How could three economical Depression-era battleships be designed to face ships such as Bismarck or Yamato?
Short answerDevelop a faster Nelson-type ship with 16-inch guns, stronger machinery, and a superfiring forward battery.
NotesNelson and Rodney offer the newest proven starting point available in the period. Their armour and 16-inch battery already provide a credible answer to later heavy battleships, but their speed is the obvious limitation. More boilers could raise the design to roughly 28 knots, while a superfiring arrangement would let all nine guns bear forward. This economical approach modifies a sound baseline instead of inventing an entirely new ship.