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    neat...
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    (Original post by 4Ed)
    neat...
    yet the formulae are nearly impossible to derive if you don't know them.
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    how was ur interview (besides answering that question)
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    (Original post by 4Ed)
    how was ur interview (besides answering that question)
    Quite difficult i made some silly mistakes but came through better near the end. In the test, i got 2 completely correct questions, 1 partly correct, and attempted q.3 which the professors got stuck on
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    Q3 being the one u mentioned
    sounds pretty good.... u reckon u'll get in?
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    (Original post by 4Ed)
    Q3 being the one u mentioned
    sounds pretty good.... u reckon u'll get in?
    Dunno, i personally thought i'd done really badly, but we'll have to wait and see.
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    well u've prolly done enough to get pooled at least, and trin math candidates r prolly first to get looked at in pool. not saying u wont get in of course.
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    (Original post by 4Ed)
    well u've prolly done enough to get pooled at least, and trin math candidates r prolly first to get looked at in pool. not saying u wont get in of course.
    Thanks for your support, but I really can't tell, I got the impression that i didn't come over as being exceedingly intelligent in interview, although i gues i did pick the hard question(s).
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    well last yr i had a stats prob where i ended up with a result where the sum of all the probs in part A was 5 and part B 13...... which made me look really stupid. i got pooled tho (but that was a complete lottery, so didn't get picked up).
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    (Original post by 4Ed)
    well last yr i had a stats prob where i ended up with a result where the sum of all the probs in part A was 5 and part B 13...... which made me look really stupid. i got pooled tho (but that was a complete lottery, so didn't get picked up).
    Hehe. so there is hope
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    (Original post by theone)
    Firstly you have to prove all triples x,y,z can be written in the form:

    x= m^2-n^2
    y = 2mn
    z= m^2+n^2

    This i didn't do, but merely asserted, and had to prove it interview. After this, a neat bit of modular arithmetic, or trying all the possibliites if you don't know this, makes the answer drop out.
    How did you do this? I think i have a proof but it is strange. Consider a right angled triangle with hypotenuse z, and angle 2A. x = cos2A , y = sin2A, and z^2 = x^2 + y^2. letting m = cosA and n = sinA gives the above results. This seems dodgy(ish)
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    (Original post by 4Ed)
    well u've prolly done enough to get pooled at least, and trin math candidates r prolly first to get looked at in pool. not saying u wont get in of course.
    Yeah, they often get pooled to Clare, hey hey hey...lol.
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    (Original post by It'sPhil...)
    How did you do this? I think i have a proof but it is strange. Consider a right angled triangle with hypotenuse z, and angle 2A. x = cos2A , y = sin2A, and z^2 = x^2 + y^2. letting m = cosA and n = sinA gives the above results. This seems dodgy(ish)
    i've seen taht before...... i think it mite be right dunno (ahve to ask theone)
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    (Original post by Adhsur)
    Yeah, they often get pooled to Clare, hey hey hey...lol.
    lol..... u may get a chance to meet theone
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    I found this maths question online. I think it is a joke because it is literally impossible:

    A 'snooker' table (measuring 8 metres by 4m) with 4 'pockets' (measuring 0.5m and placed at diagonal slants in all 4 corners) contains 10 balls (each with a diameter of 0.25m) placed at the following coords:

    2m,7m...(white ball)
    ...and red balls...
    1m,5m... 2m,5m... 3m,5m
    1m,6m... 2m,6m... 3m,6m
    1m,7m... 2m,7m... 3m,7m


    The white ball is then shot at a random angle from 0 to 360 degrees.
    Just to make it clear, a ball is 'potted' if at least half of the ball is in area of the 'pocket'

    Assuming the balls travel indefinitely (i.e. no loss of energy via friction, air resistance or collisions), answer the following:

    a: What exact angle should you choose to ensure that all the balls are potted the quickest?
    b: What is the minimum amount of contacts the balls can make with each other before they are all knocked in?
    c: Same as b, except that each ball - just before it is knocked in - must not have hit the white ball on its previous contact (must be a red instead of course).
    d: What proportion of angles will leave the white ball the last on the table to be potted?
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    Here it is the solution to your problem

    We may assume, without loss of generality, x,y,z share no common factor, since all pythagorean triples, if they share a common factor, can have that factor divided to get x,y,z without a common factor. Therefore we may state that x,y,z are pairwise coprime, i.e. No two of them share a common factor, else the third would also share this factor.

