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    (Original post by ukdragon37)

    You should find a mathmo to give you more accurate answers.
    No, I vote they keep asking you questions:p:
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    (Original post by Slumpy)
    No, I vote they keep asking you questions:p:
    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.
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    (Original post by ukdragon37)
    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?
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    (Original post by bananarama2)
    Well we'll have to grill you about college life. What are the north court bathrooms like?
    Here's a pic from the website.
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    (Original post by Lord of the Flies)
    Here's a pic from the website.
    :rofl: I'm intrigued as to what search yielded that
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    (Original post by ukdragon37)
    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.
    Thanks of the responses... I shall now return to my STEP-induced coma and continue to plan my ascent into the mysterious world of advanced mathematics

    Emmanuel doeeeeeee
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    (Original post by bananarama2)
    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 :puke: 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.
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    (Original post by ukdragon37)
    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 :puke: 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.
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    (Original post by bananarama2)
    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.
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    (Original post by ukdragon37)
    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 stayed in North Court cloisters for my interview It was lovely, although I couldn't for the life of my work out what the view was of I seem to remember someone saying something about a staircase being refurbished. I'd be me to get the mouldy shower though, but It can't be worse than my brothers. Thanks for the info.
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    (Original post by bananarama2)
    :rofl: I'm intrigued as to what search yielded that

    It's just a typical French bathroom.
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    (Original post by ukdragon37)
    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 :eek:
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    (Original post by Jkn)
    Well this says the opposite :eek:
    I don't look quite so stupid now
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    (Original post by Jkn)
    Well this says the opposite :eek:
    :lol: PRSOM
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    (Original post by Jkn)
    Well this says the opposite :eek:
    :hand: exactly.
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    (Original post by bananarama2)
    I don't look quite so stupid now
    (Original post by joostan)
    :lol: PRSOM
    (Original post by ukdragon37)
    :hand: exactly.
    Comedy gold :lol: I'm going to post it everywhere now :lol: :lol:
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    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.
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    (Original post by Felix Felicis)
    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?
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    (Original post by such)
    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?
    Ha! I presume you mean the Olympiad? I'm not signed up to the mentoring scheme, I just found it on the internet ages ago
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    Hah, OK, coincidentally this exact question appeared on the UKMT senior mentoring scheme this month. This is probably the first question posted on here that I can do I have to start somewhere I guess!

    Solution 151
    Constructive proof.
    

1 = 1^{2}

2 = -1^{2}-2^{2}-3^{2}+4^{2}

3 = -1^{2}+2^{2}

\displaystyle x +4 = x + n^{2}-(n+1)^{2}-(n+2)^{2}+(n+3)^{2}, n\in\mathbb{N}
    From the rules above it is possible to make any integer by starting with an integer from 0 to 3, and adding or subtracting an integer multiple of 4. Furthermore, it is possible to make any integer in infinitely different ways, by adding on some multiple of 4 and then subtracting that multiple again.
 
 
 
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