Long and winding road

Sri Lanka's Triumph

Picture Gallery

Long and winding road to the 50th International Mathematical Olympiad

In 2006 our Sri Lankan team did extremely well at the IMO by winning 3 Bronze medals and 2 Honorable Mentions, and obtaining a team total of 71 points. This performance was a significant improvement from our performance in 2003 – Sri Lanka Olympiad Mathematics Foundation was formed in 2004 and a new Sri Lankan Mathematical Olympiad was introduced in the same year:

But then in 2007 GCE Advanced Level Exam was shifted from April to August. This created a problem to potential IMO participants who have to do the GCE Advanced Level Exam in the same year as they have to sit the Advanced Level Exam right after returning from the IMO – IMO is usually held in the second week of July. Many good students who could make to the 2007 IMO team including Sashindra Silva from De Mazenod College who won a Bronze medal at the 2006 IMO opted to skip the IMO as they chose to give priority to GCE Advanced Level Exam. This trend has continued since then and as only the students less than 20 years of age not studying in a university can participate in the IMO, our teams did not do well at the IMO in 2007 and 2008 since some of the best students opted to skip the IMO.

So to improve the performance of our teams at the IMO we came up with an extensive program in 2009. The preparations for the IMO 2009 started with the publishing of the book “Introduction to Olympiad Maths” by Chanakya J. Wijeratne in December 2008
and gifting a copy of the book to the 99 students who won High Distinction Certificates at the Sri Lankan Mathematical Olympiad 2008 at the Awards Ceremony held on January 03, 2009. The Sri Lankan Mathematics Competition 2009 was held on March 07, 2009 at 11 examination centers including Jaffna and Trincomalee for more than 3500 registered students – In February 2008 “Challenging Maths” and “Abiyogathmaka Ganithaya” which contain detailed solutions to Sri Lankan Mathematics Competition papers during 2004 to 2007 were published.

Top 40 students at the Sri Lankan Mathematics Competition 2009 and the top 9 students at the Vidusara Competition were invited to the Sri Lankan Mathematics Challenge Competition 2009 Pool (altogether there were 46 students) and on April 11, 2009 they were given a free copy of the book “Easy Olympiad Maths” published by Chanakya J. Wijeratne in April 2009 containing solutions to the Sri Lankan Mathematics Challenge Competition 2004 to 2008 and other problems, a chapter on methods of proof, and a chapter on theorems and results in Olympiad mathematics. Photocopies of the unpublished book “Number Theory, Mathematical Methods of Proof and Geometry” written in Sinhala by Chanakya J. Wijeratne and Dayal B. Dharmasena were also made available. Also, this pool was invited to the following two seminars.

April 18, 2009
9.00 – 12.00 : Methods of Proof and Combinatorics by Chanakya J. Wijeratne
1.00 – 3.00 : Geometry by Supun T. Samarakoon
3.00 – 5.00 : Number Theory by Thameera P. Senanyake
April 25, 2009
9.00 – 12.00 : Number Theory by Thameera P. Senanyake
1.00 – 4.00 : Combinatorics by Chanakya J. Wijeratne
4.00 – 5.00 : Geometry by Supun T. Samarakoon

The Sri Lankan Mathematics Challenge Competition 2009 was held on May 02, 2009 and the top 17 students were selected for further training and testing.

Prime 17

1. L. Lajanugen, Highlands Central College , Hatton
                                    2. G. R. B. R. Gamlath, Royal College , Colombo 07
3. G A Rusiru Rangika, Rajasinghe Maha Vidyalaya, Wallasmulla
                        4. M. D. Y. Fernando, Ananda College , Colombo 10
5. S. Krishanthan, St. Anthony’s College, Kandy
                                    6. W. D. A. T. K. Warnakula, St. Sebastian College , Moratuwa
                                    7. M. Y. S. Fonseka, Taxila Central College , Horana
8.  A. B. K. Fernando, Richmond College, Galle                                
9.   I. D. Fernando, St. Sebastian College, Moratuwa                       
10. G. A. Udayanga, Taxila Central College, Horana
11. G. L. U. Eshantha, Richmond College, Galle                                           
12. A. M. P. L. Adikaram, Kegalu Balika Maha Vidyalaya                             
13. N. R. Samarasekera – Nalanda College
14. A. M. T. S. B. Adikari – Bandarawela Central College
15. T. M. T. L. Muthugama, Royal College , Colombo 07
16. S. Chelvanithithilan, St. Patric College, Jaffna
17. H. G. W. T. Prabatha, Rahula College, Matara

This pool had students with diverse backgrounds in mathematics. L. Lajanugen, G. R. B. R. Gamlath, M. D. Y. Fernando, A. B. K. Fernando were N. R. Samarasekera former IMO participants. G. A. Rusiru Rangika was going to do his GCE Ordinary Level exam in December. Some had done their ALs – A. M. T. S. B. Adikari had all island rank one in GCE AL 2008. Some were going to do ALs in August – N. R. Samarasekera got all island rank in GCE AL 2009.

