X-Monotonic Arrows (Mini)
(Published on 31. March 2026, 07:00 by protheph)
I’ve been playing with a new constraint. This 6x6 is designed to be an easy introduction to the mechanic. If you enjoy the logic, check out the full 9x9 puzzle here: X-Monotonic Arrows.
Rules:
- Normal 6x6 Sudoku Rules Apply: Fill every row, column, and 2x3 box with the digits 1-6 without repetition.
- X-Monotonic Arrows: The digit X in the first cell seen by a gray arrow outside the grid determines a sequence of X cells in the arrow's direction (including the first cell). This sequence must be strictly monotonic (either strictly increasing or strictly decreasing).
Have fun!
Solution code: Row 6
Comments
on 7. April 2026, 00:59 by dzamie
For people who were confused like me: "no negative constraint" doesn't (just) mean "not all possible arrows are necessarily shown," it means "the monotonic sequence is *at least* X cells long."
--> 234 is valid, because "23" is monotonic, even though "234" is also monotonic.
on 5. April 2026, 17:05 by Plok
X-montonic rules are very unclear. Wht would help is 3 different examples in the rule set.
I read your correction in the comments, but from the rule set I expect 1 to be impossible as there is always at least a sequence of 2 after a X = 1.
on 1. April 2026, 02:10 by SanFranSam
There were two things that confused me. First, i think of a sequence as being 345. But a legitimate set of numbers for an arrow would be 356. Maybe string or series or set (of numbers) would be better. Also the first number is not a constraint. So an arrow could start with a 1. But by definition it would be at least 2 long. Perhaps this is what you meant by no negative constraint.
on 31. March 2026, 18:44 by Supertaster
That was fun. I was afraid the possibility of 1 would create too many ambiguities, but it solved quite nicely, thanks.
on 31. March 2026, 16:53 by faltenin
Fun new constraint! Took a few minutes to wrap my brain around the implications but after that it went very smoothly.
on 31. March 2026, 09:38 by protheph
Thanks for the feedback! To clarify the logic: the rule states the sequence is X cells long. When X = 1, the sequence consists of only that first digit. Since a single digit is monotonic by default, the arrow effectively provides no restriction on any cells following it.
on 31. March 2026, 09:23 by Jen118266
How can the digit x equal 1 when the following digit can not also be 1 it will be an increasing sequence?
on 31. March 2026, 08:20 by michael_787
Took me a couple of minutes to grasp the implications of this rule. After that it was a smooth solve. Great puzzle, thank you.
