Junior Olympiad of Mathematics (JOM) 2013

The third camp of IMO 2014 is approaching soon (over!), and in the second camp we, the senior team, organized a competition called Junior Olympiad of Mathematics (JOM) 2014 to the juniors. The leaders were How Si Yu and How Si Wei, both in their Pre-U and took part in IMOs 2010-2013 (one of them being the Malaysia’s first, and the only gold medalist till now.) I am not really involved in this (except proposing some problems), so there’s nothing to say.

But I was one of the leaders in 2013, with Justin as my partner.

5 July 2012: Inspiration.

On the departure day to IMO 2012, the deputy leader and 6 of us were waiting in the KLIA departure hall for our flight, scheduled 2:00 am. Tick tock tick tock, doing countdown with boredom. Justin broke the silence by talking about ELMO 2012 (a competition by the black team in MOP of USA) shortlist, which was just published at that time, with full of enthusiasm. “Look at the name: Every Little Mistake ->0”, he said.

“Here’s problem A10: Given A_1-A_8 as points of cyclic octagon and B_i=intersection of lines A_i A_{i+1} and A_{i+3} A_{i+4}. Prove that B_i all lies on a conic. Apparently he created this problem after learning Bezout’s theorem.”

“Hmm…with Bezout’s theorem the 8 points are solutions of equations of degree 2.” “And that solves it!” Hmm, I couldn’t pretend that I knew it.

After the second paper of IMO (where we exited the hall with frustrations towards P4 and P5), we thought about mimicking the USA and have our own Olympiad. The first step is to have a name! 6 of us just played around of “MOM’ and 5 other permutations of it. (All due to Justin’s ardent persuasion of the cool thingy).

20 July 2012: Propose for action.

Justin was really serious: he reminded us about the sketch in our heads and I quickly thought about a problem and posted with alacrity, which ended up in N6 of the shortlist (Those who were involved in IMO 2012 would know exactly how I obtained this idea):

“Find all functions f:Z->Z such that for every prime p, p divides ab+bc+ca if and only if it divides f(a)f(b)+f(b)f(c)+f(c)f(a)”

August 2012: Colour the sketch in order to become a picture.

Justin and I attended the Summer Conference of Tournaments Of Towns in Russia, and had further discussion on it: should it count in selection; will the training team endorse it; were we (the seniors) good enough to set the problems from them; blah blah blah… It kept me engrossed to it.

Meanwhile, Si Yu proposed a problem, where he claimed as generalized Muirhead’s theorem, turned out as an A8. His creations in the shortlist are generally brutal.

October-November 2012: Call for action.

After obtaining consent from Mr. Suhaimi, we worked it out: Justin invited all seniors (and past Olympians, for those who made to the 3rd camp previously) into Facebook group, and motivated everyone to post problems in the group. Those who had alternative solutions to a problem were cordially welcomed. It worked, where we had about 15 problems by mid of December.

It worth noting that how we met bottleneck where the problem bank were in imbalance state: lack of Geometry and Number Theory problems. I quickly sent out a reminder and it yielded a positive feedback.

IMO 2012 Camp 1 (14-18/12/2012): Convergence made great thoughts.

Carlton hotel was a fantastic training venue, and seniors had a room for it. While being a lecture room, it was a discussion room for JOM 2013 too (surreptitiously, at least to the juniors). More ideas, more solutions, more comments, and more time for face-to-face meetings and discussions. Some of us (Zi Khang, Si Wei, I, etc) created new problems there.

By the end of the camp, we collected 20 problems in total. Bingo! 10 more problems to go to make a complete shortlist.

19-31 December 2012: Final miles to the complete model.

The deadline had drew near, so we worked our brain hard to gather more ideas, ranging from the contemporary fashion: Gangnam Style to the classical geometry problems.

To our delight, the action was getting prompt: more than 10 problems were proposed in that period, and subtracting those appeared in other Olympiads (unintentionally) we had 29 in total: as many as those in typical IMO Shortlist. Moreover, the composition is balanced: 7 Algebras, 7 Combinatorics, 7 Geometries and 8 Number Theories. An extol from Mr. Suhaimi for “problems of great depth and breath” was given upon Justin’s email of the shortlist to him: he would monitor the voting process soon.

1-13 January: Ballots and judgements.

The slot was fixed: 2 hours for Day 1 and 4 hours for Day 2 (on the last 2 days of camp). A good decision would be: Easy + Medium for Day 1, and Easy + Medium + Hard for Day 2.

The initial date for the camp was 18-22 January, which made Mr. Suhaimi to set a deadline for voting: 11 January (Friday). He later wanted it to be done by Thursday: where we acted promptly and asked for votes on easy problems on 3rd January. Several comments by Mr. Suhaimi and Mr. Ikhwan were then given. On the next day, we opened for hard problem.

