if all the coils has a piece of core in them already the inductance can not be change, unless you move the core in and out of the coil which that is not the case here. The only thing that can change the inductance of the coils is the AL value of the core material. This is why this needs to be discussed,
also the 100% connected is good for " theatrical " in real life there are losses ect.. just pointing it out that everyone not to be so critical on this.
for a description of functionality this 100% works... Vs the gap... where the % is more like 0-100% depending on the gap
for we are talking about thinking through this thing...
now we start talking about mutual inductance, adding inductance and opposing inductance...
can you go in to that again for us...
post the Grob pages for us... that should be helpful as well
~Russ