Statistics

Point-rank graph for the total score; blue line – before moderation; black line – after moderation.

One can say that the simple questions were slightly too simple: the linear trend at the middle of the graph breaks at the right-hand-side of the graph, where the curves turn steeply down. Meanwhile, the difficult questions were difficult, indeed, and provided a good separation between the very best contestants; this is evidenced by another steeper segment at the left-hand-side.

Further, let us have a look on the distribution of the theoretical and experimental marks separately.

For theory, the linear trends extends down to the rightmost corner of the graph: none of the questions was too simple! As for experiment, the graph is qualitatively very similar to the graph of the total scores.

Let us dwell even more into details, and have a look the distribution of points for all the theoretical problems.

Simple questions of problem T1 were simple, indeed: the total cost of these were 3×0.8=2.4 pts, and ca 40% of the contestants got at least as much. However, the supposedly medium difficulty questions, each worth of 1.2 and totalling in 3.6 pts, were actually quite difficult: answering all the simple and medium questions would result in 6 pts, and only 6% of contestants got 6 or more points.
The contestants with top scores are as follows (all gold medalists).
12.1: Attila Szabó (HUN);
10.9: Eric Schneider (USA);
10.2: Hengyun Zhou (CHN);
10.1: Yijun Jiang (CHN);
9.3: Ilya Vilkoviskiy (KAZ);
9.1: Paphop   Sawasdee (THA), Wenzhuo Huang (CHN);
8.7: Chien-An Wang (TWN);
8.2: Wonseok Lee (KOR);
7.7: Jun-Ting Hsieh (TWN);
7.6: Ding Yue (SGP);
7.5: Kuan Jun Jie, Joseph (SGP);
7.2: Sooshin Kim (KOR), Siyuan Wei (CHN);
7.0: Phi Long Ngo (VNM).

Next, about Problem T2. As you can see, this is a problem with a perfect balance between simple and difficult questions: there is almost a linear line connecting the upper left corner with the lower right corner. The contestants with top scores are as follows (all gold medalists unless otherwise noted).
8.0 pts: Chien-An Wang (TWN), Yijun Jiang (CHN);
7.9 pts: Jun-Ting Hsieh (TWN), Tudor Giurgică-Tiron (ROU);
7.8 pts: Hengyun Zhou (CHN), Chi Shu (CHN), Rahul Trivedi (IND), David Frenklakh (RUS, Silver), Kacper Oreszczuk (POL, Bronze),
7.7 pts: Wenzhuo Huang (CHN), Siyuan Wei (CHN), Jaemo Lim (KOR), Tanel Kiis (EST, Silver).

Finally, the Problem T3. A slight score saturation can be observed for this problem: the curve "hits the roof" (i.e. the maximal vale of  pts) at the left upper corner. There would have been probably a better balance between difficult and easy questions if the hint about the Keplers laws were not given in the text of the problem. However, including the hint was the wish of the International Board, and the problem set as a whole was difficult enough even with the hint included …

The contestants with a full score (9.0 pts; all gold medalists):Attila Szabó (HUN), Paphop Sawasdee (THA), Chien-An Wang (TWN), Siyuan Wei (CHN), Yuichi Enoki (JPN), Rahul Trivedi (IND), Puthipong Worasaran (THA), Tudor Giurgică-Tiron (ROU), Ngoc Hai Dinh (VNM), Alexandra Vasilyeva (RUS, Silver), Volodymyr Sivak (UKR, Silver), Bijoy Singh Kochar (IND, Silver), Nurzhas Aidynov (KAZ, Silver), Cristian Zanoci (MDA, Bronze).
 

Further, let us have a look on the experimental problems.

The Problem E1 has a nice distribution at the left upper corner, but too steep fall-off at the right edge – the simplest tasks of this problem were perhaps too simple. The contestants with top scores are as follows (all gold medalists unless otherwise noted).
10: Jaan Toots (EST);
9.9: Kai-Chi Huang (TWN), Ivan Ivashkovskiy (RUS);
9.8: Wei-Jen Ko (TWN);
9.7: Attila Szabó (HUN), Siyuan Wei (CHN);
9.6: Allan Sadun (USA);
9.5: Hengyun Zhou (CHN), Chien-An Wang (TWN);
9.4: Wonseok Lee (KOR);
9.3: Jun-Ting Hsieh (TWN);
9.2: Eric Schneider (USA), Wenzhuo Huang (CHN);
9.1: Ngoc Hai Dinh (VNM), Alexandra Vasilyeva (RUS, Silver), Chi Shu (CHN).

