How to power and distribute Ten speaker pairs?

Speakers are 8 ohms. A pair in each room. Ten rooms total with volume controls in each(i have not checked if they are impedance matching yet). There is no need for a main zone or 5.1 as this system will be seperate from the home theaters in the house. Do I still have to get a receiver with zone 2 capability? I only want to play one source at a time and one source is okay in every zone at one time. How do I distribute audio to all rooms? I don't know if I need two receivers and then a speaker selector or one receiver with zone 2 an amp and then speaker selector or what??? Finding an amp with 20 channels has been difficult too. I have looked all over this forum, can someone explain what I need?

Also, The audio wires are going into a circuit board thing, I am not familiar with. It says "left", "right", "amp", "tap" and has two big (2 inches square) silver boxes built into it that say ohm ratings i think for example 1.4 ohms, 16 ohms, 4 ohms, 8 ohms and so on. Ten 16-4 lines are connected to the "left" and "rights" and one 16-4 is connected to the part that says "amp". then the big silver things say "tap" near them are connected to the board itself.

I hope my question is not unclear, I will try to summarize....
What receiver and amp combo will power ten rooms of audio and should I be taking the circuit board thing into consideration or is that just a connecting block type thing?

I think that the circuit board i was referring to is a speaker bus or in other words a speaker selector???

So if that is true, I would not need the product that was linked would I?

I just got off the phone with crutchfield, they wanted to know the efficiency of the speakers before they recommended a specific solution. They were thinking about using one dual zone receiver to power everything?? NAD amp I think they said.

This would be for background music and they would only need one or two zones on at a time anyway. Can a receiver with zone 2 out going into the speaker bus circuit board and the out to the speakers be all I need?

does having only one zone on at a time make any difference regarding powere for hooking up to zone 2 out for all ten rooms? Or is it going to be just as weak as all rooms playing at once? So an impedance matching speaker selector and an amp that can handle how many watts out of zone 2?