A collaboration with SamuPiano. We decided to combine the octopus-rules from ThePedallingPianist with the Chess-Lines constraint. There is an example puzzle available further down on the page. Thanks to all the testers. Happy solving!
These images show a 5x5 example puzzle (left) and the corresponding solution (middle). All arms have the same length - they take 2 steps on either side of the octopus. The arms are rotationally symmetric - since there is an arm ending in the top-right corner, there must also be an arm ending in the bottom-left corner. The arm on the positive diagonal acts as a bishop (68486). The arms next to it are pawn (41474) and rook (25413). The last arm is a knight (29492). The two cells connected by the 4 clue on the top-right sum to 4 (1+3) and are part of the rook arm (a rook can connect 1 and 3). The last image illustrates why a 1 on a knight-line can only be connected to 6 or 8.
Play the Example Puzzle on SudokuPad.
Solution code: Column 5, top to bottom (9 digits)
on 10. June 2024, 23:34 by gdc
@Deino42 they must be on the same arm and directly connected.
on 10. June 2024, 23:28 by Deino42
Are the cells that the given lines point to part of the same tentacle as the given line? (e.g. if r7c3 is a blue line, is r6c4 also part of the blue line?) Also, if they are part of the same tentacle, are they directly connected, or could there be another cell between? Such as a blue line going r7c3, r7c4, r6c4?
on 10. June 2024, 16:14 by SamuPiano
Collaborating with you was so much fun! I'm very happy with how this one turned out :)