 Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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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