Meanwhile, Problem E2 was intended to be a difficult problem, aimed for finding the winner of the best experimentalist's prize, and difficult it was: it had actually no easy tasks, as evidenced by a concave shape of the curve. The contestants with top scores are as follows (all gold medalists unless otherwise noted).
8.8: Chi Shu (CHN);
8.5: Kai-Chi Huang (TWN);
8.3: Christoph Schildknecht (CHE, Silver);
8.1: Ivan Ivashkovskiy (RUS);
7.7: Attila Szabó (HUN);
7.5: Hengyun Zhou (CHN), Huan Yan Qi (SGP);
7.4: Lev Ginzburg (RUS);
7.2: Abdurrahman  Akkas (TUR, Silver);
7: Kristjan Kongas (EST, Silver);
6.9: Yu-Ting Liu (TWN), Adam Brown (GBR, Silver);
6.7: Kevin Zhou (USA), Frank Bloomfield (GBR, Bronze).

And now, it is time to have a look on the most difficult questions (tasks). Let us start with the three parts of Problem 1.

I was quite sure that q. iii of Part A is very difficult for the contestants, and q. iii of Part C is extremely difficult, and I was not mistaken. However, I did believe that q. iii of Part B is not that difficult (just difficult, not "very" nor "extremely"), and my colleagues from the Academic Committee did agree. However, here we were mistaken: Part B turned out to be the most difficult part!

So, Part 1A: only ca 20% of students were able to figure out the correct shape of the trajectory. Meanwhile, there was also a considerable number of those who got everything correctly done, including q. iii! This is an interesting case, because in order to be able to solve this problem, only a moderate physical education is needed. This is evidenced by the fact that among the best solvers of Part 1A, there are several students whose overall results were not so good; one can only hypothesize that had they passed a full course of physics covering all the Syllabus of IPhO, they would have been able to get gold medals. The contestants with top scores are as follows (all gold medalists unless otherwise noted).
4.5 pts: Attila Szabó (HUN), Hengyun Zhou (CHN), Eric Schneider (USA), Wenzhuo Huang (CHN), Yijun Jiang (CHN), Rahul Trivedi (IND), Ilya Vilkoviskiy (KAZ), Kuan Jun Jie (SGP), Joseph Ramadhiansyah Ramadhiansyah (IDN, Honourable Mention);
4.4 pts: Paphop   Sawasdee (THA), Jeffrey Cai (USA, Silver), Puthipong Worasaran (THA), Nathanan Tantivasadakarn (THA);
4.2 pts: Michele Fava (ITA, Bronze);
4.1 pts: Ding Yue (SGP);
4 pts: Hakon Tásken (NOR, Participation Certificate).

Part 1B: the list of top-solvers is shorter than before, because all the others just did not get enough marks for q. iii to be qualified as someone who really solved this problem. As usual, everyone below got a gold medal unless otherwise noted.
3.9 pts: Jun-Ting Hsieh (TWN);
3.8 pts: Attila Szabó (HUN);
3.6 pts: Sooshin Kim (KOR);
3.5 pts: Yijun Jiang (CHN);
3.4 pts: Siyuan Wei (CHN), Kai-Chi Huang (TWN), Wonseok Lee (KOR);
3.3 pts: Ihar Lobach (BLR);
3.1 pts: Wenzhuo Huang (CHN);
3 pts: Georgijs Trenins (LVA, Silver), Karlo Sepetanc (HRV, Honourable Mention).

