on the path that he passes through at the same time on both days?

Don't think DLS is relevent, logically it would take 3hrs to walk uphill and only 2hrs to walk downhill. @Abby22 If the poor guy was in a wheelchair with no brakes the time difference would be huge LOL.

 

[TomGeorge]

Spoiler

Need to edit it.
"it" should be 11, eleven.

 

[G Lockwood]

Spoiler

As we don't know what speed the monk travelled at any time, it cannot be assumed he covered the 3 hours at the same pace, as coming down we cannot assume he travelled at the same speed. He could have stopped for breaks, he could have ran down at times. Any variations could apply. Therefore, I don't believe we can state if he would have passed the same spot at the same time at any given time.

 

[Mikev]

Spoiler

Spoiler

Need to edit it.
"it" should be 11, eleven.

Thanks for pointing out the typo, now edited