The following program was conducted to this pool.

May 07, 2009
9.00 : Take Home Exam 1
May 16, 2009
9.00 : Submitting answers to Take Home Exam 1 and collecting Take Home Exam 2
9.00 – 12.00 : Discussion on SLMCC 2009 and the pool’s performance by Chanakya J. Wijeratne
1.00 – 3.00 ; Movie “Young Beautiful Minds” on the training of the UK team for IMO 2006
May 23, 2009
9.00 : Submitting answers to Take Home Exam 2
9.00 – 1.30 : IMO Team Selection Competition 2009

Twelve students turned up for IMO Team Selection Competition 2009and their results are given below:

 

At the end of this program the following team was selected to represent Sri Lanka at the 50th IMO. M. Y. S. Fonseka, Taxila Central College, Horana was ranked 7th and he made to the team as the 4th ranked Rusiru Ghambeera Arachchi, Rajapaksha Central College, Weeraketiya withdrew from the team due to medical reasons. He was later diagnosed with bone cancer in his left leg. He could do only six subject at the GCE OL exam. At the moment he is recovering at the Sri Jayewardene Hospital after knee replacement surgery. We wish him well! Hope that he can make it to the next IMO.
                                   
                                    1. L. Lajanugen, Highlands Central College , Hatton
                                    2. G. R. B. R. Gamlath, Royal College , Colombo 07
                        3. M. D. Y. Fernando, Ananda College , Colombo 10
4. S. Krishanthan, St. Anthony’s College, Kandy
                                    5. W. D. A. T. K. Warnakula, St. Sebastian College , Moratuwa
                                    6. M. Y. S. Fonseka, Taxila Central College , Horana

This team underwent the following training:

June 1 - 27, 2009
Training at the Department of Mathematics, University of Colombo from Monday to Saturday from 8.30 to 4
June 28th to July 8th
Residential Training Camp at the National Institute of Education, Maharagama
July 3, 2009
9.00 - 1.30 Mock IMO Day 1
July 4, 2009
9.00 - 1.30 Mock IMO Day 2
The training of the team was conducted mainly by Supun T. Samarakoon, Thameera P. Senanyake and Chanakya J. Wijeratne. It should be emphasized that this whole program was conducted through volunteer work with only minimal subsistence money paid to the volunteers. The team was led by Chanakya J. Wijeratne (Leader) and Thameera P. Senanayaka (Deputy Leader) at the IMO. Thameera is a student of University of Moratuwa and was a contestant at the IMO in 2005 and 2006. Sri Lankan contestants and the Deputy Leader arrived in Bremen, Germany on July 13, 2009 for the competition.

