Was it really a thirteen year old schoolgirl who is to be thanked for the Spitfire having eight Brownings instead of four? I'm afraid a family myth has been given credence by journos who know nothing of the development of aircraft in the thirties.
My bet would be that it was all worked out by a chap called RJ Mitchell and his team to meet the Air Ministry specification for a new eight gun monoplane fighter to compete with the Hurricane.