Results after Problem 7

The list of the contest leaders after the seventh problem:

Points for Problem No 7:

Correct solutions (ordered according to the arrival time; best solutions in bold):

1. Szabó Attila (Hungary)

2. Nadezhda Vartanian (Russia)

3. Jakub Šafin (Slovak)

4. Nikita Sopenko (Russia)

5. Alexandra Vasileva (Russia)

6. Adrian Nugraha Utama (Indonesia)

7. Selver Pepić (Bosnia-Herzegovina)

8. Ilie Popanu (Moldova)

9. Ion Toloaca (Moldova)

10. Petar Tadic (Montenegro)

11. Andrew Zhao (United States)

12. Lars Dehlwes (Germany)

13. Jakub Supeł (Poland)

14. Teoh Yee Seng (Malaysia)

15. Ng Fei Chong (Malaysia)

16. Ivan Tadeu Ferreira Antunes Filho (Brazil)

17. Cristian Zanoci (Moldova)

18. Kohei Kawabata (Japan)

19. Dinis Cheian (Moldova)

(The list is ordered according to the arrival time)

This list of correct solutions is ordered according to the arrival time. There are also two incorrect solutions. The number of registered participants: 259 from 44 countries.

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The hints have been given as follows. For the second week: first, note that the correct solutions submitted thus far can be roughly divided into three categories: (a) fully geometric; (b) fully geometrical constructions, but some geometrical construction elements are motivated arithmetically; (c) first step is done geometrically, the next steps involve measurements (angles and/or distances), calculations, and using the calculation results for drawing. Second, keep in mind that everything you need to know for solving this problem is covered by Formula sheet Eq VI-8 (however, this knowledge needs to be applied creatively).
 

The hints for the last 10 days are aimed to help finding the fully geometric solution and are given in the form of questions to think about. (A) Where does lay the intersection point of the images of two parallel lines? (B) Consider two infinitely distant light sources which are at an angular distance from each other. What is the angular distance between the images of these sources, as seen from the centre of the lens?

The hints for the last 7 days: use the answer to the question (A) to find one of the focal planes of the lens. On that focal plane, it is possible to mark two points P and Q the images of which are at infinity, separated from each other by an angular distance of . The centre of the lens needs to lie on a certain curve, which can be drawn using the points P and Q, together with the answer to the question (B).

The final hint for the last 4 days: if you were successful in answering the previous questions, you just need to repeat the last steps two find another curve where the center of the lens also needs to lie.