A recent post and Stiv's answer provided inspiration for a new puzzle. I posted a study for this puzzle earlier; this is the bigger effort envisioned. I hope you enjoy!
This puzzle consists of four different logic puzzles: a Nonogram, a Nurikabe, a Kakurasu, and a Slitherlink, which need to be solved simultaneously. The clues for the first three puzzles are given in the following diagram:
The red numbers, at the top and to the left, are the Nonogram clues. The yellow numbers in the grid itself are the Nurikabe clues. The blue numbers at the bottom and to the right are the Kakurasu clues. The Slitherlink clues are given in this diagram:
As you might guess with this presentation, there is something funny going on. Not all of the Slitherlink clues are valid. A Slitherlink clue is only valid if its color matches the combination of the corresponding squares in the other three puzzle grids that are shaded. So for example, a red Slitherlink clue is only valid if the corresponding square in the Nonogram grid is shaded, and the corresponding square is not shaded in the Nurikabe and Kakurasu grids. Specifically the combinations are:
- White - no shading in any grid
- Red - Shaded in Nonogram, not shaded in Nurikabe and Kakurasu
- Orange - Shaded in Nonogram and Nurikabe, not shaded in Kakurasu
- Yellow - Shaded in Nurikabe, not shaded in Nonogram and Kakurasu
- Green - Shaded in Nurikabe and Kakurasu, not shaded in Nonogram
- Blue - Shaded in Kakurasu, not shaded in Nonogram and Nurikabe
- Purple - Shaded in Nonogram and Kakurasu, not shaded in Nurikabe
- Black - Shaded in all three grids
In the Nurikabe grid, the squares containing the clues themselves are considered unshaded.
Shading is determined by the background color in the Slitherlink clue; the coloration of the numeral is for legibility only and has no significance for the puzzle. A box around the numeral is solely to highlight the white background, and has no significance for the puzzle.
If a Slitherlink clue is invalid, it provides no information about the Slitherlink. The number may match the ultimate path, or it may not.
An accepted solution will have the solution for all four puzzles, as well as a description of the logic used to derive the solution.
As a final note: the set of four puzzles with the given connections does have a unique solution, but that does not mean that each of the component puzzles does, absent the given connections. The puzzles are meant to be solved simultaneously, not in sequence.
As I was going through the puzzle, I found it easier to work each individual puzzle in its own grid. These individual grids are provided here:
For the ColorblindThe CSV below has the colors of the Slitherlink clues, with Bl for blue and Bk for black:
W,R,O,Bl,Y,O,G,Bk,P Bk,G,G,Y,Bk,G,W,O,W P,R,Bk,O,P,W,O,Y,R O,Bl,R,R,Y,W,Y,Bl,Y Bk,W,Y,Y,R,O,G,R,W O,G,R,Bk,Y,Bk,G,Y,Bk R,Y,P,Y,G,Bl,Bl,Y,Y G,O,Bl,Bl,G,O,Bk,P,Bl P,P,Bl,P,P,Bl,G,Bl,Bk
This type of puzzle has not appeared on PSE before, at least not by this name. The rules are simple. The columns, left to right; and rows, top to bottom; are labelled with the values 1 though 9. When the grid is shaded, a row (column) sum is the sum of the values associated with the columns (rows) of the shaded squares in that row (column). The goal is to shade the grid so that the row and columns sums, presented at the right and bottom, respectively, are simultaneously satisfied.