A Monk's Journey

Logic Level 3

There is a sacred hill where monks pray. At each hour, a monk leaves the base for the top of the hill. Also at each hour, a monk leaves from the top of the hill for the return journey. Traversing the hill takes 4 hours in either direction and there is only one path.

If a monk starts his journey from the bottom at 12 noon, exactly how many monks will he pass along the way to the top?

Note: Include any monks that he passes at the bottom or top of the hill.

The answer is 9.

5 solutions

Satyen Nabar
Mar 12, 2014

For each of the 4 hours the monk travels, there will be another monk that leaves the top to return. It would be tempting to think the answer is 4.

But this is incorrect. The reason is some monks are already on their way down. This factor contributes another 4 monks who get crossed.

There is also one extra monk who gets crossed: the one who is leaving just as the monk reaches the top.

In effect the monk will cross the monks who left the top at 8 am, 9 am, 10 am, 11 am, 12 noon, 1 pm, 2 pm, 3 pm and finally the monk who leaves the top at 4pm as he reaches. Thus total of 9.

But the question says how many monk did he cross on the way ...... not when he finishes or starts......

Arnab Mondal - 7 years, 2 months ago

if in every hour one monk only leaves then the 12 noon monk should not be included because that monk is him

Dean Clidoro - 7 years, 3 months ago

The monks he crosses are the ones who leave from the TOP of the hill

Satyen Nabar - 7 years, 3 months ago

It should be 8, as the monk who leaves the top at 4pm is himself.

Ravi Badam - 7 years, 2 months ago

@Ravi Badam – The question implies that each monk takes time at the top to pray. Presumably for some positive integer number of hours.

Steven Perkins - 7 years, 2 months ago

I actually found it easier to go by half hours. My reasoning here may suck, but he sees the first guy before he really starts, meaning the second guy is an hour away, then half an hour after he starts the guy who would be finishing at 1 sees him. At 12:30. Then the guy who finishes at 2 would be seeing him at 1, since he is 1 hour away from his journey and he is one hour in. Then he will meet the guy at 1:30 who started at 11 since he is currently 1.5 hours away and that means that guy had been on for 2.5 hours since see once again, it is 1:30 and he had started at 11. And continuing this way until the end where he sees the guy who is just leaving when he gets there. But you forgot to mention if anyone was on the hill whatsoever (unless I accidentally skipped this part) meaning that it is possible the answer is 0 since he would be the first to travel up.

Daniel Preston - 5 years, 10 months ago

Vikram Kumar
Mar 20, 2014

First he comes across 4 monks who have left in the previous 4 hours before he starts his journey (one at starting point and rest three in between his path).
Secondly he comes across the person who starts the journey from top of hill at the same time he starts his journey from bottom at the mid point of his journey exactly at 2:00 PM.
Thirdly he comes across 4 monks who will start his journey in the next 4 hours after his start of journey (three in between his path and the last one at the end point of the top of the hill).

Anton Shkrunin
Aug 21, 2015

It's all too tempting to think i know best, it's 5 monks: one at the bottom when our subject starts, one at the top just about to leave and three in between at each hour interval. Took me two failures to start to think seriously.

To solve it, i fixed the current time (12PM) and positions of all monks on their way to the top (our subject) and to the bottom (stretched at hourly intervals from the mountaintop down to the bottom). Looking at the resulting diagram and seeing how the monks move, you can figure out that our subject meets a passer by every half an hour, plus one at the bottom and one at the top, since they start 4 hours before and 4 hours after our subject, accordingly.

Doesn't this question assume people are only staying an hour at the top or bottom to pray? What if they stayed there for 24 hours? Wouldn't he pass a lot more monks at the top and bottom?

Brian Coari - 5 years ago

Vaibhav Zambad
Mar 31, 2014

Since in every 1 hour ,a monk moves from up to down so when a monk will start moving up on 12 ,he will pass the monks who started on 3,4,5,6,7,8,9,10 and 11 so the answer is 9.

Niranjan Ketkar
Mar 22, 2014

When monk starts the journey,He crosses another monk who has started the journey at 8 am ,and he reaches top at 4 pm when another monk has just started the journey;thus all the monks between 8 to 4 will cross him.{8,9,10,11,12,1,2,3,4}--->> 9

A Monk's Journey

The answer is 9.

5 solutions

0 pending reports