Mathematical and Physical Journal
for High Schools
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Problem B. 4682. (January 2015)

B. 4682. For a given positive integer \(\displaystyle k\), find the largest positive integer \(\displaystyle m\) such that the following statement should be true: If at most \(\displaystyle m\) of \(\displaystyle 3k\) different points in the plane are collinear, then the points can be divided into \(\displaystyle k\) groups of three such that the points in each group form a triangle.

Suggested by A. Frank, Nagykovácsi

(5 pont)

Deadline expired on February 10, 2015.


Statistics:

76 students sent a solution.
5 points:Andó Angelika, Baran Zsuzsanna, Csépai András, Fekete Panna, Gáspár Attila, Katona Dániel, Kovács Péter Tamás, Lajkó Kálmán, Mócsy Miklós, Molnár-Sáska Zoltán, Nagy Dávid Paszkál, Nagy-György Pál, Németh 123 Balázs, Schrettner Bálint, Szebellédi Márton, Szőke Tamás, Tóth Viktor, Williams Kada.
4 points:Bursics Balázs, Döbröntei Dávid Bence, Hansel Soma, Jenei Dániel Gábor, Kovács 246 Benedek, Nagy Simon József, Schwarcz Tamás, Váli Benedek.
3 points:6 students.
2 points:27 students.
1 point:15 students.
0 point:2 students.

Problems in Mathematics of KöMaL, January 2015