It is strange, that "magic" six. I've never got to the bottom of it, but it goes back a long way, since I recall references to it in one of those 1940s-50s boys' story books set in minor public schools of the most highly regarded mediocrity in syllabus and teaching.
"References"... actually lingering descriptions of trousers being "dusted" by the house-master, and screams spelled "Yarooo!" and suchlike; the six strokes being not maximum but standard. Though in one chapter the three boys in trouble had an "impot" I think it was called - "imposition", or lines. Apparently, copying 100 lines from some Classical Latin ode or other of victoriously bellicose doings.
Funny - or worrying. Ask me what I had for dinner yesterday and I'd have to think for a minute or so. Give me a recollection of past physical punishments and I remember school-boy books from half a century ago.
Some cite Jimmy Edwards in the radio and TV comedies, Whacko!, but he certainly did not invent that six strokes even if the phrase "Six of the Best" were from him, or his writers. It pre-dates those shows.