Problem K. 424. (September 2014)
K. 424. Arrange the whole numbers 1 to 10 in the figure, so that the sum of the numbers along each line segment containing exactly four circles is 23, and the sum of the numbers along each line segment containing exactly three circles is 16. How many different arrangements are there? (Arrangements obtained from each other by rotation or reflection are also considered different.)
Deadline expired on October 10, 2014.
103 students sent a solution. 6 points: Agócs Katinka, Korpás Isabel, Kós Anna, Kubovics Márton, Kulcsár Simon, Nagy Viktor, Németh Csilla Márta, Paulovics Péter, Sisák László Sándor, Slenker Balázs, Szarka Álmos, Tószegi Fanni, Valkó Bence, Wenczel Kata. 5 points: Csuha Boglárka, Encz Koppány, Gyűrűs Boldizsár, Harsányi Benedek, János Zsuzsa Anna, Mihályházi Péter, Nagy Marcell, Páhoki Tamás. 4 points: 5 students. 3 points: 8 students. 2 points: 11 students. 1 point: 35 students. 0 point: 16 students. Unfair, not evaluated: 6 solutions.