First post - I've been a long time lurker and it's time to give something back. I spent hours on this and although I think it's too early for direct spoilers, here are some hints.
If I've got this right, 9 across contains a synonym for the number to be modified, which is split. The contest is one which takes place between two universities every year and "case" here means "contents" (as in a case of wine, I suppose).
In post 22, Buzzybee has inadvertently hit on part of the answer to 17,14,8! This too contains a synonym (split) of a number to be modified as well as another more straightforward modification.
I'm loth to criticise Paul as he's one of my favourite setters, but can anyone approaching this in the spirit of Victor Borge really be expected to guess at split synonyms (and a reversal)?