I am having hard time proving this either right or wrong.
Let's take for example a river, does the water flowing down follow the least resistant path?
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The river will not always follow the along the path of least resistance because as water flows, its momentum increases. If a river follows a bend/curve in the land, it may slosh against the bank or even go over the bank--but eventually, it will lose some of its momentum & then flow to a lower elevation or seep through the earth to a lower elevation. So as you can see the direction & momentum of water movement depends on other factors.
Not necessarily. Imagine two containers connected by a narrow hose that is just below the water line, and a big hose (like a syphon) above the water line.
The path of least resistance would be the large hose - but you need to "prime" the hose for the water to find / choose that. If you don't, then the water will flow through the small hole. Not the path of least resistance. The "most available" path of least resistance.
And if you have more than one hole under the water line, the water will flow through all of them; it may flow more through the wider hose, and less through the narrow one - but it will use all of them. It won't find the "path of least resistance", but the distribution of flow that will lead to the least "total" resistance.
Of course you might have to define "path of least resistance" more carefully...
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