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Results after Problem 9

The list of the contest leaders after the ninth problem:

Points   Name Country School Physics teacher
22.9081   Szabó Attila Hungary Leőwey Klára High School, Pécs Simon Péter, Dr Kotek László
20.645   Nikita Sopenko Russia Lyceum No.14, Tambov Valeriy Vladimirovich Biryukov
15.8787   Jakub Šafin Slovak Pavol Horov Secondary, Michalovce Jozef Smrek
13.8851   Lars Dehlwes Germany Ohm-Gymnasium Erlangen Martin Perleth
13.8105   Ilie Popanu Moldova Lyceuum "Orizont", Chisinau Igor Evtodiev
12.2307   Alexandra Vasileva Russia Lyceum "Second School", Moscow A.R. Zilberman, G.F. Lvovskaya, G.Z. Arabuly 
10.8732   Ivan Tadeu Ferreira Antunes Filho Brazil Colégio Objetivo, Lins, São Paulo  
9.5043   Ion Toloaca Moldova liceul "Mircea Eliade" Igor Iurevici Nemtov; Andrei Simboteanu
9.0645   Cristian Zanoci Moldova Lyceuum "Orizont", Chisinau Igor Evtodiev
8.7917   Nadezhda Vartanian Russia Smolensk Pedagogical Lyceum Mishchenko Andrei Anatolievich
8.4407   Dinis Cheian Moldova Lyceuum "Orizont", Chisinau Igor Evtodiev
7.8954   Kohei Kawabata Japan Nada High School  
7.372   Petar Tadic Montenegro Gimnazija ,,Stojan Cerovic" Niksic Ana Vujacic
6.8529   Jakub Supeł  Poland 14th School of Stanisław Staszic, Warsaw Włodzimierz Zielicz
5.8911   Papimeri Dumitru Moldova Lyceuum "Orizont", Chisinau Igor Evtodiev
5.6695   Brahim Saadi Algeria Preparatory School for Science & Technology of Annaba Derradji Nasreddine
5.1254   Ng Fei Chong Malaysia SMJK Chung Ling, Penang  
4.3821    Adrian Nugraha Utama Indonesia SMA Sutomo 1 Medan Manaek Nababan
4.2554   Selver Pepić Bosnia-Herzegovina Fourth Gymnasium Ilidža, Sarajevo Rajfa Musemić
4.2425   Ulysse Lojkine  France Lycée Henri IV, Paris M. Lacas
3.7517   Luís Gustavo Lapinha Dalla Stella Brazil Colégio Integrado Objetivo, Barueri, Brazil Ronaldo Fogo
3.4205   Bharadwaj Rallabandi India Narayana Jr. College, Basheer Bagh, India Vyom Sekhar Singh
3.3956   Teoh Yee Seng Malaysia SMJK HENG EE,Penang; SMJK CHUNG LING,Penang  
3.374   Lorenzo Comoglio  Italy Liceo Scientifico del Cossatese e Valle Strona Chiara Bandini
2.5937   Mikhail Shirkin Russia Gymnasium of  Ramenskoye  Petrova Elena Georgyevna
2.2747   Kai-Chi Huang Taiwan Taipei Municipal Chien-Kuo High School Shun-Ju Liu
2.1   Krzysztof Markiewicz Poland XIV Highschool in Warsaw Robert Stasiak
2   José Luciano de Morais Neto Brazil Colégio Ari de Sá Cavalcante Leonardo Bruno
2   Jaan Toots Estonia Tallinn Secondary Science School Toomas Reimann
1.9801   Mekan Toyjanow Turkmenistan Turgut Ozal Turkmen Turkish High School Halit Coshkun
1.9487   Abishek Anand India Kendriya Vidyalaya,Durg N.D.Sahu
1.81   Meylis Malikov Turkmenistan Turgut Ozal Turkmen Turkish High School Halit Coshkun
1.7444   Andrew Zhao United States Webster Thomas High School Dykstra, William 
1.4641   Hideki Yukawa Japan Nada high school  
1.4641   Bruno Bento Barros de Araújo Brazil Ari de Sá Cavalcante Edney Melo
1.2334   Rajat Sharma India Pragati Vidya Peeth,Gwalior Mr. Rakesh Ranjan
1.21   Midhul Varma India Vidyadham Junior, Hyderabad  Manikanta Kumar
1   Task Ohmori Japan Nada High School T.Hamaguchi
1   Stefán Alexis Sigurðsson Iceland Menntaskólinn í Reykjavík Martin Swift 
1   Stavros Efthymiou Greece Rhodian PediaPhysics, Rhodes Mihalis Zirihidis
1   Sharad Mirani  India Prakash Higher Secondary School Ruchi Sadana, Sunil Sharma
1   Lev Ginzburg Russia Advanced Educational Scientific Center, MSU, Moscow I.V. Lukjanov, S.N. Oks
1   Jun-Ting Hsieh Taiwan Taipei Municipal Jianguo High School Mr. Shun-Ru Liu
1   Han Kheng Teoh Malaysia SMJK Chung Ling  
0.99   Shinjini Saha Bangladesh Cephalon International School Dr. Khorshed Ahmed Kabir
0.9   Subarno Saha Bangladesh Cephalon International School Prof. Khorshed A. Kabir, Prof. Arshad Momen
0,9   Jôhanes Sebástian Paiva Melo Brazil Colégio Ari de Sá Cavalcante Eduardo Kilder; Italo Reann
0.81   Liara Guinsberg Brazil Colégio Integrado Objetivo, São Paulo, Brazil Ronaldo Fogo
0.6561   Jorge Torres Ramos Mexico Unidad Academica Escuela Preparatoria Emiliano Zapata Gelacio Atondo Rubio
0.5134   Siddharth Mohan India Aggarsain Public School  Kavita Mahajan, Monika Gupta

