PC2025-P1 Best solutions and final results

Problem 1 – Interaction force

In total, 233 solutions were submitted for problem 1, of which 63 were correct. Congratulations to everyone who managed to solve it!

There were 41 correct solutions submitted before the first hint was published, and only those were considered as candidates for the best solution awards. Additionally, since there were so many well-written solutions to choose from, hand-written solutions were not considered this time, sorry about that!

A vast majority of solutions were based on Legendre polynomials expansion of the Laplace equation solution in spherical coordinates. That was definitely not the intended solution, but nevertheless a valid brute-force approach. If you can solve by brute-force, why waste time trying to figure out something trickier! Still, since Physics Cup is by intention were you show off your creativity, such brute force solutions did not warrant a best solution award per se; still, below are also linked some examples of well-written solutions using Legendre polynomials.

While there were no intended solutions (the one written by me – JK – can be found here), there were solutions without Legendre polynomials. These were using the fact that the solution to the boundary value problem (electrostatic potential on the ball’s surface takes the values dictated by the electric field inside the sphere) outside the sphere is unique, and by guessing – and verifying – that this condition is satisfied by the field provided by an ideal quadrupole at the centre of the ball. These were the solutions provided by Ethan Lu, Hui Xiang Sim, and Siddhaarth Dharani.

There were very few of the contestants who figured out the reason for giving the strong inequality in the problem statement. Among those who were considered as candidates for the best solution award, only Ilan Mihelja with Hegedić , Eric Wang, Kai Wen Teo, Ethan Lu, and Moritz Rohner did that.

Finally, Enej Jauk did what no-one else did, he checked if relativistic effects could be relevant by studying the properties of different materials.

The total bonus of 1 pts is evenly distributed between these eight contestants.

Apart from that, here are two nicely written solutions with Legendre polynomials, one studying the potential magnetic forces in case of non-magnetic materials, and the other – providing useful figures, by Abhiram Cherukupalli and Aljaž Erman, respectively.

Final results for Problem 1

Pre-university students:

First name	Surname	Country	School/University	P1 date time DD/MM/YY 00:00:00	P1 Score
Mihkel	Rannut	Estonia	Tallinna Reaalkool	13/10/24 19:27	2.0
Alp	Terliksiz	Türkiye	Enka Science and Technology Highschool	15/10/24 10:49	1.9
Darius	Graur	Moldova	Liceul Teoretic Orizont	15/10/24 15:44	1.8
Enej	Jauk	Slovenia	Gimnazija Bežigrad	15/10/24 21:12	1.725
Saskia	Põldmaa	Estonia	Tallinn Secondary School of Sciences	15/10/24 17:32	1.7
Kai Wen	Teo	Singapore	Raffles Institution	16/10/24 06:46	1.625
Tomas	Razbadauskas	Lithuania	Kaunas University of Technology Gymnasium	16/10/24 12:35	1.4
Daniils	Koselevs	Latvia	Jauno Lideru Vidusskola	16/10/24 14:43	1.3
Jingyang James	He	Singapore	Raffles Institution	17/10/24 09:00	1.2
Aljaž	Erman	Slovenia	Gimnazija Kranj	22/10/24 11:57	1.1
Yisi	Liu	China	The First High School of Changsha	19/10/24 12:09	1.1
Moritz	Rohner	Luxembourg	Lycée de Garçons Esch (LGE)	27/10/24 11:35	1.025
Siddhaarth	Dharani	Singapore	NUS High School	23/10/24 16:19	1.025
Nikhil	Kodali	United States	Cupertino High School	23/10/24 22:01	1.0
Raiq Babazade	Murad Khalil, Ibrahim Valehli	Azerbaijan	Physics, Mathematics and Informatics lyceum	22/10/24 14:27	1.0
Owen	Zhou	United States	Basis Scottsdale	26/10/2024 22:40:00	1.0
Richard	Yang	United States	Iowa City West High School	26/10/2024 14:54:00	1.0
Bahaa Aldeen	Melhem	Syria	Gap year	20/10/2024 11:09:00	1.0
Saurya	Shrestha	Nepal	St. Xavier’s College, Nepal	26/10/24 20:42	1.0
Mohammed	Alarfaj	Saudi Arabia	Dhahran Ahliyya Schools	26/10/24 22:02	1.0
Grigorii	Grechkin		School CPM	26/10/24 21:08	1.0
Mahammad	Jafarli	Azerbaijan	Technical-Humanitarian Lyceum	1/11/24 17:23	0.9
Matías	Páez	Argentina	E. E. S. N°6	28/10/24 11:32	0.9
Zeyneb	Mehemmedli	Azerbaijan	TTEL	21/10/2024 12:21:00	0.9
Lukas	Gabriel	Austria	Albertus Magnus Gymnasium	03/11/2024 03:48:00	0.9
Alex	Secrieru	Moldova	LT “Orizont”	27/10/24 17:35	0.855
Rahul	Nandi	Bangladesh	Chattogram College	10/11/24 12:09	0.8
trocin	ruslan	Moldova	lPLT Orizont	06/11/2024 08:08:00	0.8
Ogtay	Latifli	Azerbaijan	Republican Physics-Mathematics and Informatics lyceum	07/11/2024 19:02:00	0.8
Mert Andac	Karan	Türkiye	Bahcesehir High School for Science and Technology	9/11/24 09:04	0.72
Joris	Boruta	Lithuania	KTU gymnasium	10/11/24 12:42	0.72
Federico	Roccaforte	Italy	IIS Concetto Marchesi	14/11/2024 15:38:00	0.7
Kanishk	Jain	India	ALLEN Kota	10/11/24 22:49	0.665
Oytun	Er	Türkiye	Kadıköy Anatolian Highschool	11/11/24 17:47	0.63
Tejas Penugonda	Talha Ashraf	India/Pakistan	Nixor College	23/11/24 20:34	0.57
Doğan	Önal	Türkiye	İstanbul Atatürk High School of Science	10/11/24 19:42	0.567
Guangyuan	Chen	Singapore	Gap Year	17/11/24 14:31	0.54
Andrei	Vila	Romania	International Computer High School Bucharest	22/12/24 09:17	0.5
Amrit	Raj	India	Maa Bharti Sr. Sec. School	1/12/24 09:47	0.5
Luis Edgar	Sanchez Henriquez	El Salvador	Programa Jovenes Talentos	9/2/25 08:01	0.5
Francesco	Gariglio	Italy	IIS Majorana Moncalieri	15/12/24 10:45	0.5
Luca	Gâlea	Romania	National College Iasi	8/12/24 10:04	0.5
Italo	Vidaurre	El Salvador	Programa Jovenes Talento	15/12/25 21:49	0.5
Matthew	Chen	United States	Cupertino High School	01/12/2024 02:42:00	0.5
Kai Xin	Chen	China	GuangDong ShiYan middle school – ShenZhen High school.	19/1/25 06:36	0.45

