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This is a puzzle based on work by Rodolfo Kurchan.

Can you place a pawn, a knight, a bishop, a rook and a king on a 5x5 chess grid, such that every empty cell is attacked by at least one piece? Note that the pawn attacks the two diagonal cells directly above it.

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  • $\begingroup$ Are there any more solutions? $\endgroup$ Jun 29, 2023 at 11:56
  • $\begingroup$ Is it possible to solve 5x6? $\endgroup$ Jun 29, 2023 at 11:56
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    $\begingroup$ If you give another knight, it's possible. I think with the original ones it's not possible. In my answer if you move the rook down one row, and switch the knight to the square it currently is attacking, only 2 squares are uncovered though. If you replaced the king with queen, you can almost cover 6x6 $\endgroup$
    – justhalf
    Jun 30, 2023 at 18:55

5 Answers 5

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This arrangement of pieces should work:

enter image description here

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    $\begingroup$ Ah, jou beat me in only 1 minute. Well done :) $\endgroup$
    – Lezzup
    Jun 25, 2023 at 12:34
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    $\begingroup$ @Lezzup thanks :) I would've submitted it faster if not for the restriction that I need to have at least 30 characters aside from the image XD "This should work" -> "This arrangement should work" -> "This arrangement of pieces should work" lol $\endgroup$
    – justhalf
    Jun 25, 2023 at 12:40
  • $\begingroup$ Technically, the square with the knight is nobody attacking. But in my solution I've got the same problem with the square where the king is located. I am not sure if there is a better answer? ;) $\endgroup$
    – Lezzup
    Jun 25, 2023 at 12:41
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    $\begingroup$ The puzzle only requires that every "empty cell" be attacked. Those occupied are not empty cells. (Oh, and someone just noticed, and I just noticed too, that your rook doesn't attack the left-most blue square, blocked by pawn) $\endgroup$
    – justhalf
    Jun 25, 2023 at 12:43
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This also works:

enter image description here r = rook, p = pawn, kn = knight, ki = king, b = bishop

Thanks @justhalf, this is works:

enter image description here

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    $\begingroup$ The knight covers a lot of squares, cool :D $\endgroup$
    – justhalf
    Jun 25, 2023 at 12:39
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    $\begingroup$ @Lezzup you can fix it by moving the rook to the other side (shifting everything to the right). This way, the knight will be the center piece $\endgroup$
    – justhalf
    Jun 25, 2023 at 12:49
  • $\begingroup$ FYI, the standard practice is to use N for knight and K for king, so you don't have to use a second letter to distinguish them. $\endgroup$ Jun 26, 2023 at 15:34
  • $\begingroup$ This is the only answer so far that is significantly different from my answer (rook on a corner, the rest covering 4x4 area similarly), nice one. $\endgroup$
    – justhalf
    Jun 28, 2023 at 8:20
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Came up with an alternative solution from the other answers

enter image description here

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Others have solved this similarly, but here's mine.

my solution: Ra5, Nd4, Kc2, Bd2, Pd3

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    $\begingroup$ f1 and f2 are both not covered here :) $\endgroup$ Jun 27, 2023 at 11:06
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    $\begingroup$ The Board here is not 5x5 , it is 5x6 , @GeorgeWilson , hence that "uncovered" area !! $\endgroup$
    – Prem
    Jun 27, 2023 at 11:18
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    $\begingroup$ I tricked you with my terrible screenshotting (-: $\endgroup$
    – Rob Grant
    Jun 27, 2023 at 11:58
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    $\begingroup$ fixed the diagram. $\endgroup$
    – Evargalo
    Jun 27, 2023 at 13:36
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    $\begingroup$ @Evargalo Thank you! $\endgroup$
    – Rob Grant
    Jun 27, 2023 at 15:04
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This is my solution.

Another variant of the bishop-pawn-knight tower My solution: Nc5 c4 Bc3 Kb2 Re1

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