Solution to Puzzle #157: Journey of a Monk

This was a very nice puzzle – not an easy one and as such I received answers from the classical die hards. People who sent the correct answers include Suman Saraf and his daughter (I think age 10!), Sid Mulherkar, Pratik Poddar and Vishal Poddar. Well done all.

Copying answers from Vishal as well as Suman that explain the same thing:

[From Vishal] For both the days, lets draw a graph between his height and time. On day 1, it will start from 0 at 6am and end at h at 8pm. It will be a continuous graph. On day 2, the graph will start from h and go till 0. We can see that there will be a point where both the lines intersect. This is the point where the monk was on both the days at same time.

[From Suman and his daughter] If we mirrored the return journey on another monk on the same day (the original one is walking up), you can see they would cross each other at some point. This is the same point where the monk will have been while come down next day 🙂

 

This is based on a mathematical theorem known as the Intermediate Value Theorem. Interested reader can read more at https://en.wikipedia.org/wiki/Intermediate_value_theorem.

Hope you enjoyed the puzzle!

 

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