It doesn't matter what's in parallel with an ideal source (unless it's another ideal source with a different potential, and then FZZZSST! BANG!!). Nothing in parallel with that resistor will change the potential across it that's set by the indicated ladder of ideal voltage sources.Disagree. At the end of the path described, resistor ‘R’ isn’t alone. There are two other resistors next to it (in parallel) right-and-center--AND one of them has an emf. If there was a short circuit, then maybe the three emfs may be ignored. But it's not even a short circuit. So why aren’t the currents through all emfs relevant? I think this problem is tougher than advertised. Someone please do the 18-by-18 matrix. Not it.