Thanks a lot, have already begun on the number theory one.
They all seem to be great resources but I have heard rumours that recently they have stopped putting the standard type inequalities on the papers because Muirhead's Theorem just kills them. Has anyone else heard anything like this and is it true?
Thanks a lot, have already begun on the number theory one.
They all seem to be great resources but I have heard rumours that recently they have stopped putting the standard type inequalities on the papers because Muirhead's Theorem just kills them. Has anyone else heard anything like this and is it true?
That is kinda true, but they may still appear, especially asymmetric inequalities and those involving squares being more than 0
Thanks a lot, have already begun on the number theory one.
They all seem to be great resources but I have heard rumours that recently they have stopped putting the standard type inequalities on the papers because Muirhead's Theorem just kills them. Has anyone else heard anything like this and is it true?
Yh they still might put them in there, or if one makes a problem tricial they could put a note and say (Muirhead cannot be used) although I doubt they would. Inequalities come up every 4-5 years anyway. I guess one is due tbh.
Looking back to the 1960's and early 1970's it amazes me how easy the IMO used to be back then (I don't think it the level is much higher than difficult BMO1).
Looking back to the 1960's and early 1970's it amazes me how easy the IMO used to be back then (I don't think it the level is much higher than difficult BMO1).
Lol yep. First paper first question prove this is irreducible 21n+4/14n+3 or something. But then there werent any rounds before tbh like BMO or national contests and it was a few countries.
Ok, so on the most part, it's fine. Your proof for why one area was a quarter of the other was not needed, since it comes straight away from the fact that AB=4AD and also, the formula you quoted for phi was wrong. Areas should be in square brackets, eg [APD]. But yeah, correct on the whole.
Ok, so on the most part, it's fine. Your proof for why one area was a quarter of the other was not needed, since it comes straight away from the fact that AB=4AD and also, the formula you quoted for phi was wrong. Areas should be in square brackets, eg [APD]. But yeah, correct on the whole.
Oh yh forgot the sinheta. Cheers yh I forgot about the square brackets thing. So one would not have to consider the sintheta=0 and sin(theta-alpha)=0 cases? As I divide through by them To get to my final two expressions.
Oh yh forgot the sinheta. Cheers yh I forgot about the square brackets thing. So one would not have to consider the sintheta=0 and sin(theta-alpha)=0 cases? As I divide through by them To get to my final two expressions.
Well, those cases are degenerate. I would recommend just using similar triangles tbh, it saves a lot of time and algebra. If you see a lot of terms cancel, that should probably suggest similar triangles to you. If you use similar triangles, you could also possibly gain some new information about angles from information about lengths.
Well, those cases are degenerate. I would recommend just using similar triangles tbh, it saves a lot of time and algebra. If you see a lot of terms cancel, that should probably suggest similar triangles to you. If you use similar triangles, you could also possibly gain some new information about angles from information about lengths.
Yh I seen they were similar but didnt use those ratios. For some reason in my head it went similar triangles->ratios of areas