MathDB
min no of cells, with known cover by 1x10 dominos in 1000x1000 chessboard

Source: Balkan BMO Shortlist 2015 C3

August 5, 2019
combinatoricscoveringdominoesChessboard

Problem Statement

A chessboard 1000×10001000 \times 1000 is covered by dominoes 1×101 \times 10 that can be rotated. We don't know which is the cover, but we are looking for it. For this reason, we choose a few NN cells of the chessboard, for which we know the position of the dominoes that cover them. Which is the minimum NN such that after the choice of NN and knowing the dominoed that cover them, we can be sure and for the rest of the cover?
(Bulgaria)