In your little picture you have the following labeled.
One white
Two blacks
Power
Common??
This adds up to five
Yes.
But here you say:
No, just two blacks and one white.
Which leaves the rest of what is in that box in question. We need to know every conductor that enters that box in order to figure out what the person that made the installation was doing.
Four cables come into the box by the door (second picture):
1) One with two conductors for the porch light (and irrelevant here);
2) One with a line (black) and a common (white) and no ground wire;
3) One with a black (runner?) and a white (for a purpose presently unknown);
4) One with a black (runner?) and a white that had been clipped short.
1- Yes it is very relevant as without know what is in the switch box it would be impossible to give an answer.
2- This is the supply (I think) which would have one black hot and one white grounded neutral but not a common.
3- Not a runner and we will figure out what the white is for as we go along
4- A bad idea although it was common practice just after the knob and tube days when electricians was learning how to use cable. This method has never been a code compliant method of installing three way switches.
So, and concerning the circuit in question: The box ended up with two blacks and only one white when somebody long ago apparently ran a second cable to get only a black runner (and clipped its unneeded white).
I have never in 42 years of doing electrical work ever heard of a runner except for the young man that kept running back and froth from the job and the van or port-a-john.
It is the white wire in #2 above that I am calling a common, and that cable is the one that brings power to the 4" box. The switch you can see in picture #2 is the switch for the porch light, and it is connected to the conductors in cable #2 and works just fine.
It is important that when talking about electrical circuits to use the correct terminology so there won’t be a lot of confusion.
We'll quit calling the grounded neutral conductor a common conductor. In premises wiring the grounded neutral is not a common conductor. On a three way switch there is a common screw and this screw will always get a hot or a switch leg.
If the porch light is using the 2 two wire cables then I would think that the two white conductors are under a wire nut and the two blacks are on the switch. Is this correct?
If this is correct so far then the three wires left;
3) One with a black (runner?) and a white (for a purpose presently unknown);
4) One with a black (runner?) and a white that had been clipped short
are for the three way switch. These wires will in no way connect to the conductors in the 2 two wire cables connected to the porch light.
Understood ... but the white wire in cable #3 above might be the common side of the light if the white wire in picture #1 is its feed, and if so, it would need to be connected to the common in cable #2 in order to complete the circuit for the light.
Again it ain’t called a common wire just because it is white. It would be better to call it a “cracker†wire than a common wire. (a little humor there)
When you started this line of questioning about these three way switches in
this post how many conductors and cables are in this switch? Is it is like the first one with a cut white wire in one of the cables? Are there three two wire cables in that switch box?
Give us a little more information here please.
I will venture so far as to say I don't think you are going to get the fan and light to work separately of each other just because there aren't enough switches.