Sri Lanka’s Triumph at the 50th International Mathematical Olympiad

The International Mathematical Olympiad (IMO), the world championship in mathematics for students under 20 years of age, was held during July 10-22, 2009 in Bremen, Germany for the 50th time. At this IMO there were 565 contestants from 104 countries. A country can send a team of six contestants to this competition and the team should have a deputy leader and a leader. Contestants have to solve six tough problems in Geometry, Number Theory, Algebra and Combinatorics. These topics in mathematics are in general taught at secondary schools in most countries in the world. But only Geometry among these topics is taught to some extent in Sri Lanka. Also, the problems at IMO are much harder compared to GCE Advanced Level Combined Mathematics problems as they always involve new ideas previously not found in other IMO problems. Training and motivating for this kind of competition is quite hard.
But two students of the Sri Lankan team, Lajanugan Logeswaran from Highlands Central College, Hatton and Buddhima Gamlath from Royal College, Colombo 07 won Bronze medals at the IMO. Unfortunately Lajanugan missed the Silver medal by two points and Sankalpa Fonseka from Taksila Central College, Horana missed the Bronze medal by two points. Also Tharindu Warnakula from St. Sebestian College, Moratuwa; Dileepa Fernando from Ananda college, Colombo 10 and Sankalpa Fonseka from Taxila Central College, Horana won Honourable Mentions for completely solving at least one problem. Sri Lankan team was led by Thameera P. Senanyake (Deputy Leader) and Chanakya J. Wijeratne (Leader).
Sri Lankan team got a total of 74 points and Sri Lanka was ranked 50th above Sweden, Norway, Spain, Denmark, Austria, New Zealand, Finland, Ireland, Philippines, Pakistan, Bangladesh and 41 other countries – this is the best IMO performance by a Sri Lankan team so far beating the previous best performance of 71 points in the 47th IMO in Slovenia. Sri Lankan students did not have the best of conditions before going into the first day of the competition on July 15th. Sri Lankan contestants and the Deputy Leader arrived in Bremen, Germany on July 13th. Lajanugan had fever on July 14th and he was taken to the hospital in the afternoon but he was not treated there and was asked to come back after 4. Meru Alagalingam, the guide of the Sri Lankan team tried hard but he could not do much as he was new to Bremen and Jacobs University where the competition was held. He was born in Germany after his parents migrated to Germany after 1983 July riots in Sri Lanka. He was in the final pool of 18 for the selection of the German team to the IMO 2008. Now by the time Lajanugan saw a doctor after 4 he didn’t have fever and therefore he was not given any medicine. But he was not ok and even in the morning of the first day of competition he was not ok. But he kept on working even in the night before the competition! Dileepa did not get his checked in luggage when he arrived in Bremen and had to spend a day languishing about it before he finally got it back!! And the team couldn’t do anything regarding jetlag before leaving Sri Lanka like other teams do before the competition.
Yet, Lajanugan came up with a beautiful pure Geometry solution to problem no. 2 using similar triangles and the Power of a Point Theorem. Sankalpa too used similar triangles like Lajanugan but he used Coordinate Geometry instead of the Power of a Point Theorem. But Gamlath used concylic points and Trigonometry to solve the same problem. All three got perfect scores of 7 for this problem. In problem no. 1 in Number Theory, Lajanugan, Gamlath, and Warnakula came up with three different arguments using modulo arithmetic leading to a contradiction to solve the problem. Again, three perfect scores! But in problem 4 on Day 2 things did not go that well! In this Geometry problem all possible values of a certain angle of a triangle has to be found. Finding these values is not that difficult but one needs to verify the values after finding them. Though Dileepa, Lajanugan, Krishanthan and Sankalpa correctly found the values, only Dileepa verified them. So only one perfect score and scores of 6, 6, and 5 for this problem!

All of those countries mentioned above in the 3rd paragraph have well funded IMO selection and training programs conducted throughout the year. For example, Pakistan team is selected and trained in the following long process. First a selection test consisting of 70% MCQs and 30% essay type problems is given to about 10,000 students. MCQ part of the test is machine graded. Then 50 students are selected for the next round and they are given training in a few residential camps under the guidance of a professional foreign IMO coach. After each residential camp there is a selection test and the pool is down sized, and after the last residential camp the team is selected. These programs are well funded. But Pakistan team could win only one Bronze medal and get a total of 21 points. But the Sri Lankan team was selected and trained by the Sri Lanka Olympiad Mathematics Foundation, a nonprofit organization dedicated to popularizing mathematics at school level in Sri Lanka, without any sponsorship from the government or the private sector, and foreign IMO coaches. The selection process of the Sri Lankan team to the IMO started with the Sri Lankan Mathematics Competition 2009 which was taken by more than 3500 students, and conducted, set and marked by volunteers. This competition was held on March 07, 2009 at 11 examination centers including Jaffna and Trincomalee. The Ministry of Education provided more than half of the exam centers and volunteers for these centers. Then the Sri Lankan team had two one day workshops on IMO problem solving before the Sri Lankan Mathematics Challenge Competition 2009. Top 40 students at the Sri Lankan Mathematics Competition 2009 and the top 9 students at the Vidusara Competition were invited to the Sri Lankan Mathematics Challenge Competition 2009 and 17 students were selected from this competition to IMO Team Selection Competition 2009. After the team was selected they were given training at the Department of Mathematics, University of Colombo from June 1 - 27, 2009 everyday from Monday to Saturday from 8.30 to 4. Then they were given training in a residential training camp at the National Institute of Education, Maharagama from June 28th to July 8th. The training of the team has been conducted mainly by Supun T. Samarakoon, Thameera P. Senanyake and Chanakya J. Wijeratne on a volunteer basis. Students used the following books published by the Sri Lanka Olympiad Mathematics Foundation in their training as text books published abroad are not available and not easily accessible: Challenging Maths, Introduction to Olympiad Maths and Easy Olympaid Maths. It is hard to imagine that all this have been achieved only through the volunteer work. The IMO program in Bangladesh has many sponsors from both the private and government sectors, and not only their students get free air passage they also have money to send an observer – observers have to pay for their accommodation in addition to air passage! And Bangladesh is planning to host the IMO in 2020. It is high time that sponsors came forward to fund the IMO program in Sri Lanka.
After the competition was over Sri Lankan students had time to enjoy going on excursions mingling with students from other countries, and at times teaching some math to other students – they taught the students from Singapore the Cot Rule! Chanakya and his deputy Thameera had to work hard marking the answer scripts of their students during July 16th to 18th. And the following day everybody had opportunity to attend lectures of 6 great mathematicians; Terence Tao, Timothy Gowers, Jean-Christophe Yoccoz, Bela Bollobas, Stanislav Smirnov, and Laszlo Lovasz, who are former IMO medal winners and meet them afterwards as part of the 50th anniversary celebrations of the IMO – Three of them, Terence Tao, Timothy Gowers, and Jean-Christophe Yoccoz are Fields Medal (the most prestigious award in mathematics) winners.
But on July 20th the entire Sri Lankan team including Leader and Deputy Leader had fun on Wangerooge island! The Awards and Closing Ceremony was held the following day and the team left for Sri Lanka early morning on July 22nd.

