Hi guys, here's the topic of the "Oliforum contest", the competition for training that i'm arranging from some weeks . i'll try to sumarize all details about it, be carefully. 1- The contest is made of some rounds(I think 3 max). 2- Each round is made of only 3 problems, and i will give points 0 to 7: 6 for all correct solutions, 7 for only elegants and correct solutions (similar to ML contest). 3- It is tought for high-school student, and also for undergraduate or higher student, but you cannot use non-elementary-theory, otherwise the solution is invalid. 4- All begins from italian-oliforum and the classification is unique. 5- The first round starts on 12:00 of 20 september and it ends on 24:00 of 21 seprember, so saturday and sunday. NB. All times (date and hours) are according to ROME MERIDIAN (+2GTM), please attention! 6- Enrollment is not necessary, it sufficies to send me solution. 7- I’ll take in consideration time of arriving solutions only for the first place if there are more 21/21 points. 8- Way of sending solutions. - You need to send solutions to both email address: pao_leo88@hotmail.it and leonettipaolo@gmail.com in a unique pdf file (so, with attachment) of a right size; - The pdf file must be written with Latex (or a way that I can understand); - You rename the pdf file as your nickname (the same of yours in ML); - You need to write nothing in the email; - Try to be clear in solutions! I’ll estimate it! {If (and only if) you are not able to create a pdf in latex model, you can send me a email in .doc format with solutions, as latex or in a way that i (and all correctors) can understand}. Later, I'll make a list below this topic where i'll write all names of who sent me solutions in right way. For all doubts and questions, ask me Thanks for the attentions And good luck Paolo Leonetti Italian version
Problem
Source:
Tags: email, LaTeX, calculus, derivative, geometry, cyclic quadrilateral
20.09.2008 12:53
OLIFORUM CONTEST - ROUND 1 Question 1 Prove that in the set $ S=\{2008,2009,. . .,4200\}$ there are $ 5^3$ elements such that any three of them are not in arithmetic progression. Question 2 Let $ ABCD$ be a cyclic quadrilateral with $ AB>CD$ and $ BC>AD$. Take points $ X$ and $ Y$ on the sides $ AB$ and $ BC$, respectively, so that $ AX=CD$ and $ AD=CY$. Let $ M$ be the midpoint of $ XY$. Prove that $ AMC$ is a right angle. Question 3 Let $ a,b,c$ be three pairwise distinct real numbers such that $ a+b+c=6=ab+bc+ca-3$. Prove that $ 0<abc<4$. NB. In problem 1, we'll not accept merely numerical solutions.. Good work
Attachments:
olicontest.pdf (27kb)
20.09.2008 17:29
hey boyypa wen is the last date or time for sending it!
20.09.2008 20:27
from now you have still about 28 hours! so, it is the midnight (24:00) of tomorrow! NB in problem 3 you cannot use derivatives or calculos!
21.09.2008 01:12
Contestants who sent me solutions: A Cave sumita Madhukar_Daftary NickNafplio turcas_c mod_2 Rigel dima_ukraine kamyar1991 giove bestiedda Akashnil fede90 String Alex89 Broniran julio14 silouan quicktimeplayers nicelbole tomci0 eucla mhdi Algebert
21.09.2008 12:30
In problem 3, we have a,b,c not equal to zero, right?
21.09.2008 13:09
NickNafplio wrote: In problem 3, we have a,b,c not equal to zero, right? we have that a,b,cmust be all distinct..if they are \neq 0 may be a consequence
21.09.2008 13:49
bboypa wrote: NickNafplio wrote: In problem 3, we have a,b,c not equal to zero, right? we have that a,b,cmust be all distinct..if they are \neq 0 may be a consequence Ok, I think I found a solution, but I cannot write it in microsoft word (I dont know how to write some symbols), someone told me that I can send the solution to you by private message here, can you accept it by pm?
21.09.2008 14:16
try to write in doc. as latex model (with use of dollars for your forumlas) and send it to my email, (it is the same that you're writing in a pm); sumita sent me his solution in notepad, (always as latex), it goes right too.
21.09.2008 14:26
bboypa wrote: try to write in doc. as latex model (with use of dollars for your forumlas) and send it to my email, (it is the same that you're writing in a pm); sumita sent me his solution in notepad, (always as latex), it goes right too. Now I sent you a solution with microsoft word. Check your e-mail and tell my if my solution is right please. If I solve the other 2 problems, I will send you the solutions in doc as latex
21.09.2008 20:02
in problem one i prove more strong than the purpose of the question. more than 130
21.09.2008 20:37
i have a solutoin with more that 220.
