Building a Second World War navy around five gun calibers

Which five gun calibers would you choose for an entire navy at the start of the Second World War?

The proposed set is 40 mm, 4.5-inch, 6-inch, 9.2-inch, and 16-inch weapons for light AA through battleship armament.

Clarke chooses 40 mm for a weapon expected to remain useful throughout the war. For general-purpose work, he prefers 4.5-inch guns as a compromise between the different advantages of 5-inch weapons. Six-inch guns equip the light cruisers, while 9.2-inch guns give the heavy cruisers a distinct capability despite the availability of more modern 8-inch weapons. The battleship choice is 16-inch, partly because a super-heavy shell design becomes available during the period. A preferred 16.5-inch option falls outside the exercise's available choices.