Combinatorics · Board configurations · Constructions · Parity · Pairing
In the game Minesweeper, mines are placed on some cells of an \(a \times b\) board (\(a, b \in \mathbb{N}\)), and on every remaining cell one writes the number of neighbouring cells that contain a mine. Two cells count as neighbours when they have at least one common vertex.
Decide whether there exist numbers \(a\) and \(b\) and an arrangement of mines on an \(a \times b\) board such that exactly \(2019\) cells contain no mine and the number written on every one of them is:
a) \(3\); b) \(4\); c) \(7\).
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Serbian Municipal Competition 2019, high school grade I, category A, problem 5. Organized by the Mathematical Society of Serbia (DMS). Source