Points for Problem No 9:

points   Name
3.4505   Ulysse Lojkine 
2.8531   Szabó Attila
2.5937   Nikita Sopenko
2.3579   Petar Tadic
1.9487   Abishek Anand
1.7716   Alexandra Vasileva
1.6105    Adrian Nugraha Utama
1.3956   Teoh Yee Seng
1.331   Lars Dehlwes
1.331   Kohei Kawabata
1.1   Ivan Tadeu Ferreira Antunes Filho
1.1   Selver Pepić
1   Jakub Šafin
1   Ilie Popanu
1   Ion Toloaca
1   Cristian Zanoci
1   Nadezhda Vartanian
1   Dinis Cheian
1   Lorenzo Comoglio 
1   José Luciano de Morais Neto
1   Mekan Toyjanow
1   Meylis Malikov
1   Stefán Alexis Sigurðsson
1   Stavros Efthymiou
1   Jun-Ting Hsieh
1   Han Kheng Teoh
0.99   Shinjini Saha
0.9   Ng Fei Chong
0.9   Subarno Saha
0.6561   Jorge Torres Ramos
0.5134   Siddharth Mohan
0.5134   Rajat Sharma

Correct solutions (ordered according to the arrival time; best solutions in bold):

1. Szabó Attila (Hungary)

2. Nikita Sopenko (Russia)

3. Petar Tadic (Montenegro)

4. Abhishek Anand (India)

5. Ulysse Lojkine (France)

6. Alexandra Vasileva (Russia)

7.  Adrian Nugraha Utama (Indonesia)

8. Lars Dehlwes (Germany)

9. Kohei Kawabata (Japan)

10. Selver Pepić (Bosnia-Herzegovina)

11. Jakub Šafin (Slovak)

12. Teoh Yee Seng (Malaysia)

13. Ng Fei Chong (Malaysia)

14. Nadezhda Vartanian (Russia)

15. Meylis Malikov (Turkmenistan)

16. Mekan Toyjanow (Turkmenistan)

17. Han Kheng Teoh (Malaysia)

18. Lorenzo Comoglio (Italy)

19. Stefán Alexis Sigurðsson (Iceland)

20. Ion Toloaca (Moldova)

21. Ilie Popanu (Moldova)

22. Siddharth Mohan (India)

23. Jorge Torres Ramos (Mexico)

24. José Luciano de Morais Neto (Brazil)

25. Stavros Efthymiou (Greece)

26. Shinjini Saha (Bangladesh)

27. Shubarno Saha (Bangladesh)

28. Cristian Zanoci (Moldova)

29. Dinis Cheian (Moldova)

30. Ivan Tadeu Ferreira Antunes Filho (Brazil)

31. Jun-Ting Hsieh (Taiwan)

32. Rajat Sharma (India)

 

The number of registered participants: 268 from 46 countries.

———————-

The following hints have been given on 10th June. The easiest way to solve the problem is (a) by expressing the initial momentum p from the Lorentz invariant of the electron, m_0^2c^4=E^2-p^2c^2, where m_0 is the rest mass, and E – the full relativistic energy (ie. the sum of the rest energy and the kinetic energy; note that kinetic energy is not a useful concept for relativistic problems); (b) by using the fact that the full energy of the photon is given by the modulus of its momentum, here the full energy of the two photons E=(|\vec p_1|+|\vec p_2|)c.


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