Problem 155

[nefedov]

I'mIt is not entirely clear to me: does the solution need to take into
account all possible capacitor connection schemes?
Is a scheme like this possible?

#               C4
#         *-----||------*
#         |  C1     C2  |  C3       
#   in >--*--||--*--||--*--||--*--> out
#                |      C5     |
#                *------||-----*

If so, it appears that calculating the resulting capacitance of this
circuit is not a trivial task in itself. The resulting capacitance
can not be expressed in terms of a combination of series and parallel
connections. Note that C1 through C5 may differ: for instance, they
could be made up of two or three identical capacitors.

[grok123]

It is not entirely clear to me: does the solution need to take into
account all possible capacitor connection schemes?
Is a scheme like this possible?

#               C4
#         *-----||------*
#         |  C1     C2  |  C3       
#   in >--*--||--*--||--*--||--*--> out
#                |      C5     |
#                *------||-----*

If so, it appears that calculating the resulting capacitance of this
circuit is not a trivial task in itself. The resulting capacitance
can not be expressed in terms of a combination of series and parallel
connections. Note that C1 through C5 may differ: for instance, they
could be made up of two or three identical capacitors.

Any capacitor circuit is comprised of two sub-circuits arranged in either series or parallel with one another. The problem statement does not mention any taps.

[nefedov]

Thanks, I understand that circuits like this one are prohibited. Still, let me be a bit of a stickler for detail.
Capacitors C1, C2, and C3 are connected in series; C4 is in parallel with C1 and C2; C5 is in parallel with C2 and C3. I don't understand which taps are being referred to or where the contradiction with the problem statement lies.

[DJohn]

The problem gives you rules for constructing circuits starting from a single capacitor. At each step, only the two terminals of the previously-constructed sub-circuits are available - none of the internal connections are. Your circuit, were it to be allowed, would require access to those internal connections. It's not allowed because there is no way, under the rules of the problem, to build it.

A useful rule in Project Euler is that if a problem looks like it's about something from the real world, it usually isn't. That's only decoration. Knowing about the real-world thing is a disadvantage because it tempts you to bring in a lot of extra information that isn't a part of the problem.

[nefedov]

Thank you. I think I understand the problem statement.
Anything that isn’t entirely clear is intuitively obvious.