The Ultimate Maths Competition Thread

Original post by ben167

Does anybody have a nice solution to BMO1 2007/8 question 1? I used algebra but got stuck

Algebra is the way to go. It should work out nicely tbh.

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Reply 102

ben167

Original post by physicsmaths

Algebra is the way to go. It should work out nicely tbh.

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I know but i got to a stage where it stopped working because I needed to find out 2007^4 which is huge

Reply 103

ben167

@physicsmaths how would you solve it?

Reply 104

Original post by ben167

I know but i got to a stage where it stopped working because I needed to find out 2007^4 which is huge

Let n=2007 then do the algebraic division to get a quadratic.

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Reply 105

Euclidean

Signing up to this for summer. Wanna get good at problem solving before I go to uni cause atm I'm shocking, didn't even qualify for BMO :lol:

Reply 106

a fun geo question. Latex is screwed anyway so i'm too lazy to fix it
Given a triangle $ABC$ satisfying $AC+BC=3\cdot AB$. The incircle of triangle $ABC$ has center $I$ and touches the sides $BC$ and $CA$ at the points $D$ and $E$, respectively. Let $K$ and $L$ be the reflections of the points $D$ and $E$ with respect to $I$. Prove that the points $A$, $B$, $K$, $L$ lie on one circle.

Reply 107

Could anyone check that its x=0 y=1 and x=3 y=-4 as the solutions to bmo1 1987 question 1. Many thanks

Reply 108

ok another one
find the number of solutions to

y^2 = x^3(x^2-5000)

where

x,y \in \mathbb{Z}_p

and p is a prime congruent to 3 mod 4.

Reply 109

I feel like I am solving most of the geometry problems using trig is that looked down upon like calculus in olympiads?

Reply 110

Original post by 11234

I feel like I am solving most of the geometry problems using trig is that looked down upon like calculus in olympiads?

Nah it aint looked down upon. Its looked at better then coordinate bashes and stuff.

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Reply 111

Original post by physicsmaths

Nah it aint looked down upon. Its looked at better then coordinate bashes and stuff.

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But i find doing it by pure euclidean is the hardest

Reply 112

Original post by 11234

But i find doing it by pure euclidean is the hardest

give an example

Reply 113

Original post by gasfxekl

give an example

Like using constructions and similar triangles and stuff

Reply 114

Original post by 11234

Like using constructions and similar triangles and stuff

practice is key.

Reply 115

Original post by gasfxekl

practice is key.

I know do you have any geometry questions you would be happy to share. Sorry I couldnt understand the previous geometry question you posted without latex

Reply 116

Btw guys Irish Mathematical Olympiads is another massive source of questions at the exact level of BMO1/2 so you can do thos if you run out.

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Reply 117

Original post by 11234

I know do you have any geometry questions you would be happy to share. Sorry I couldnt understand the previous geometry question you posted without latex

lol dw that ones kinda hard
idk bmo has a lot of nice geometry questions. how much do you know about cyclic quadrilaterals etc?

Reply 118

Original post by gasfxekl

lol dw that ones kinda hard
idk bmo has a lot of nice geometry questions. how much do you know about cyclic quadrilaterals etc?

ptolemys theorem and that the opposite angles add to 180

Reply 119