Water Ballast Design Challenge...

I was assuming that gravity will empty any tank on an even keel, but read on.

I will describe the 1st scenario: no pump from tank to tank-only from sea to tank. This is the most interesting one.

You got 2 forward tanks 1 & 2, two aft tanks 3 & 4. (count the tanks clockwise from the forward port tank 1). Three valves: two for and aft three-position valves a & b, and two-position seacock valve c .

Valve a, pos 1: 1 > 2 or 2 > 1, pos 2: 1 > c or c > 1 pos 3: 2 > c or c > 2.
Valve b, pos 1: 3 > 4 or 4 > 3, pos 2: 3 > c or c > 3 pos 3: 4 > c or c > 4.

By combining all three valves you can divert water from any tank to any other tank and from any tank to the sea, and vice versa, or deny any water movement at all at any ballast configuration. This is the minimum number of valves that can do this.

Under gravity only
Say all tanks are empty - boat is heeled to port, all valves closed. Open valve c, and switch valve a so that water flows from sea into tank 1. Turn valve a off, change tack - too much forward trim - need to fill aft port tank 4, change tack again, open valve b so that water flows from sea to 4, close valve b, change tack, and everything is nice. Change tack: switch both a and b valves so that water flows to starboard tanks, switch them off; great. Rounded the mark, and now running - switch a, b and c valves to empty all water from tanks. I hope you get the picture polarity.

using the pump this is the interesting bit
All empty, heeled to port - want to fill starboard tanks: open c, switch a and b to corresponding pos, turn the pump on, and off you go.

Now say you want to pump from 2 and 3 to 1 and 4: can't be done the normal way. But what you can do, is pump from sea, to 1 and 4, and empty 2 and 3. I say its beautifull. In this case you would need to make valve c a three pos valve as well, with it's own double outlet, so that as your pumping in you are empyting at the same time. I think that is superfluouse.

If your tanks are all below sea level at all heeling angles - you can still use this system.

I hope this clears things up.