Solenoid switch controller
As has been suggested in the comments: put the solenoids in parallel. In fact your idea where you put then in series with a switch for each won't work. As soon as one switch is open none of them will work. 

More important: for outside circuitry you want to stick to a low voltage. It is safe. 

I think your concern is that you need ~35Amps to have them all on. You could put two of them in series with one switch per pair. You would then need a 48V transformer of ~17.5 Amps. But you still have the same amount of watts so the transformer will be about the same size (and cost).

What also has been mentioned is that the current will be much higher when you switch them on. If you use a computer, you should program it, so it never switches them all on at the same time. That way you can get away with the 35Amps transformer. 

You will end up with a bundle of 87 wires. I don't know how these solenoids are placed. If they are far apart you might put a tiny relay at each so you have one set of power cable and very thin control cables. The cost is cable versus an extra relay. 

Ultimately you could place a tiny controller (They come in as small as 6 pins) at each solenoid and use a protocol. (e.g. a UART). You need only three wires then, but that may be beyond your capabilities. (It has the advantage that you can interface the system to your computer using a standard USB-serial adapter. )