    Now it is impossible for all x,y,z to be even since then we have a common factor of 2. Similarly they can not all be odd since odd +odd =/= odd. Now if two are even, this implies the other one is odd. So We can only have 2 odd and one even. Now we make take, without loss of generality, y to be even. Thus y = 2k.

    But y^2 = 4k^2 = z^2 -x^2 = (z+x)(z-x). Now z+x and z-x can not both be even, since then z would share a common factor with x and they would not be pairwise coprime. Thus each of z+x, z-x must represent a perfect square for (z+x)(z-x) to be a perfect square. Also, in order to get our factor of two, one of them must be even. Say z+x = 2n and z-x = m. Then y = 4m^2n^2 and y = 2mn. And i have to go now, but the rest follows from this...

    And hey, adhsur, you never know what might happen.
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    (Original post by Adhsur)
    What are the flaws of induction, what is a circular argument, why is murder wrong, etc etc.
    that's not that bad

    i would say it's easier than what i would expect.

    (Original post by Adhsur)
    Well, it has certainly been a long two days, but I'm finally back from cambridge! Since you are all keen to know (or perhaps not) maybe I should tell you about my interviews...

    First of all, they were NOTHING like expected - I had revised all this really clever stuff but none of it was asked. I wasn't asked my interests, my reasons for choosing philosophy, about my personal statement, anything! Nothing general at all which is a shame. In fact, I got into the interviews and they just kinda plunged me straight away into all sorts of weird questions on what I would do in certain situations and what I think of certain arguments. One of the interviews went through the written test which I did the evening before..which they said was done amazingly well (But hey, maybe they say that to everyone to be encouraging?)

    My answers were alright I SUPPOSE. They could probably tell my voice was shaking all the way through and I was being VERY inarticulate. They did try and challenge what I said but I kept my ground reasonably well.

    What I noticed was that the interviews seemed to be SO short that I didn't think they covered much at all - i don't think they really got to know me or know what my potential is...it was such a quick hazy blur both times!!

    I'm a bit blank now, and I'm almost certain I won't get in (judging from the apparently brightness of all the other applicants). I heard they'll accept about 4 people out of well over 20 which is bizarre if true. I certainly am not expecting to get an offer - however, I must say it will be heartbreaking not to when my two days here have led me to get SO attached to cambridge, the atmosphere and the types of people...it would really be wonderful to go there.

    Any other questions, please ask!
    we ve got exactly the same feeling, i really liked cam after the interview, coz i didnt attend any open days, that was the first chance to meet the senior there and they were quite nice! i liked the atmosphere and i really wanna be there!
    iam really unsure about my interview and i dont even know if it went well ! i am getting even more confused now! why do we have to worry about all this? why do we have to guess their stupid feelings about us?whats our fault? being too good?
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    (Original post by hell manager)
    we ve got exactly the same feeling, i really liked cam after the interview, coz i didnt attend any open days, that was the first chance to meet the senior there and they were quite nice! i liked the atmosphere and i really wanna be there!
    iam really unsure about my interview and i dont even know if it went well ! i am getting even more confused now! why do we have to worry about all this? why do we have to guess their stupid feelings about us?whats our fault? being too good?
    Surely it's not being good enough to know whether we're in?
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    (Original post by Adhsur)
    Well, it has certainly been a long two days, but I'm finally back from cambridge! Since you are all keen to know (or perhaps not) maybe I should tell you about my interviews...

    First of all, they were NOTHING like expected - I had revised all this really clever stuff but none of it was asked. I wasn't asked my interests, my reasons for choosing philosophy, about my personal statement, anything! Nothing general at all which is a shame. In fact, I got into the interviews and they just kinda plunged me straight away into all sorts of weird questions on what I would do in certain situations and what I think of certain arguments. One of the interviews went through the written test which I did the evening before..which they said was done amazingly well (But hey, maybe they say that to everyone to be encouraging?)

    My answers were alright I SUPPOSE. They could probably tell my voice was shaking all the way through and I was being VERY inarticulate. They did try and challenge what I said but I kept my ground reasonably well.

    What I noticed was that the interviews seemed to be SO short that I didn't think they covered much at all - i don't think they really got to know me or know what my potential is...it was such a quick hazy blur both times!!

    I'm a bit blank now, and I'm almost certain I won't get in (judging from the apparently brightness of all the other applicants). I heard they'll accept about 4 people out of well over 20 which is bizarre if true. I certainly am not expecting to get an offer - however, I must say it will be heartbreaking not to when my two days here have led me to get SO attached to cambridge, the atmosphere and the types of people...it would really be wonderful to go there.

    Any other questions, please ask!

    Well, it's over now, so here's to being excepted! (Hopefully)
 
 
 
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