Provisional results: 14 people marked their ballots (28 votes), where C3 won it hands down, and N2 was chasing tightly after it.

The training team then sent a belated new-year-surprise to all of us: camp date changed to 14-18/1 on Sunday (6th), again because of availability (though I knew beforehand that there were chances for that to happen.) I understand: Permata Pintar is a school where office administration can only be done on weekdays. What to do? Close the voting for easy problems (C3, N2) and open for medium ones.
Wait a minute: these weren’t easy, at least for those who studied MO within 3 months. Technically (in IMO) we should redo voting, but for the time’s sake + everyone’s endorsement we made them medium problems. Also: some comments on further voting  y Mr. Suhaimi. It seemed that everyone was influenced by him and the voting went surprisingly fast: we had P1-5 (EMEMH) as A2, N2, N1, C3, G4 on Tuesday. Well, looking on he surface the re-voting for easy was done by cursory, but during that moment geometry problem(s) could be fit only to P5. Meanwhile, A2 is a good inequality problem, not too hard yet not that trivial. N1 is an collaborative effort of all seniors (unlike others which were proposed individually).

Score giving: Generous or stingy?
Scheme making was the greatest headache: the standard “any complete solution worths 7 points” is obvious, but breaking down in partials: nope.
We suggested the proposers of problems to make the scheme, and it went magnificently well: comprehensive (according to what we thought) scheme done according to the solutions (some has at least 2 solutions).

Nothing was complete without logo, there were 2 proposals, but Justin’s Geogebra figuration on JO13 won “juries'” heart:

On Wednesday and Thursday, the final thing prior to the competition was to make soft copy using LaTeX programme. Justin was thankfully proficient in handling it (despite typo) and he made use of template (for LaTeX programme of a past IMO paper) well to insert logos and problem statements. That was the end of preparation.

And the paper is ready! Have a look at the solutions:
Solutions – Junior Olympiad 2013

17-18 January: the big day for juniors.
Day 1: 2:30-4:30 pm

While the juniors took the JOM paper 1, the seniors took the daily test. Time flies soon and the end of exam approached instantly.

After JOM, the seniors need to mark the papers. I’m here not to see our observation, but on the difficulty of marking: the “comprehensive” scheme was just inadequate: we didn’t consider all possible approaches and restricted ourselves solely into the scheme based on official solutions. How to overcome it? It’s by pointing out the problem and think about the scheme as complement.

Day 2: 7:30-11:30 am.

I remembered some juniors showed their amusement upon looking at the paper: probably because of the P4 Fake Gangnam Style. That’s just a glance: I was more concerned on my senior final paper for Top 24 shortlisting process.

Also, it’s the grand finale of the second IMO 2013 camp, and it wasn’t viable for every one of us to grade. The only possible approach: split papers into graders.

After the exam: Awards giving decisions.
Two implications came from the JOM paper: award cut-offs, and selections to the IMO 3rd camp. Here are some notable statistics:
1. The top scorer scored 32/35 (4 complete solutions along with 4 points for substantial progress for P5).
2. Cut-off points: 25 for Gold, 15 for Silver and 10 for Bronze. HMs for those scoring 7,8 or 9. This cut offs are based on the IMO system.
3. Best answered problem was P3, where about half of them solved it completely. It was not hard to see the invariant.
4. Despite being harder, candidates answered P2 better than P1. For P2, proving impossibility for a=2,3 can be done easily by last digit analysis, and that gave a lot of points. On the other hand, besides getting the correct answer (i.e. 1) for P1, there was not great room for partial solutions.

July 2013: Showing our effort to the world!
We were impressed by countries who gave us their national problems as gifts to us, and this time we could finally come out with one extra gift: JOM 2013 papers. Mr. Suhaimi gave it to some of the leaders, and I was sure that the brightest peers we met in Colombia would enjoy it.

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Acknowledgement
Nothing is possible without help and support from everyone. I would like to thank everyone for the success of JOM 2013, including but not limited to:
1. Education Ministry of Malaysia, who patronizes and supports the IMO program.
2. ExxonMobil Malaysia, for funding IMO program every year since IMO 2010.
3. Pusat Permata Pintar, for giving us venue to camp, and lend a big helping hand in running IMO camp 2 smoothly (logistically).
4. Malaysian Mathematics Sciences Society, especially Professor Arsmah. The team took up the responsibility in having IMO training, which had never been easy.
5. Trainers, especially the head trainer, Mr. Suhaimi for academic wellness of JOM papers.
6. My JOM partner, Justin Lim Kai Ze. He was the “Secretary General” of the project (note: no official position for the senior team) : a leader who compiled all documents (tasks of Secretary).
7. The senior team, for problem proposals, voting and marking scheme. This is the best proof of “Unity is the strength”. Special thanks to former Olympians like Ying Hong and Afiq for their enthusiastic involvement although they were not in IMO 2013 training camp.