Finally, Part 1C: note that ca half of those who performed very well here (listed below) lost 0.2 in q. i for drawing too curved field lines. There were only four contestants who got the idea of magnetic charges and realized it flawlessly (these are the first three in the list below, and Kunal Singhal). However, owing to the fact that there is also another way of calculating the force (via integrating over dipoles), several contestants got a correct estimate of the force, and collected thereby enough marks to be listed below.
4.5 pts: Ilya Vilkoviskiy (KAZ);
4.3 pts: Chien-An Wang (TWN);
4.2 pts: Paphop   Sawasdee (THA);
4 pts: Wonseok Lee (KOR), Wei-Jen Ko (TWN);
3.9 pts: Eric Schneider (USA);
3.8 pts: Attila Szabó (HUN), Yuichi Enoki (JPN), Hengyun Zhou (CHN);
3.7 pts: Phi Long Ngo (VNM);
3.6 pts: Kazumi Kasaura (JPN);
3.5 pts: Kunal Singhal (IND, Silver);
3.4 pts: Yu-Ting Liu (TWN);
3 pts: Jun-Ting Hsieh (TWN), Siyuan Wei (CHN), Ivan Tadeu Ferreira Antunes Filho (BRA).

The rest of the theoretical test was not that difficult (q iii of Problem T3 would have been quite difficult, but with the hint inserted by International Board, it no longer was). So, we don't dwell more in the theoretical results, and switch to the really tricky experimental tasks: A-iv and B of Problem E2.

In the case of Task A-iv, the number of those who really got the correct idea how to measure C(V) was really small – essentially only those who are listed below.
2.6 pts: Kuan Jun Jie, Joseph (SGP), Kai-Chi Huang (TWN), Lev Ginzburg (RUS), Ivan Ivashkovskiy (RUS);
2.5 pts: Chi Shu (CHN), Qiao Gu (DEU), Kevin Zhou (USA), Allan Sadun (USA)
2.4 pts: Yu-Ting Liu (TWN), Kristjan Kongas (EST, Silver), Adrian Nugraha Utama (IDN), Tudor Giurgică-Tiron (ROU), Sebastian Linß (DEU, Silver).

Finally, Task B. There was a surprisingly small number of those contestants who noticed that the difference in the graphs of Part A and Part B is localized to the region of negative differential resistance. As for the explanation of the phenomenon (which consists of three key elements), none of the contestants managed to list all the key elements flawlessly, and the only one to get it almost done (with some omissions in the average current part) was Christoph Schildknecht; the next two in the list below mentioned one key element. And so, the best results for Task 2B:
2.9 pts: Christoph Schildknecht (CHE, Silver);
2.3 pts: Attila Szabó (HUN);
2.1 pts: Chi Shu (CHN);
2 pts: Kai-Chi Huang (TWN), Luka Ivanovskis (LVA, Honourable Mention).

For those who want to go beyond this statistical analysis, there is also an Excel file (the names of those who got less than 12.4 pts are stripped ).

The problems of the 43rd IPhO have been thought to be difficult, and it has been even stated that the problem set was the most difficult one during the last 20 years. In order to make a comparative study about how difficult the problems actually were, several type of data are needed, which are not freely available for all the olympiads. Still, I managed to get more or less what is needed (overall number of participants, number of medals, medal boundaries in points, the scores of the absolute winners) for the period covering 1994-2012; the graph is shown below. (The last two digits of the year are shown alongside the curve – except for some curves in the central densely populated region; note that the curves which are based only on the number of medals and on the medal boundaries are interpolated and smooth.)

Even with these data, the IPhO-s apart as much as 19 years are not fully comparable: I have got a feeling that in average, the preparation level of the leading group of contestants has risen significantly. So, the graph here does not allow comparison of the absolute difficulties of the problems, but only relative ones – relative to the preparation level of the students. One should also bear in mind that the scores of absolute winners have a high intrinsic variability (there is essentially no statistical averaging); c.f. this year: the first and second places were separated by a huge margin of 3 pts.

And so, the conclusion is: the claim that we had the most difficult problem set for the last 20 years is slightly exaggerating: the problems in Beijing, 1994, were even more difficult, at least in relative terms, and at least when ignoring the contestants with ranks from 2 to 6.
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Jaan Kalda
Academic Committee of IPhO-2012