Spigotless variable-temperature fluid (e.g., water) valve openable with a dispensing device and with optional back-pressure relief

A method, comprising:

• inserting a valve-opening-and-fluid-dispensing device into a receptacle of a fluid valve by engaging a groove of the device with a protrusion of the receptacle;
• in response to inserting the valve-opening-and-fluid-dispensing device into the receptacle, allowing a fluid to flow from a cold input port of a mixer and/or a hot input port of the mixer to an output port of the mixer, through a cavity and the receptacle, and out from the valve-opening-and-fluid-dispensing device;
• and
• adjusting, with the mixer, a ratio of a flow of fluid from the cold input port to the output port to a flow of fluid from the hot input port to the output port.

A structure, comprising:

• a water-supply-and-distribution system having hot- and cold-water outlets;
• an exterior partition;
• a water valve disposed in the exterior partition and including:
• hot- and cold-water inlets coupled to the hot- and cold-water outlets;
• a receptacle having a protrusion configured to engage a groove of a valve-opening-and-water-dispensing device;
• a cavity having a front end in communication with the receptacle and having a rear end;
• a mixer having hot- and cold-water input ports coupled to the hot- and cold-water inlets and having an output port in communication with the rear end of the cavity;
• and
• a valve assembly disposed in the cavity, configured to allow fluid to flow from the output port through the cavity in response to a valve-opening-and-water-dispensing device being disposed in the receptacle, and configured to prohibit water from flowing from the output port through the cavity in response to the valve-opening-and-water-dispensing device being absent from the receptacle.