Blue Arrow
(Published on 10. February 2025, 20:35 by Kaktuslav)
Chaos construction: Divide the grid into orthogonally connected regions, each containing exactly 9 cells. Place the digits 1-9 exactly once in every row, column, and region.
Jumping arrow: The digits along the arrow sum to the three-digit number displayed in the attached pill. The arrow passes through the centers of all cells that are not part of the pill (note that consecutive arrow cells are not necessarily adjacent; for example, a portion of the arrow follows r7c1 → r7c3 → r8c1).
Region sum line: The arrow functions as a region sum line: along the arrow, every maximal sequence of digits within the same region has the same sum. I.e. when all non-pill cells are arranged in sequence according to the order in which the arrow visits their centers, this sequence will be composed of disjoint contiguous segments with equal sums. Two consecutive cells in this sequence belong to the same segment if and only if they are part of the same region.
Inequalities: The inequality sign points to the smaller digit.
Solution code: Negative diagonal (top-left to bottom-right, no spaces)
Comments
on 15. February 2025, 03:35 by l_ugray
Wow. What an idea. That was very enjoyable, thank you!
on 13. February 2025, 06:21 by Playmaker6174
Despite solving this while being basically half tired and also the given premise, once having the right thought, I found the region building surprisingly clean throughout, and the irregular resolution afterwards was great fun too!
on 12. February 2025, 23:45 by MattYDdraig
Excellent puzzle. I was pulled into a false sense of security by the easy opening, but this got a lot tougher for a while until spotting a key breakthrough. Really good.
on 12. February 2025, 20:29 by Kaktuslav
Clarification of the region sum condition for the "jumping" line.
on 12. February 2025, 20:28 by Myxo
Very cool construction!
on 11. February 2025, 15:26 by gfoot
Thanks - it is a brilliant construction, interesting and fun to solve with a nice logical flow and not too difficult once you figure out how to do it! And I love the way the arrow starts out nice and regular, but starts to get progressively more drunken and chaotic towards the end!
on 11. February 2025, 14:14 by gfoot
Wow, amazing setup, looking forward to solving it!
Could you clarify "every maximal sequence of digits within the same region" - does this mean that, within a sequence, the arrow is allowed to leave the region and reenter it so long as it doesn't go through a cell outside the region?
e.g. using the example given in the instructions, if r7c1 r7c3 and r8c1 were in one region but r7c2 and r8c2 were in another, would the first three cells there count as a single sequence even though the arrow crosses the region border?
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Kaktuslav: Thanks for pointing out the ambiguity. Yes, in your example this would be a single sequence. A cell should be considered visited by the arrow only when the arrow reaches its center (in particular each non-pill cell is visited exactly once).