21.09.2008 21:21
sumita wrote: i have a solutoin with more that 220. now, i'm too..
22.09.2008 01:06
When will solutions be posted? Will we receive our answers correction?
22.09.2008 01:25
mhdi wrote: When will solutions be posted? Will we receive our answers correction? @mhdi&all others: thanks for partecipating! i hope the problems were good for you.. however in this days i'll post problems also on olimpic section (i'll put a link here) and during this week i (and other correctors) try to get the final graduation for the first round about solutions, if in the link there are no exsaustive, then i'll post the easiest and shortest ones.. still, thanks to all cheers paolo
22.09.2008 01:29
bboypa wrote: mhdi wrote: When will solutions be posted? Will we receive our answers correction? @mhdi&all others: thanks for partecipating! i hope the problems were good for you.. however in this days i'll post problems also on olimpic section (i'll put a link here) and during this week i (and other correctors) try to get the final graduation for the first round about solutions, if in the link there are no exsaustive, then i'll post the easiest and shortest ones.. still, thanks to all cheers paolo Is there any link with the solutions?
22.09.2008 02:01
First problem Second problem Third problem however, when i'll post graduation, i'll attach also ufficial solution
22.09.2008 13:22
hi bboypa when the second round will be start? what is the graduation??? totally this work is very good so i hope this is be continued and have prize....
22.09.2008 16:21
Kamyar1991 wrote: hi bboypa when the second round will be start? what is the graduation??? totally this work is very good so i hope this is be continued and have prize.... second round will be after two weeks from now i think.. however i'll contact you by email and i'll post dates on this post. the graduation will be max tomorrow, thanks of all..
22.09.2008 19:54
Kamyar1991 wrote: what is the graduation??? I think he means gradation (results i.e. giving points)
23.09.2008 15:03
sorry my english is not very good
23.09.2008 17:20
here there are the results: there are only contestant whit score > 7 points: I- giove - (Oliforum) FULL SCORE -21 points II- Akashnil - (Mathlinks) -21 points III- silouan -(Mathlinks) - 21 points IV- tomci0 - (Mathlinks) - 21 points V-(ex-aequo) - sumita -(Mathlinks : 7/6/7) -20 points julio14- (Oliforum: 7/7/6) - 20 points VII- Kaymar1991 - (Mathlinks: 6/7/6) - 19 points VIII-A Cave - (Yahoo: 7/7/2) - 16 points IX- (ex-aequo)- Rigel - (Oliforum: 6/6/1) -13 points mhdi - (Mathlinks: 0/6/7)- 13 points algebert - (Oliforum: 0/7/6)- 13 points XII- nicelbole - (Oliforum: 7/0/5) - 12 points XIII- turcas(linker) - (Mathlinks: 0/7/3) - 10 points XIV- dima_ukraine - (Mathlinks: 0/7/2) - 9 points Thanks for having partecipated to : NickNafplio(Mathlinks) fede90(Oliforum) String(Oliforum) Alex89(Oliforum) Broniran(Mathlinks) Eucla(Oliforum) Bestiedda(Olifrum) Quicktimeplayers(Oliforum) Madhukar_daftary(Yahoo) mod_2(Oliforum) *Honorable mention goes to A Cave , who sent all solutions in less of 4 hours (and invalidating half of third exercise only for a misunderstood with regulament..) NB to all others contestant i'll send an email with his personal score..! Best regard Paolo & other correctors
23.09.2008 19:43
The second round is for everyone or only for those who solved more than one of the three problems?
23.09.2008 20:24
NickNafplio your solution to the third problem is perfect, one of the best! 7points ! however, no, everyone can partecipate to every round.. next round will be saturday 4 october at the same hours! cheers to all
23.09.2008 20:58
bboypa wrote: NickNafplio your solution to the third problem is perfect, one of the best! 7points ! however, no, everyone can partecipate to every round.. next round will be saturday 4 october at the same hours! cheers to all Ok, thanks
24.09.2008 19:13
here there are solutions of Tomci0, a clear and elegant example of solutions
Attachments:
21) TomciO.pdf (44kb)