Digital Paint By Number and Paint By Number Place (Redux)

So I had a great time at home visiting with family. The only slight sore spot was the reappearance of the Paint By Number/Hanjie book entitled "Paint by Sudoku" which has nothing to do with Sudoku at all (my father was getting into this style of puzzle, and this was the best of the available books at the stores). After complaining about the extent to which sudoku is reframing all existing puzzles, I made a complicated variant several months ago that sort of fit the name. It led to an interesting geometric variant of the standard grid for solving a straight sudoku puzzle so I posted it, even though the picture was a bit unrefined.

I mentioned at that time that I had discovered two great ideas for puzzles and I introduced one of those ideas as Battleship Sudoku. Now, finally, I can unveil the other great idea, which is a very publishable variation of sudoku that truly earns the title "Paint By Sudoku". The methodology also lends itself nicely to what I will call "Digital Paint By Number" puzzles. You'll find examples of both new types in this entry (enjoy!):



First the meat. Start with the standard Paint By Number style where you shade cells to form a picture. Imagine adding numbers into the grid; the outside numbers now no longer refer to just the count of consecutive shaded cells, but rather the sum of consecutive shaded cells. Just as in digital battleships, the sizes of the sums and the numbers allow for a different kind of elimination when solving. I haven't worked a lot to perfect the style (far too busy with other things), but I wrote a reasonable example on the plane home for the holiday season and you can try it out here.


(Click here for solution).


Now, onto the pudding. Imagine a puzzle that uses this same concept, but takes a standard sudoku grid with the regular rules as its starting point. You could easily put any set of sums over an existing sudoku puzzle (that is solvable on its own) and reward the solvers for doing the sudoku by letting them color it in and get a picture. You could even just give numbers on the side to indicate "shade 1, 3, 4, 6 wherever they occur in this row" or something like that. Its so trivial a concept, I expect Conceptis or someone else to use it pretty soon (either from seeing this entry, or more likely not).

However, it would be awesome to combine the coloring of the picture with the solving of the sudoku itself, and I've tried that below with this digital paint-by-numbers/japanese sums style sudoku. They come in three difficulties, as indicated, and I think you'll enjoy the hidden theme that links the pictures. Keep in mind that there must be at least one blank square between any shaded regions. Having some experience with Killer Sudoku/Kakuro certainly won't hurt as dealing with the sums becomes very important.




(Click here[1], here[2], here[3] for solutions).