Why won't any electrons flow through the resistor R2?

[Plutonium88]

So I was doing a circuit with some friends, and the circuit breaks down such that There is what looks like a parallel circuit, with one branch containing just the wire, and the other branch containing a resistor. The answer to the question shows that the electrons will not flow through this resistor(R2). Why is this the case? Is there literally no electrons going throug the resistor? How do they know not to take that path?

So the answer R = R1 + R3

Mathematically how do we know this is being discluded? Or are we just assuming nothing will go through the resitor R2?

 

[haruspex]

Try putting in a resistance on the other leg and calculating what current will go through each. Then see what happens when the extra resistance goes to zero.

 

[Plutonium88]

Try putting in a resistance on the other leg and calculating what current will go through each. Then see what happens when the extra resistance goes to zero.

So in the limiting case where R2 -> 0 you just end up with the other resistance?

 

[haruspex]

So in the limiting case where R2 -> 0 you just end up with the other resistance?

According to the diagram, you already have a resistance R₂. I'm adding a resistance R₄ in parallel with it. Find an expression for the fraction of the current that would pass through that, then see what happens as R₄ tends to zero.