$2018\times 2018$ field is covered with $1 \times 2$ dominos, such that every $2 \times 2$ or $1 \times 4,4 \times 1$ figure is not covered by only two dominos. Can be covered more than $99\%$ of field ?
Source: Moscow Olympiad 2018, Grade 11, P8
Tags: combinatorics
$2018\times 2018$ field is covered with $1 \times 2$ dominos, such that every $2 \times 2$ or $1 \times 4,4 \times 1$ figure is not covered by only two dominos. Can be covered more than $99\%$ of field ?