Logic Masters Deutschland e.V.

Hello.

People were asking for more HITBOX puzzles, but there's only so much you can do with the idea.

I did notice some similarities with some of my other recent puzzles that use some sort of global constraint (like the King's puzzles or the Archer's, signaling position, global vs global). Looking back at some of these puzzles, the crossroads rule almost presented itself.

My first version had two given digits, but thankfully someone on Discord noticed that a single digit should be enough, which really makes it a "miracle sudoku".



Normal Sudoku rules apply.

Hit Points: Within each 3×3 box, the nine cell positions are numbered 1–9, from left to right and then top to bottom. A cell is a hit point when its digit matches its position number within the box. For example, in box 1, the digit 6 is a hitpoint only if it occurs in r2c3 (=position 6). Every 3×3 box must contain exactly three hit points.

Circles and Crossroads: Place exactly one circle in every row, every column, and every 3×3 box. The digit in a circled cell must equal the number of its 3×3 box, with the boxes numbered from left to right and top to bottom.

The digits 1–9 can be divided into two types of sets: Entropic sets: (123), (456), (789) Modulo-3 sets: (147), (258), (369)

For every row circle and column circle, their intersection is a crossroads cell. If two circled digits belong to the same set, the crossroads cell must contain the third digit from that set.

For example: Circles containing 1 and 2 give 3 at their crossroads. Circles containing 1 and 4 give 7 at their crossroads.

Have fun.