I made up a new logic puzzle based on the games Numberlink and Chess, and thought it ended up rather interesting. The solution, as usual, is unique.

The starting and ending positions of 7 chess pieces are shown on the board. Find the trajectories of the pieces, if you know that they do not overlap and completely cover the board.

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Remark: Every two consecutive squares in the Queen's trajectory are either diagonally or horizontally/vertically adjacent. Every two consecutive squares in the Rooks' trajectories are horizontally/vertically adjacent. Every two consecutive squares in the Bishops' trajectories are diagonally adjacent. Every two consecutive squares in the Knights' trajectories are 2 horizontal and 1 vertical cells apart, or 2 vertical and 1 horizontal cells apart.

  • $\begingroup$ @Alconja, the knight trajectories are not continuous. $\endgroup$ May 14 '18 at 2:55
  • $\begingroup$ Was trying to make it a bit clearer for people who hadn't played the game, but you're right, perhaps I've introduced potential confusion... Perhaps you can think of better wording? (Nice puzzle btw) $\endgroup$
    – Alconja
    May 14 '18 at 2:57
  • $\begingroup$ @Alconja, thanks. Let's revert it back to the original wording and I will think tomorrow for a better one? I have added a detailed description in the remark, but indeed it will be good to come up with a succinct and precise formulation. $\endgroup$ May 14 '18 at 3:00
  • $\begingroup$ Nice idea to connect these two :) $\endgroup$
    – ABcDexter
    May 14 '18 at 8:35

I believe this works (under the assumption that paths consist only of the squares visited by each piece, not by the lines created, allowing diagonal lines to "cross" each other, and the knights' obvious need to "jump"):


  • $\begingroup$ Couldn't the black knight take a1, or the black rook g1 and h1, or the queen g3 and g4? Or does the question also intend to impose the additional unstated restriction that the piece trajectories cannot branch off? $\endgroup$
    – noedne
    May 14 '18 at 3:30
  • $\begingroup$ @noedne - I don't follow... you mean as in capture the pieces? I was assuming (perhaps incorrectly), that the primary ruleset was numberlink, but with chess based movement (i.e. no piece will take anything, they'll all just avoid each other) $\endgroup$
    – Alconja
    May 14 '18 at 3:37
  • $\begingroup$ In Numberlink you're only supposed to connect numbers together and no more (in particular you can't go further in a line), so I suspect the same applies here $\endgroup$
    – phenomist
    May 14 '18 at 3:37
  • $\begingroup$ @Alconja Sorry, by "take," I meant travel through that square. $\endgroup$
    – noedne
    May 14 '18 at 3:38
  • 1
    $\begingroup$ @Alconja's interpretation and solution are correct. I will accept this tomorrow:) $\endgroup$ May 14 '18 at 3:44

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