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    $\begingroup$ The problem with 3 cells and $n>4$ is The American Mathematical Monthly problem 12137 (October 2019). $\endgroup$
    – RobPratt
    Commented May 19, 2020 at 22:08
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    $\begingroup$ I had trouble understanding the problem because I imagine the rook jumping from the start to the destination cell. You should make clear that all the cells between the start and the end of each move must be shaded. The shaded region must be orthogonally connex. $\endgroup$
    – Florian F
    Commented May 19, 2020 at 22:28
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    $\begingroup$ @BernardoRecamánSantos math.lsu.edu/~mahlburg/teaching/handouts/2018S-3903/12008.pdf $\endgroup$
    – RobPratt
    Commented May 20, 2020 at 3:30
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    $\begingroup$ Connex doesn't seem to be the right term, according to Wikipedia's definition. "Orthogonally connected" probably gets the point across well enough. $\endgroup$
    – N. Virgo
    Commented May 20, 2020 at 13:12
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    $\begingroup$ Sorry, I thought it was a typo like othogonally. 😉 $\endgroup$
    – RobPratt
    Commented May 20, 2020 at 13:24