University students:

University	Ilan Mihelja	Ivan Hegedić	Croatia	University of Zagreb, EPFL	15/10/24 15:36	2.025
University	Adrian, Bruno, Daniel	Serrano Capatina, Pontecorvo, Gonzalez Filipov	Switzerland	École Polytechnique Fédérale de Lausanne	14/10/24 22:31	2.0
University	Eric	Wang	United States	Massachusetts Institute of Technology	16/10/24 22:41	1.825
University	Karlo	Maksimović	Croatia	University of Zagreb	16/10/24 19:15	1.75
University	Guy	Ginzberg	Israel	The Open University of Israel	17/10/24 09:26	1.6
University	Sifat Ahmed	Tushar	Bangladesh	University of Dhaka	17/10/24 15:14	1.5
University	Ethan	Lu	United States	Ohio State University	18/10/24 00:36	1.425
University	Dhruv	Shah	India	Massachusetts Institute of Technology	17/10/24 15:37	1.4
University	Hui Xiang	Sim	Singapore	National University of Singapore	18/10/24 01:53	1.275
University	Yaroslav	Kondrachuk	Ukraine	National University of Singapore	18/10/24 14:31	1.1
University	Abhiram	Cherukupalli	United States	California Institute of Technology	20/10/24 18:18	1.1
University	Emerson Franzua	Aldana Gavarrete	Honduras	Universidad Nacional Autónoma de Honduras	26/10/2024 15:47:00	1.0
University	Iaroslav	Pozdniak		Moscow Institute of Physics and Technology	20/10/24 14:37	1.0
University	Federico	Mastroforti	Italy	University of Bologna	18/10/24 20:12	1.0
University	Štěpán	Plass	Czech Republic	Univerzita Karlova	22/10/24 22:35	0.95
University	Animesh	Pradhan	India	Indian Institute of Science(IISc), Bengaluru	3/11/24 07:11	0.9
University	Bayram Alp	Şahin	Türkiye	Boğaziçi University	20/10/24 00:06	0.9
University	Jia Xuan	Tan	Singapore	University of Cambridge	45598.81111	0.9
University	Armen	Gazazyan	Armenia	Yerevan State University	17/11/24 20:29	0.54
University	Ravan	Najafli	Azerbaijan	KAIST(Korean Advanced Institute of Science and Technology)	23/11/24 21:44	0.54
University	Michał	Kołodziejczyk	Poland	Warsaw University of Technology	20/12/2024 19:22:00	0.5
University	Kenneth	Luo	Canada	University of Toronto	14/12/24 23:41	0.5
University	Konstantin	Rodionenko		ITMO University	07/12/2024 20:00:00	0.5
University	Marinus	Lehmann	Germany	University of Potsdam	15/12/24 21:49	0.5