Results after Problem 5
The list of the contest leaders after the fifth problem:
Points 

Name 
Country 
School 
Physics teacher 
12,725 

SZABÓ Attila 
Hungary 
Leőwey Klára High School, Pécs 
Simon Péter, Dr Kotek László 
11,535 

Nikita Sopenko 
Russia 
Lyceum No.14, Tambov 
Valeriy Vladimirovich Biryukov 
8,168 

Ilie Popanu 
Moldova 
Lyceuum "Orizont", Chisinau 
Igor Evtodiev 
7,7004 

Jakub Šafin 
Slovak 
Pavol Horov Secondary, Michalovce 
Jozef Smrek 
7,5883 

Lars Dehlwes 
Germany 
OhmGymnasium Erlangen 
Martin Perleth 
6,0833 

Ivan Tadeu Ferreira Antunes Filho 
Brazil 
Colégio Objetivo, Lins, São Paulo 

5,8911 

Papimeri Dumitru 
Moldova 
Lyceuum "Orizont", Chisinau 
Igor Evtodiev 
5,8689 

Ion Toloaca 
Moldova 
liceul "Mircea Eliade" 
Igor Iurevici Nemtov; Andrei Simboteanu 
5,6695 

Brahim Saadi 
Algeria 
Preparatory School for Science & Technology of Annaba 
Derradji Nasreddine 
5,5407 

Dinis Cheian 
Moldova 
Lyceuum "Orizont", Chisinau 
Igor Evtodiev 
5,1968 

Jakub Supeł 
Poland 
14th School of Stanisław Staszic, Warsaw 
Włodzimierz Zielicz 
5,0844 

Cristian Zanoci 
Moldova 
Lyceuum "Orizont", Chisinau 
Igor Evtodiev 
4,919 

Alexandra Vasileva 
Russia 
Lyceum "Second School", Moscow 
A.R. Zilberman, G.F. Lvovskaya, G.Z. Arabuly 
3,8105 

Kohei Kawabata 
Japan 
Nada High School 

3,7997 

Nadezhda Vartanian 
Russia 
Smolensk Pedagogical Lyceum 
Mishchenko Andrei Anatolievich 
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 
2,5937 

Mikhail Shirkin 
Russia 
Gymnasium of Ramenskoye 
Petrova Elena Georgyevna 
2,1 

Krzysztof Markiewicz 
Poland 
XIV Highschool in Warsaw 
Robert Stasiak 
2 

Jaan Toots 
Estonia 
Tallinn Secondary Science School 
Toomas Reimann 
1,903 

Petar Tadic 
Montenegro 
Gimnazija ,,Stojan Cerovic" Niksic 
Ana Vujacic 
1,8606 

Lorenzo Comoglio 
Italy 
Liceo Scientifico del Cossatese e Valle Strona 
Chiara Bandini 
1,6214 

Ng Fei Chong 
Malaysia 
SMJK Chung Ling, Penang 

1,4641 

Hideki Yukawa 
Japan 
Nada high school 

1,21 

Midhul Varma 
India 
Vidyadham Junior, Hyderabad 
Manikanta Kumar 
1 

Teoh Yee Seng 
Malaysia 
SMJK HENG EE,Penang; SMJK CHUNG LING,Penang 
Hong Siang Ean, Loh Pei Yee 
1 

Task Ohmori 
Japan 
Nada High School 
T.Hamaguchi 
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 
0,9801 

Mekan Toyjanow 
Turkmenistan 
Turgut Ozal Turkmen Turkish High School 
Halit Coshkun 
0,81 

Meylis Malikov 
Turkmenistan 
Turgut Ozal Turkmen Turkish High School 
Halit Coshkun 
0,81 

Liara Guinsberg 
Brazil 
Colégio Integrado Objetivo, São Paulo, Brazil 
Ronaldo Fogo 
0,792 

Ulysse Lojkine 
France 
Lycée Henri IV, Paris 
M. Lacas 
0,72 

Rajat Sharma 
India 
Pragati Vidya Peeth,Gwalior 
Mr. Rakesh Ranjan 
0,5648 

Selver Pepić 
BosniaHerzegovina 
Fourth Gymnasium Ilidža, Sarajevo 
Rajfa Musemić 
Points for Problem No 5:
3,8876 

Nikita Sopenko 
2,5678 

SZABÓ Attila 
2,1436 

Ilie Popanu 
1,9487 

Papimeri Dumitru 
1,6105 

Cristian Zanoci 
1,435 

Dinis Cheian 
1,2958 

Lorenzo Comoglio 
1,0567 

Ng Fei Chong 
1 

Teoh Yee Seng 
0,9703 

Jakub Šafin 
0,81 

Ion Toloaca 
0,7217 

Lars Dehlwes 
0,5648 

Selver Pepić 
0,5134 

Petar Tadic 
Correct solutions (ordered according to the arrival time; best solutions in bold):
1. Szabó Attila (Hungary)
2. Nikita Sopenko (Russia)
3. Ilie Popanu (Moldova)
4. Papimeri Dumitru (Moldova)
5. Dinis Cheian (Moldova)
6. Cristian Zanoci (Moldova)
7. Ng Fei Chong (Malaysia)
8. Lorenzo Comoglio (Italy)
9. Jakub Šafin (Slovak)
10. Lars Dehlwes (Germany)
11. Petar Tadic (Montenegro)
12. Ion Toloaca (Moldova)
13. Teoh Yee Seng (Malaysia)
14. Selver Pepić (BosniaHerzegovina)
(The list is ordered according to the arrival time)
Also, there are two incorrect solutions and two solutions, which are based on correct principles, but contain some mistakes.
Overall number of registered participants: 247 from 42 countries.
—————
Since the number of correct solutions was relatively low, the following hints were given by the end of the third week:
– study the formula sheet (section V3) to get an idea of how many eigenfrequencies you need to find; if in difficulties counting the number of oscillators, take it equal to the number of degrees of freedom (how many independent loop currents are needed for a superposition to represent arbitrary current distribution of the circuit);
– make use of the strong inequalities at as early stage as possible, to simplify the mathematical task;
– study the section VIII of the formula sheet; particularly useful are pts. 11, 5, 3, 2 (though, depending on your approach, you may not need all of these formulae).
– in order to find the natural frequencies, you can write down the system of differential equations, and based on that system, write down the characteristic equation, the solutions of which are the natural frequencies. However, note that you can avoid writing down the differential equations. Instead, you can make use of the concept of current and voltage resonances. So, for a voltage resonance, there will be a nonzero voltage amplitude U between two nodes A and B, even if there is no current flowing into the node A (and from the node B). Indeed, if the impedance between the nodes A and B is , we can write U = IZ, hence a nonzero U is compatible with I=0 if . Therefore, natural frequencies can be found as the solutions of the equation .
