PC2026-P2 Best solutions and final results

Problem 2

In total, 144 solutions were submitted for problem 2, of which 33 were correct. Congratulations to everyone who successfully solved it!

There were 5 correct solutions submitted before the first hint was published, and only those were considered as candidates for the best solution awards.

The award winners are as follows.

Alon Hart (bonus: 0.3 pts) gives a clear physical explanation of how distinct velocity peaks develop and how collisions can erase them. Counting the particles encountered by an incoming molecule provides an economical collision estimate, while explicit checks establish the validity of the expansion used.

Vaibhav V (bonus: 0.3 pts) obtains the result with exceptional economy. Balancing thermal spreading against the cubic deformation of the flow identifies the relevant initial gas segment; its column density then gives the collision probability without needing to follow the growing local density.

Joshua Wang (bonus: 0.3 pts) directly connects the evolving velocity distribution to the required peak-to-valley contrast and checks the approximations used. Comparing the short timescale of peak formation with the local collision time completes a compact analytical solution.

Francesco Gariglio (bonus: 0.1 pts) relates the required peak contrast to the initial interval from which molecules can arrive with few collisions. Helpful figures illustrate the compression, and the discussion distinguishes the regimes in which the small-distance approximation applies.

Final results for Problem 2

Pre-university students:

First name	Surname	Country	School/University	P2 date time DD/MM/YY 00:00:00	P2 Score
Sudipto Sen	Tawhid Bin Omar	Bangladesh	St. Joseph Higher Secondary School	8/12/25 16:38	1.729
Siddhaarth	Dharani	Singapore	Gap Year	9/12/25 17:04	1.629
Qingxiang	Liao	China	Shenzhen College of International Education	10/12/25 15:31	1.529
Aryan	Lalwani	India	Gap Year	13/12/25 16:00	1.51
Dominik	Erdélyi	Hungary	Budapesti Fazekas Mihály Gimnázium	13/12/25 17:59	1.41
Luka	Smiljanic	Serbia	Mathematical Grammar School	13/12/25 18:05	1.31
Nithilan	Ravikumar	India	Nil	18/12/25 08:00	1.048
Kwonheon	Lee	South Korea	Seoul Science Highschool	21/12/25 06:38	1.02
Kai Wen	Teo	Singapore	Gap year	1/1/26 15:48	0.64
Davi	Pinheiro Tsuchie	Brazil	Objetivo Integrado	28/12/25 23:37	0.6374
Lee	SinHyeok	South Korea	Seoul Science High School	3/1/26 05:21	0.486
Vaiibhav	G	India	Chinar Public School	10/1/26 06:29	0.45
Antonia	Radu	Romania	“Mihai Viteazul” High School Ploiesti	15/1/26 20:30	0.3645

University students:

First name	Surname	Country	School/University	P2 date time DD/MM/YY 00:00:00	P2 Score
Alon	Hart	Israel	Hebrew University of Jerusalem	23/11/25 18:08	2.3
Joshua	Wang	United States	MIT	30/11/25 08:50	2.1
Vaibhav	V	India	United Institute of Technology	3/12/25 07:18	1.9
Francesco	Gariglio	Italy	Università degli Studi di Torino	6/12/25 09:18	1.7
Guy	Ginzberg	Israel	The Open University of Israel	29/11/25 17:15	1.56
Md Mustakim Bin	Alam		Novosibirsk State University	7/12/25 15:20	1.31
Vinícius	Ferreira Rodrigues	Brazil	University of Iowa	7/12/25 21:53	1.21
Alessandro	D’Orazio	Italy	University of Pisa	9/12/25 14:04	1.2
uravg	gamer	Taiwan	Kshewan University	14/12/25 11:10	1.01
Ethan	Lu	United States	Ohio State University	14/12/25 17:13	0.8
Kadyrberdi	Yazdurdiev	Turkmenistan	Magtymguly Turkmen State University	20/12/25 07:39	0.8
Samuel	Altman	Indonesia	Jakuma State Collegium	21/12/25 11:54	0.8
Erik	Kaniewski	Estonia	Taltech	15/12/25 02:03	0.72
Kushal	Thaman	India	Stanford University	15/12/25 18:43	0.72
Arslan Jumayev	Davut Alybayev	Turkmenistan	Magtymguly Turkmen State University	24/12/25 10:50	0.7
Jonathan	Burger	Germany	Karlsruher Institut für Technologie	14/12/25 14:57	0.6832
Davut	Alybayev	Turkmenistan	Magtymguly Turkmen State University	11/1/26 10:15	0.45
Sathya	Nistri	Italy	Università di Pisa	30/12/25 10:32	0.4374
Larrance	Xing	United States	University of Chicago	18/1/26 08:24	0.3645
Adrian	Rewkowski	Belarus	Jagiellonian University	17/1/26 12:40	0.35