I having problem to solve the below question:
Given $2020\times 2020$ chessboard, what is the maximum number of warriors you can put on its cells such that no two warriors attack each other. Warrior is a special chess piece which can move either:
- $3$ steps forward and one step sideways in any direction, or
- $2$ steps forward and $2$ steps sideways in any direction.
Answer Given: 2020 *505
Got Solution from one friend: Strategy: Put the warriors in $(4k+1)$ columns.
Proof 1)We can easily notice that warriors can't attack warriors in his own column. So we can arrange the warriors in the above mentioned arrangement. 2) The warriors of $(4k+1)$column can attack warriors of $4k,4k-1,4k-2$ columns . So we can't put the warriors in those cells.
So the maximum number of warriors that can be put is $2020 \times 505$