Results after Problem 7

The list of the contest leaders after the seventh problem:

Points for Problem No 7:

 3,2913 Sabó Attila 2,9921 Nadezhda Vartanian 2,72 Jakub Šafin 2,4728 Nikita Sopenko 1,7716 Adrian Nugraha Utama 1,7538 Alexandra Vasileva 1,6889 Ilie Popanu 1,6105 Selver Pepić 1,5354 Ion Toloaca 1,089 Petar Tadic 1 Lars Dehlwes 1 Ivan Tadeu Ferreira Antunes Filho 1 Dinis Cheian 1 Cristian Zanoci 1 Kohei Kawabata 1 Teoh Yee Seng 0,9344 Andrew Zhao 0,9 Ng Fei Chong 0,6561 Jakub Supeł

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

1. Szabó Attila (Hungary)

3. Jakub Šafin (Slovak)

4. Nikita Sopenko (Russia)

5. Alexandra Vasileva (Russia)

7. Selver Pepić (Bosnia-Herzegovina)

8. Ilie Popanu (Moldova)

9. Ion Toloaca (Moldova)

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 $\alpha$ 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 $90^\circ$. 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.