Ok detective, here's what we know about today's case:
- 5 digits have been killed in a short amount of time. Their positions and identities have been marked on the grid in red.
- There have been 4 different shooters that all belong to the same underground organization, all their members identify themselves as a 1 on the grid.
- At the sides of the grid you can find 2 spots marked with an X, those represent where our team found bullets embedded into the side of a building, most likely meaning that those bullets did not kill anyone.
- Thanks to some witnesses we were able to mark additional arrows on the grid.
We were also able to apprehend one of these criminals and this is what we were able to get out of them:
- Their position at the time of the crime has been marked on the grid in gray.
- While we were unable to pinpoint the exact locations of the other 3 shooters, we were able to narrow them down to 3 killer cages containing one criminal each.
- At the time of the arrest, the criminal was visibly shaken and kept repeating "We didn't get a single one of them..."
- Once pressured, the shooter revealed that the organization's plan was to get rid of a specific digit but they refused to reveal the targets' identities.
Lastly, by analysing past activities of the organization, we were able to determine the decision making process of single members during violent situations, here's a summary:
The criminal, always a number 1, will only shoot if the following conditions are met:
- Their position is followed (or preceded) by a 2 and then a 3; The direction from the 1 to the 3 is considered the "BACK".
- There is a target in their line of sight, a target is considered in line of sight if a segment can be drawn from 1 to the target by moving only in one orthogonal direction; the shooter does not check the "BACK" direction for targets.
Once the line of sight has been determined, a shot is taken along that line of sight.
The victim is then determined as follows:
- Each digit found along the line of sight is either bigger than the previous one or a victim.
- The bullet is stopped at the first victim encountered or, if no digit was smaller than the previous one, it will strike the side of the grid leaving an X mark.
In these examples, the shooter is "activated" by belonging to a 3-2-1 triplet and by seeing a target (digit number 5) in its line of sight.
The shots are highlighted in grey and victims are in red.
Notice how, even though the examples show 4 "shots" there are only 3 victims and of those only 1 is the actual target of the shooter.
Standard 9x9 Sudoku rules.
Killer cages: The regions between dotted lines contain no repeated digits and sum to the number on the top left.
Arrows: Digits along an arrow must sum to the digits in the circle read left to right.
Sudokupad link with answer check