x+y>z (Dynamic Fog)
(Published on 12. March 2026, 16:44 by Hanks)
Hi everyone! I wanted to make a sudoku puzzle which relates to a math theorem called the Triangle Inequality. It states that a triangle with side lengths {x,y,z} can be formed if and only if x+y>z, y+z>x, and z+x>y. Thanks to Kyunitar, SennyK, Cassinii, and many others for testing. I hope you enjoy the puzzle!
Rules:Normal sudoku rules apply.
TRIANGLE INEQUALITY LINES: all digits are distinct on a red line. Furthermore, any three distinct digits {x,y,z} on a red line satisfy the Triangle Inequality: x+y>z, y+z>x, and z+x>y.
GERMAN WHISPER LINES: adjacent digits on a green line have a difference of at least 5.
INEQUALITY SIGNS: an inequality sign points to the smaller of the two digits it sits between.
DYNAMIC FOG: entering a correct digit clears fog in its cell, and may or may not clear fog in other cells.
Solution code: Digits in row 9
Comments
on 13. March 2026, 17:54 by TMNF
I loved it, really amazing
Thank you
on 13. March 2026, 14:34 by Flinty
Very nice :)
on 13. March 2026, 08:55 by WvdWest
Nice new constraint. Once you comprehend the working of it, makes it a fluid solve.
on 12. March 2026, 19:20 by wunder108
Very nice puzzle! Thanks for sharing
on 12. March 2026, 19:14 by dzamie
Oh that's neat! I often see stuff like this with the restriction focused on *adjacent* digits, so having it restrict *any* set of three brought a different mode of logic around.
on 12. March 2026, 16:48 by SennyK
Very fun puzzle with clever interactions, nicely done! :-)
