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    (Original post by TheMagicMan)
    You shouldn't feel dumb. It's the last question on a BMO. If you find it easy at 18/19 you're part of a very small group.
    Hey, do you know how to do Q1 and Q2 from this? http://www.bmoc.maths.org/home/bmo2-2006.pdf
    For q1 i got 4/9 but I has math-ing out of my ass lol.

    Also has question 1 from this- http://www.bmoc.maths.org/home/bmo2-2001.pdf have anything to do with a recurrence relation?
    Thanks
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    (Original post by demigawdz)
    Hey, do you know how to do Q1 and Q2 from this? http://www.bmoc.maths.org/home/bmo2-2006.pdf
    For q1 i got 4/9 but I has math-ing out of my ass lol.

    Also has question 1 from this- http://www.bmoc.maths.org/home/bmo2-2001.pdf have anything to do with a recurrence relation?
    Thanks
    For q1
    Spoiler:
    Show
     x=acos\theta , y=asin\theta
    For q2
    Spoiler:
    Show
     x+y=2^a , x-y=2^b, where  a+b=k, a\geq b

    And yeah, I solved it by using a recurrence relation, but there are probably other methods.
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    (Original post by Renzhi10122)
    And yeah, I solved it by using a recurrence relation, but there are probably other methods.
    Thank you!
    For q1 I tried using partial differentiation lol.
    Not sure if that would get anywhere.

    I'm glad my idea is correct for the recurrence one and I'd be very chuffed if I actually manage to figure it out.
    btw how long does it take you to figure them out?
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    (Original post by demigawdz)
    Thank you!
    For q1 I tried using partial differentiation lol.
    Not sure if that would get anywhere.

    I'm glad my idea is correct for the recurrence one and I'd be very chuffed if I actually manage to figure it out.
    btw how long does it take you to figure them out?
    Well, I've done them before when I was preparing for BMO2, apart from q1 2006, and that one took me about 20 minutes to realise 'TRIG!' and then that was done.
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    (Original post by Renzhi10122)
    Well, I've done them before when I was preparing for BMO2, apart from q1 2006, and that one took me about 20 minutes to realise 'TRIG!' and then that was done.
    How well did you do in the BMO's?

    I'd also be curious to know how you prepared for it.
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    (Original post by demigawdz)
    How well did you do in the BMO's?

    I'd also be curious to know how you prepared for it.
    Got 47 in BMO1 and 26 in BMO2. I just did a bunch of questions for BMO2, didn't really do much for BMO1. Have you done BMO before?
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    (Original post by Renzhi10122)
    Got 47 in BMO1 and 26 in BMO2. I just did a bunch of questions for BMO2, didn't really do much for BMO1. Have you done BMO before?
    I've never taken the exams before but I've done a few questions and many more partial attempts.
    I reckon I will finish the intro to number theory handbook by ukmt by the time of the exams but nothing else in terms of revision other than a few questions ext....

    For BMO2 all I've done is make a few partials with a hint or two and figured out that question I spoke about earlier needed to use a recurrence relation.
    :/
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    (Original post by demigawdz)
    I've never taken the exams before but I've done a few questions and many more partial attempts.
    I reckon I will finish the intro to number theory handbook by ukmt by the time of the exams but nothing else in terms of revision other than a few questions ext....

    For BMO2 all I've done is make a few partials with a hint or two and figured out that question I spoke about earlier needed to use a recurrence relation.
    :/
    Ah, that's fine then, you'll have plenty of time when they come round next year.

    What did you get for p/q?
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    (Original post by Renzhi10122)
    Ah, that's fine then, you'll have plenty of time when they come round next year.

    What did you get for p/q?
    Haven't done it yet :/
    I will try it today but at the mo I have S1 revision :/ (not hard really but it needs to be done I suppose)
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    (Original post by demigawdz)
    Haven't done it yet :/
    I will try it today but at the mo I have S1 revision :/ (not hard really but it needs to be done I suppose)
    Ah k. Ugh it's so boring to do S1 past papers.
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    (Original post by Renzhi10122)
    Ah k. Ugh it's so boring to do S1 past papers.
    yh
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    (Original post by demigawdz)
    Hey, do you know how to do Q1 and Q2 from this? http://www.bmoc.maths.org/home/bmo2-2006.pdf
    For q1 i got 4/9 but I has math-ing out of my ass lol.

    Also has question 1 from this- http://www.bmoc.maths.org/home/bmo2-2001.pdf have anything to do with a recurrence relation?
    Thanks
    Q1:
    These are a couple of obvious ways that are certainly feasible.

    Lagrange multipliers.
    The constraint is a cubic: just solve it!
    Some kind of trig/hyperbolic substitution should work

    Q2

    Factorise as the difference of two squares and it should be clear what to do.




    And yes a recurrence relation should be fine
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    (Original post by shamika)
    I'm getting these from somewhere but I think some of these are beautiful problems which hopefully someone with C1-4 can do (except 18, which ironically might be the easiest). Hope you don't mind the influx!
    If you don't mind- where are you getting these from? I'd be interested to know.
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    (Original post by demigawdz)
    If you don't mind- where are you getting these from? I'd be interested to know.
    I really can't remember! So sorry. I think I amended some problems to try to make them as easy as possible without making them 100% trivial
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    (Original post by shamika)
    I really can't remember! So sorry. I think I amended some problems to try to make them as easy as possible without making them 100% trivial
    ah ok
    nvm
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    Problem 495 *

    Two players take it in turn to move a king that has been initially placed on one of the centre squares of a chessboard. You lose if you move the king to a square he has previously occupied (including the initial starting square). Who wins the game, the first or the second player? Is there a winning strategy?
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    (Original post by Renzhi10122)
    Problem 495 *

    Two players take it in turn to move a king that has been initially placed on one of the centre squares of a chessboard. You lose if you move the king to a square he has previously occupied (including the initial starting square). Who wins the game, the first or the second player? Is there a winning strategy?
    8*8=64 squares => 63 moves from the centre piece.
    Assuming all the squares are met (for example the players went in a spiral) then the 2nd player wins.(I have a picture as a sort of proof which explains it)
    (I'm not sure how mathematical this solution is supposed to be btw).
    This sort of reminds me of a MAT question.
    As for a winning strategy idk at the mo
    I think I also have an example where the 2nd person loses.
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    (Original post by demigawdz)
    8*8=64 squares => 63 moves from the centre piece.
    Assuming all the squares are met (for example the players went in a spiral) then the 2nd player wins.(I have a picture as a sort of proof which explains it)
    (I'm not sure how mathematical this solution is supposed to be btw).
    This sort of reminds me of a MAT question.
    As for a winning strategy idk at the mo
    I think I also have an example where the 2nd person loses.
    Either player can win (as you said, there are cases for each), but both players want to win, so your spiral isn't a proof: you've considered one case only. Your answer isn't exactly what I was looking for, but keep trying. I can say that the solution isn't particularly mathematical.
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    What we know is that whoever goes first wants to force a spiral (or other systematic method to stop going onto an old square) and whoever goes second needs to try to force that move. Will have a good think about it next week when I have s chess board at my disposal, unless it's already solved

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    Tile the chessboard with dominoes. Winning strategy for player 1: always stay on the current domino.
 
 
 
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