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Part of 2017 Romanian Master of Mathematics

Problems(1)

Minimal Numbers of Sticks

Source: Romanian Masters 2017 D2 P2

2/25/2017
Fix an integer n≥2n \geq 2. An n×nn\times n sieve is an n×nn\times n array with nn cells removed so that exactly one cell is removed from every row and every column. A stick is a 1×k1\times k or k×1k\times 1 array for any positive integer kk. For any sieve AA, let m(A)m(A) be the minimal number of sticks required to partition AA. Find all possible values of m(A)m(A), as AA varies over all possible n×nn\times n sieves.
Palmer Mebane
combinatoricsRMMRMM 2017Tiling