The Proof is Trivial!

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

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?

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.

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.
:/

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)

Ah k. Ugh it's so boring to do S1 past papers.

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

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.

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

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.