Logic Masters Deutschland e.V.

I need to give riffclown a huge shoutout as the inspiration for this puzzle. The 159 + Knightmare constraints nearly create a perfectly blank miracle puzzle all by themselves! Amazingly, a blank grid with only 159 and Knightmare rules in play has only 4 possible solutions. Furthermore, if you start with any one solution, you can mirror it top-bottom to get a second solution, and then mirror those two solutions left-right and replace every digit x with 10-x to generate the remaining two solutions. Both of these transformations preserve logic with respect to both constraints, so that means there is essentially only one solution to 159 + Knightmare that just gets expressed 4 different ways due to symmetry. In fact, there are a few places where only a single given digit with 159 + Knightmare will result in a unique solution (for example, here)! The problem is that logically proving this fact without brute-force searching through all possibilities seems to be extremely difficult and is probably not human-solvable. Riffclown had discovered all of this and posted several messages in Discord trying to get people interested in setting a minimal clue puzzle using the 159 + Knightmare constraints to create a new "Miracle" Sudoku. Eventually, I took the bait :) After many hours of experimentation, this is the most interesting layout of givens I was able to find that allows for a logical solve to a unique solution.

This puzzle is still not easy, so I don't think I quite attained the original goal of finding a true "Miracle" puzzle, but I assure you that the solve path has been tested by hand and is very "humanable", requiring no bifurcations if you find the right deductions. (At least one trick beyond basic Sudoku eliminations will be required, however). Both constraints are a little scan-heavy, so I know this puzzle won't be for everyone, but it is rare to find a puzzle so pure in constraint interactions, and I'm sure the beauty of this puzzle will be appreciated by the right audience.

Assuming I haven't scared you off yet, I am proud to present A Beautiful Nightmare. As near as I can tell, this is as close as you can get to a Miracle 159 + Knightmare puzzle with a logical solve path. Good luck!

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Normal Sudoku rules apply.

Knightmare: Digits a knight's move apart do not sum to 5 or 15.

159 Sudoku: A digit in column 1 indicates the column in which the digit 1 appears in that row. Columns 5 and 9 have the same rule for the digits 5 and 9, respectively.

Solve on F-Puzzles

Solve on CtC App