Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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# Problem B. 4661. (November 2014)

B. 4661. There are discs placed on some fields of a chessboard of $\displaystyle n$ columns and $\displaystyle k$ rows (at most one disc on each). Two discs are said to be adjacent if they lie in the same row or in the same column, and there is no other disc along the line segment connecting them. Each disc is adjacent to at most three others. What is the maximum possible number of discs on the chessboard?

Suggested by K. Williams, Szeged

(6 pont)

Deadline expired on December 10, 2014.

### Statistics:

 109 students sent a solution. 6 points: Adorján Dániel, Andó Angelika, Árvai Balázs, Bálint Martin, Balog Gergely, Baran Zsuzsanna, Bereczki Zoltán, Bertalan Dávid, Bursics Balázs, Csépai András, Csitári Nóra, Czirkos Angéla, Döbröntei Dávid Bence, Fekete Panna, Gáspár Attila, Glattfelder Hanna, Hansel Soma, Imolay András, Katona Dániel, Kerekes Anna, Khayouti Sára, Kovács 246 Benedek, Kovács 972 Márton, Kovács Péter Tamás, Kőrösi Ákos, Lajkó Kálmán, Leitereg Miklós, Mályusz Attila, Mócsy Miklós, Molnár-Sáska Zoltán, Nagy Dávid Paszkál, Nagy-György Pál, Németh Hanna, Porupsánszki István, Schrettner Bálint, Schwarcz Tamás, Szakács Lili Kata, Szebellédi Márton, Szőke Tamás, Tárkányi Damján, Vágó Ákos, Váli Benedek, Wei Cong Wu, Williams Kada. 5 points: 28 students. 4 points: 5 students. 3 points: 3 students. 2 points: 1 student. 1 point: 21 students. 0 point: 6 students. Unfair, not evaluated: 1 solution.

Problems in Mathematics of KöMaL, November 2014