However I’ll just point out that there are rare circumstances where the rules regarding admissions scores can be broken (though I don’t think they are particularly applicable in this case): some Cambridge colleges will view an S in the STEP-3 paper (or being selected for the IMO) as a sufficient demonstration that you are one of the best mathematicians in the world and won’t care if you haven’t even been to school. After all they don’t want to miss out on a future Ramanujan!