PC2026-P4 Best solutions and final results

Problem 4

In total, 59 solutions were submitted for problem 4, of which 37 were correct. Congratulations to everyone who successfully solved it!

There were 12 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.

Vinícius Ferreira Rodrigues (bonus: 0.3 pts) combines a careful discussion of the physical approximations with a systematic treatment of the coupled flow modes. The matrix formulation makes clear how the partition changes the growing mode, while the local contributions to the fluid inertia cancel from the required difference.

Joshua Wang (bonus: 0.3 pts) constructs the flow field using a simple geometric observation and turns the kinetic-energy calculation into a boundary integral. Combining this shortcut with symmetry and the method of images gives a particularly economical solution.

Shihao Ye (bonus: 0.3 pts) uses contour integration to evaluate the interactions between the flows through different holes. This provides an elegant alternative route to the kinetic energy, while image sources allow the partitioned vessel to be treated within the same framework.

Siddhaarth Dharani (bonus: 0.1 pts) develops an illuminating analogy with electrical conduction: the kinetic energy of the water corresponds to Joule dissipation in a conducting sheet. This allows the flow calculation to be expressed through currents and potential differences, giving the problem a useful alternative physical interpretation.

Final results for Problem 4

Pre-university students:

First nameSurnameCountrySchool/UniversityP4 date time
DD/MM/YY 00:00:00		P4 Score
QingxiangLiaoChinaShenzhen College of International Education3/2/26 07:362.0
SiddhaarthDharaniSingaporeGap Year6/2/26 18:362.0
AntoniaRaduRomaniaColegiul National “Mihai Viteazul” Ploiesti15/2/26 15:161.7
LukaSmiljanicSerbiaMathematical Grammar School22/2/26 03:471.6
AryanLalwaniIndiaGap Year22/2/26 10:551.41
VaiibhavGIndiaChinar Public School26/2/26 01:191.3
RamKumarIndiaAllen26/2/26 12:371.2
DominikErdélyiHungaryBudapesti Fazekas Mihály Gimnázium28/2/26 17:571.02
NithilanRavikumarIndiaNil28/2/26 18:310.92
HaozeLiUnited KingdomWinchester College1/3/26 11:430.9
TawhidBin OmarBangladeshSt. Joseph Higher Secondary School1/3/26 19:000.63
Sudipto SenTawhid Bin OmarBangladeshSt. Joseph Higher Secondary School9/3/26 15:020.6
AadiSinghIndiaAIS-4615/3/26 14:050.6
KanadBhattacharyaIndiaDeeksha STEM8/3/26 09:480.567
ArtyomEryominLyceum №2319/3/26 19:080.5
NatchaphonWatunyoowanichThailandShrewsbury International School Bangkok – Riverside Campus22/3/26 05:300.5
IvanErmolaevSchool 2044, Moscow31/3/26 08:260.5
SvaritJoshiIndiaKhyati World School16/3/26 11:320.475

University students:

First nameSurnameCountrySchool/UniversityP4 date time
DD/MM/YY 00:00:00		P4 Score
ViníciusFerreira RodriguesBrazilUniversity of Iowa2/2/26 03:292.3
JoshuaWangUnited StatesMIT3/2/26 09:152.2
ShihaoYeChinaTsinghua University4/2/26 11:052.1
VaibhavVIndiaUnited Institute of Technology4/2/26 15:341.7
KadyrberdiYazdurdievTurkmenistanMagtymguly Turkmen State University6/2/26 10:501.6
GuyGinzbergIsraelOpen University of Israel8/2/26 13:041.5
JonathanBurgerGermanyKarlsruher Institut für Technologie8/2/26 15:161.3
Arslan JumayevDavut AlybayevTurkmenistanMagtymguly Turkmen State University8/2/26 18:531.3
KushalThamanIndiaStanford University9/2/26 06:581.2
ErikKaniewskiEstoniaTaltech14/2/26 15:451.1
AdityaBhojIndiaIndian Institute of Technology22/2/26 05:490.9
SathyaNistriItalyUniversità di Pisa21/2/26 19:390.81
LarranceXingUnited StatesUniversity of Chicago1/3/26 09:020.72
AlessandroD’OrazioItalyUniversity of Pisa5/3/26 21:300.7
ShaocongSunChinaPeking University15/3/26 02:100.6
Md Mustakim BinAlamNovosibirsk State University12/3/26 19:560.54
NikhilKodaliUnited StatesUC Irvine18/3/26 01:520.5
DanielYiUnited StatesUniversity of Maryland College Park31/3/26 07:220.5
AdrianRewkowskiBelarusJagiellonian University27/3/26 17:480.3848