MathDB
putting queen's on the chess board.

Source: Iranian RMM TST 2021 Day3 P2

April 16, 2021
combinatoricschess

Problem Statement

In a chess board we call a group of queens independant if no two are threatening each other. In an nn by nn grid, we put exaxctly one queen in each cell ofa greed. Let us denote by MnM_n the minimum number of independant groups that hteir union contains all the queens. Let kk be a positive integer, prove that M3k+13k+2M_{3k+1} \le 3k+2
Proposed by Alireza Haghi