Logic Masters Deutschland e.V.

F-Puzzles

Standard Sudoku Rules apply to the final numerical layout.

I was curious to see how difficult it would be to create an X-Sudoku that was also Anti-Knight, Anti-King, Non-Consecutive, and Disjoint-Set. After several months of experimenting, my theory is: "Impossible".

So I decided instead to include one of the failures, complete with those cells that refused to keep all the rules.

First: It is always true that digits in cages must sum to the total in the top left corner.

And it is always true that two cells a chess king's move from each other may not be the same.

But each of the four following rules is broken at least once on the grid.

1: Anti-Knight: Digits a chess knight's move from each other may not be the same.

2: Diagonals: Digits on the two long diagonals may not repeat.

3: Non-Consecutive: Any two orthogonally adjacent digits may not be consecutive in value.

4: Disjoint Set: Cells that share the same position in the 3x3 boxes may not be the same. (i.e., if there is a 1 in the top left cell of Box 1, there may not be a 1 in any other top left cell in another box.)

Cells with a grey circle break one of the four rules.

Cells with a grey square break two of the four rules.

Cells with an open circle break three of the four rules.

No cell breaks all four rules, and empty cells successfully follow all of the rules.

The shapes in the marked cells refer to how many of the rules are broken, not how often they are broken. For example, a 5 may be adjacent to a 4 and a 6, but that counts as One Rule Broken (non-consecutive), not two.

Stop reading and solve now if you want to try it with no helpful hints!

*****

Helpful hint: That grid and all those instructions may seem daunting, but not every marked cell needs to be carefully explored. Many are, in fact, rather superfluous except in the fact that they make the negative constraint regarding empty cells possible. Find the right places to chip away, and the rest will fall into place without much additional struggle.