The Proof is Trivial!

You should find a mathmo to give you more accurate answers.

No, I vote they keep asking you questions

I don't know why they trust my answers given I'm not a mathmo. I only say what I know from observing/listening to mathmo friends.

Well we'll have to grill you about college life. What are the north court bathrooms like?

Here's a pic from the website.

That varies, but I think the reason why Cambridge likes STEP so much is because, well, they work reasonably (or at least better than A-levels) as a predictor. But that is of course no indication that you would definitely be bound by what it "predicts" based on what you get on STEP.

Again that varies from person to person, and there are plenty in both camps (just staying afloat and keeping up with exams vs. having a comfortable and time doing things beyond the course). The point is that once you get in you should be challenged regardless of your ability level.

You should find a mathmo to give you more accurate answers.

Well we'll have to grill you about college life. What are the north court bathrooms like?

Well you pick North Court for the size of the rooms (especially if you want very big or very small) and atmosphere (it seems to have far too much wood to be fire-safe), not the quality/convenience of the rooms Depending on luck you your nearest bathroom may or may not have a window or even ventilation and it's very likely to be shared across at least three or four people. There are showers, but you may have to go up or down one (or more!) flights of stairs to get to it.

Also I didn't have a sink in my grade four room in first year, although it was a very large penthouse room to compensate. The sink room was nearby.

I take it you went for North Court then? Did you enjoy it (seems like a stupid question given your response). Three or four isn't too bad (I'm comparing this to my brothers accommodation elsewhere)! Given the rest of the stuff how terrifying are the showers? Stairs are fine.

I lived in North Court for my first three years (although in the ensuites part only available to non-freshers for the last two). I actually thought it was great, including the first year, as my room overlooked the centre of court and it was spacious, peaceful and had a great view (weekly 5am rubbish trucks reversing into court not withstanding). The showers aren't that great, the ones nearest to me had mold and the walls were peeling. But you might get lucky and get one of the refurbished staircases, in which case they will have even superior plumbing than South Court.

I'm intrigued as to what search yielded that

I lived in North Court for my first three years (although in the ensuites part only available to non-freshers for the last two). I actually thought it was great, including the first year, as my room overlooked the centre of court and it was spacious, peaceful and had a great view (weekly 5am rubbish trucks reversing into court not withstanding). The showers aren't that great, the ones nearest to me had mold and the walls were peeling. But you might get lucky and get one of the refurbished staircases, in which case they will have even superior plumbing than South Court.

Well this says the opposite

Well this says the opposite

Well this says the opposite

I don't look quite so stupid now

PRSOM

exactly.

Problem 151*

Show that every integer appears in the infinite sequence:

$\pm 1^{2}, \pm 1^{2} \pm 2^{2} , \pm 1^{2} \pm 2^{2} \pm 3^{2} , ...$

and appears so infinitely many times.

Looks like somebody else is signed up to the mentoring scheme too! I think I have a solution for this.
How have you found the other questions?