Romanian Master of Mathematics

At the Romanian Master of Mathematics competition held in Bucharest on 24-29 February 2016, Joe Benton came second in the competition, scoring 27/42 and winning a gold medal.

The competition attracted 113 pre-university students from all over the world, including some of the strongest competitors from the USA, Hungary, Russia and China.

In 2014 and again in 2015, Joe won silver medals in the International Mathematical Olympiad and still has two years to go before he is no longer eligible for competing. He also won a silver medal in the International Informatics Olympiad in 2015.

One of the problems successfully solved by Joe:

Given positive integers m and n ≥ m, determine the largest number of dominoes (1 ´ 2 or 2 ´ 1 rectangles) that can be placed on a

rectangular board with m rows and 2n columns consisting of cells (1 ´ 1 squares) so that:

(i) each domino covers exactly two adjacent cells of the board;

(ii) no two dominoes overlap;

(iii) no two form a 2 ´ 2 square; and

(iv) the bottom row of the board is completely covered by n dominoes.