In case you thought I was clever
Now if these were DIVERTERS, that'd be slightly more sensible, if you had 3 devices that could send water either one way or the other then you could arrange them in a pyramid with the outputs of the top connected to the inputs of the two beneath and you could drive four hoses with three coils, but I sent the hamster at the back of my brain on a mission to try and do this with valves and then I sat down with my pencil and graph paper and said OK brainhamster what'd you think of while I was doing other stuff and the hamster went 
boss if you send me on another of these wild goose chases I swear to god