# Knights of the Square Sudoku Table

 8  .  . | .  .  . | .  .  6
.  .  4 | .  .  . | .  .  .
.  .  . | .  .  . | 9  1  .
---------+---------+--------
.  .  . | .  2  . | .  .  .
.  .  9 | 3  .  . | .  .  .
.  .  . | .  .  . | .  .  .
---------+---------+--------
.  .  . | 9  .  7 | .  .  .
9  .  . | 6  3  . | 4  .  .
.  .  . | .  .  . | 1  .  .

• Normal sudoku rules apply.
• Long diagonals contain only unique values.
• If A is a box-center, and A and B are a knight's move apart, then A and B ought to be different.

A knight's move constitutes going up/down by two followed by going left/right by one, or going up/down by one followed by going left/right by two:

. . B . B . .
. B . . . B .
. . . A . . .
. B . . . B .
. . B . B . .

• Does "diagonals" mean just the two long diagonals, or every line at 45 degrees? [EDITED to add:] Duh, must be the former since there are two diagonally-adjacent 1s in the grid already. Dec 10 '19 at 22:35
• It looks like the 9s in R2C4 and R4C5 contradict the pseudo-knight move restriction. Is that intended?
– HTM
Dec 10 '19 at 22:38
• The same with 5 at the top right.
– Moti
Dec 11 '19 at 1:25
• I believe this is unsolvable. I've tried twice to solve it deterministically, both times resulting in contradictions. Are you able to check that a solution exists satisfying the conditions? Dec 11 '19 at 4:01
• The puzzle should be solvable now. I updated the puzzle itself and the instructions. Thanks for your feedback. Dec 11 '19 at 10:01

A very tough Sudoku, but I think I got it:

• Congratulations! Dec 14 '19 at 21:06
• Well done. Can you show your working to prove this solution is unique? (I've seen some dud puzzles on PSE but I have to give OP the benefit of the doubt until proven otherwise) Jul 24 '20 at 23:48

(1) the 9s in columns 3 and 4 contradict the knight's-move restriction.

(2) a 9 cannot be placed in the middle 3x3.

• column 4 has already a 9 in row 7.

• the two spaces in column 5 are both restricted by the 9 in column 3 (same row and knight's move).

• r4c6 is in a main diagonal that already contains a 9 in column 7.

• r5c6 is within a row with a 9 in column 3.

• r6c6 is within knight's move from 9 in c4

there must be an error in the initial values.

• But the puzzle's criterion states "If A is a box-center, and A and B are a knight's move apart, then A and B ought to be different." The knight's move element is only relevant for box-centre-positioned numbers. Numbers in other spaces are not constrained by this. With this in mind, I don't think your objection holds... Please correct me if I'm wrong :)
– Stiv
Jul 24 '20 at 22:28