Paint By Sudoku!?!
Some puzzles are created by matters of happenstance. The first diagramless crossword was created when an editor took a puzzle to lunch but realized he had just the clues and not the grid. Instead of waiting to find the grid, the experiment of trying to solve with just the clues created the diagramless crossword. Well, in this case, a puzzle was created by a ridiculous combination of words in a book title.
A couple months ago, I discovered and was disappointed by the book "Paint by Sudoku." It is simply a collection of Paint By Number puzzles which were rebranded as "Paint by Sudoku". I made the comment that perhaps all puzzles could be rebranded sudoku; at the time though an idea started festering that maybe one could write a Paint By Sudoku puzzle that would do justice to the term.
I've always had in mind this trivial example of paint by sudoku:
However, this kind of format does not a hard puzzle make.
Yesterday was a slow work day and I started piecing together a larger idea for such a puzzle. My concept was to use a 16x16 grid and make a picture using 7 pixels in each square/row/column in the picture, leaving 9 spaces behind for each square/row/column for the digits 1-9. As an aside, I think taking existing 16x16 grids, blacking out the double-digit answer positions, and solving just the remaining 16x9 single-digit clues, is a very nice variant. I don't choose to make any of these on my own, as you can get the feel by just editing existing 16x16's, but it works a lot like a 16x16 just without any extra digits. In fact, I may choose, for all future 25x25's, to just go ahead and turn them into 3 different puzzles for 1-9, 10-19, and 20-25 and capture some of the complexity of the odd row-box and column-box interactions without needing 25 digits to give everyone a headache.
Anyway, my concept was to embed a picture in the grid and give just enough clues to make both the picture and sudoku solution unique. Challenge one - the huge challenge - was to actually make a picture that uses just 7 pixels in each square. I tried to make the "first" painting many artists do and I think it came out the way many first paintings do. I built in the use of color to make the picture-solving a little easier, and then went about making a valid grid fill and minimized set of clues that would completely solve both components of the puzzle.
This masterwork, which may in fact remain for the rest of time the only legitimate Paint By Sudoku ever, follows. I promise to return to saner puzzle exercises in the future, but for now I hope some people appreciate the attempt at making this puzzle.
The solution is posted on my puzzle page for those who would prefer to just see the concept in execution and not do the puzzle.
Rules: The following is a paint by sudoku puzzle. Each row/box/column will contain 7 picture elements (pixels) in one of 4 clued colors and the position of these picture elements is given by the paint by number clues as typical for those puzzles. It should be noted that, with the use of color, clues of different colors do not necessarily need to have a blank space between them in the same way that paint by number clues of the same color must have at least one blank space between them. The remaining 9 cells in each row/box/column (the "blanks" in the picture) will contain the number 1-9 just once. Some of these numbers are already given in the puzzle (yes, I even found a way to do that symmetrically), and these given numbers can be assumed to not contain colored pixels. 4 colors (orange/green/brown/gray) are used in the puzzle so make sure your print-out shows these clearly. The puzzle can likely also be solved with just all-black squares but this will be much harder (I did not playtest such a variation, but the colored version is a legitimate puzzle [edit: I should make it clearer that when I talk about an all-black version, I would have to change the clues to be appropriate for the more standard PBN puzzle style. Taking a black and white printout of this puzzle and trying to solve in just black would be a big challenge as some clues necessarily overlap with color borders]).
A couple months ago, I discovered and was disappointed by the book "Paint by Sudoku." It is simply a collection of Paint By Number puzzles which were rebranded as "Paint by Sudoku". I made the comment that perhaps all puzzles could be rebranded sudoku; at the time though an idea started festering that maybe one could write a Paint By Sudoku puzzle that would do justice to the term.
I've always had in mind this trivial example of paint by sudoku:
However, this kind of format does not a hard puzzle make.
Yesterday was a slow work day and I started piecing together a larger idea for such a puzzle. My concept was to use a 16x16 grid and make a picture using 7 pixels in each square/row/column in the picture, leaving 9 spaces behind for each square/row/column for the digits 1-9. As an aside, I think taking existing 16x16 grids, blacking out the double-digit answer positions, and solving just the remaining 16x9 single-digit clues, is a very nice variant. I don't choose to make any of these on my own, as you can get the feel by just editing existing 16x16's, but it works a lot like a 16x16 just without any extra digits. In fact, I may choose, for all future 25x25's, to just go ahead and turn them into 3 different puzzles for 1-9, 10-19, and 20-25 and capture some of the complexity of the odd row-box and column-box interactions without needing 25 digits to give everyone a headache.
Anyway, my concept was to embed a picture in the grid and give just enough clues to make both the picture and sudoku solution unique. Challenge one - the huge challenge - was to actually make a picture that uses just 7 pixels in each square. I tried to make the "first" painting many artists do and I think it came out the way many first paintings do. I built in the use of color to make the picture-solving a little easier, and then went about making a valid grid fill and minimized set of clues that would completely solve both components of the puzzle.
This masterwork, which may in fact remain for the rest of time the only legitimate Paint By Sudoku ever, follows. I promise to return to saner puzzle exercises in the future, but for now I hope some people appreciate the attempt at making this puzzle.
The solution is posted on my puzzle page for those who would prefer to just see the concept in execution and not do the puzzle.
Rules: The following is a paint by sudoku puzzle. Each row/box/column will contain 7 picture elements (pixels) in one of 4 clued colors and the position of these picture elements is given by the paint by number clues as typical for those puzzles. It should be noted that, with the use of color, clues of different colors do not necessarily need to have a blank space between them in the same way that paint by number clues of the same color must have at least one blank space between them. The remaining 9 cells in each row/box/column (the "blanks" in the picture) will contain the number 1-9 just once. Some of these numbers are already given in the puzzle (yes, I even found a way to do that symmetrically), and these given numbers can be assumed to not contain colored pixels. 4 colors (orange/green/brown/gray) are used in the puzzle so make sure your print-out shows these clearly. The puzzle can likely also be solved with just all-black squares but this will be much harder (I did not playtest such a variation, but the colored version is a legitimate puzzle [edit: I should make it clearer that when I talk about an all-black version, I would have to change the clues to be appropriate for the more standard PBN puzzle style. Taking a black and white printout of this puzzle and trying to solve in just black would be a big challenge as some clues necessarily overlap with color borders]).