Photo Gallery

Working hard on the way to the IMO…

The team went to Bremen from Amsterdam by the cityhopper…They  had no idea that a grasshopper  (Problem 6) was waiting for them at the IMO!
Problem 6  Let a1, a2, . . . , an be distinct positive integers and let M be a set of n − 1 positiveintegers not containing s = a1 +a2 +· · ·+an. A grasshopper is to jump along the real axis, startingat the point 0 and making n jumps to the right with lengths a1, a2, . . . , an in some order. Prove that the order can be chosen in such a way that the grasshopper never lands on any point in M.

Opening ceremony of the IMO 2009 in Bremen, Germany…

Dr. Angela Merkel (Quantum Chemistry), Chancellor of the Federal Republic of Germany, speaking at the Opening Ceremony of IMO 2009

Sri Lankan team is looking confidant at Jacobs University, Germany just before the competition...

Terrance Tao, the youngest Gold medal winner at the IMO, is today, at the age of 34, is the youngest senior mathematician at UCLA. He is also a Fields Medal winner. He lectured on “Structure and Randomness in the Primes”. Here he is with the Sri Lankan team.

Timothy Gowers participated once in the IMO in 1981 and scored a perfect score. His PhD advisor was Bela Bolobas. He won the Fields medal in 1998. He lectured on “How do IMO Problems Compare with Research Problems?”.

In his lecture Timothy Gowers explains the first theorem in Ramsey theory.

The logo of the Sri Lanka Olympiad Mathematics Foundation is a particular coloring of the complete graph on 6 vertices - coloring of edges by red or blue. The first theorem in Ramsey theory says that any coloring of the complete graph on 6 vertices has a triangle that is entirely red or entirely blue.
The first theorem in Ramsey theory
Theorem
Take six points, and join them all 15 pairs of points with edges. If you color each edge red or blue, then you must end up with a triangle that is entirely red or entirely blue.
Proof
Take one of the points and call it v. There are five others, so at least three of them must be joined to v by edges of the same color. Call these three x, y, and z. Without loss of generality, they are all joined to v by red edges. But then none of the edges xy, yz or xz can be red or there would be a red triangle. But that means that the edges xy, yz and xz form a blue triangle.

Prof. Bela Bolobas lectured on “The Lion and the Christian”. Bela Bolobas participated in the first three IMOs and 2 Gold Medals and 1 Silver Medal. He has written over 350 research papers in mathematics and had 35 PhD students including 9 former IMO participants. He also has written several books including “Linear Analysis”, “Combinatorics”, and “Modern Graph Theory”.

Sri Lankan team with Prof. Bela Bolabas at the Wangerooge Island, Germany,

Enjoying French Fries at the Wangerooge Island, Germany…

Lajanugan’s Felicitation Ceremony at Highlands College after he returns with the best Bronze Medal for Sri Lanka

Lajanugan was taken in a procession from Hatton town centre to the school. The procession is just starting.

Its a long procession…

 

Lajanugan is in an open vehicle…

Lajanugan’s felicitation ceremony was very well organized and colorful. He fully deserves it. Lajanugan participated in all the Sri Lankan Mathematics Competitions held so far, from 2004 to 2009. He definitely grew with the competition and came very close to winning the first ever silver medal for Sri Lanka – he scored 22 points and the cut off for the silver medal was 24 points.