Wrap-up: The Making Of This new puzzle type needs a name
This is not a solution to the puzzle, but provides notes from its poser. This type of answer has been approved by the community.
Caution: This post may contain spoilers.
In the PSE calendar system, 2019 was pretty much the Year of the Nonogram. After only a handful of nonogram-based puzzles in previous years, 2019 saw a whopping 38 of them published - more than twice the pre-2019 total:
Figure 1: Graph showing number of puzzles tagged 'nonogram', per year.
New to PSE myself in 2019, I enjoyed solving others' nonogram puzzles so much that it made me want to create one myself. However, while planning my first nonogram a tempting thought crossed my mind: Would it be possible to create a nonogram based on a sudoku, where certain numbers within the solved sudoku could somehow be indicated as forming the foundation of the nonogram?
This thought just would not go away - I had to find out...
The very first question to ask myself was: What image would be appropriate for the solution of such a nonogram? I considered any number of possibilities - something artsy, something eye-catchingly geometric, something containing a pun... but none of them felt like it made much sense as to why they should be the final outcome of a hybrid puzzle in particular. In the end I decided that this hybrid puzzle needed a name - so how about coming up with a name for it and coding that in the end solution? Now that might just work...
I settled on the name 'Nonodoku' as a hybrid of 'nonogram' and 'sudoku', preferring this to 'sudogram' as it retained more linguistic meaning, since the word 'sudoku' is actually an abbreviation of the Japanese suuji wa dokushin ni kagiru, meaning 'the numbers (or digits) must remain single' (Source: dictionary.com). Plus 'sudogram' sounded more like somebody who turns up at your door pretending to be a stripper.
So how to conceal the word 'Nonodoku' in the puzzle? I considered several options dependent on classic encoding tricks like A1Z26, Morse code, some kind of rebus, etc. But in the end I decided to go with visual impact and create a puzzle where the solver would know precisely when they had solved it because the name would be spelled out right in front of their eyes!
I then set about trying to make the nonogram work with a standard 9x9 sudoku - and quickly ran into some problems:
- How to style the letters? With 8 letters to squeeze into the grid - whilst making each a similar size, for aesthetic reasons - each letter would really have to fit into a 3x3 area of the sudoku grid. However, not all letters lend themselves all that nicely to being depicted (and yet still readable) in this way. The glyph set would end up having to look something like this:
Figure 2: Potential set of glyphs to fit a 3x3 sudoku grid.
Ultimately, this led to a larger problem...
- The uniqueness constraints of sudoku puzzles: The key feature of a sudoku is that in any given row or column each number can only appear once (hence the name's meaning in Japanese, recall). Looking at the suggested glyph set above, what becomes immediately apparent is that many rows and columns would require more than one '1' or '2' to feature in them (e.g. the second row would need to be encoded
1 2 2 1 in the nonogram - impossible with only one '1' and one '2' in its sudoku solution row). In fact, no matter how I attempted to arrange them, and yet still retain a semblance of order to enable the word to be spelled out at the end, it just would not sit right.
Since the 9x9 sudoku was putting up too much of a fight, I asked myself whether I could expand the grid to 16x16 and still make this puzzle work. I figured it was likely to be more successful, although of course the larger grid brought with it an additional complication...
- Filling the space: At this point I was still set on spelling out the name in order, but now with 16 4x4 squares to use for the letter glyphs it felt wasteful to use only 8 of them. So I contemplated several 16-letter-or-so sentences I could spell out in full, something along the lines of "THIS IS A NONODOKU":
Figure 3: Potential set of glyphs to fit a 4x4 sudoku grid with a sentence.
But still I was coming up against the issues caused by uniqueness, needing too many '1' clues for the nonogram. And so many different letters required the use of single squares in places that spelling out a whole sentence seemed to be becoming more and more impractical all the time. Eventually I decided it would be better to make each required letter in the sentence appear just once in the grid and fill the remaining 4x4 squares with shaded nonogram cells, since when these bordered other 4x4 squares containing otherwise lone cells (like on any side of a 4x4 'O'), these lone cells would immediately become part of a much longer run of shaded squares, permitting the use of higher far-less-used numbers from the sudoku instead of the useful but popular '1's. Additionally, this would then require at least one number in each 4x4 letter-box to act as an index marking its position in the target sentence.
What followed next was a long series of manual trial-and-error, attempting to find a layout which permitted me to spell out the ten T, H, I, S, A, N, D, O, K and U glyphs while making sure no row or column of the nonogram required the same clue number more than once. I will spare you the full details of this (in a nutshell: lots of copy-pasting, counting shaded cells in rows and columns, and checking the nonogram clues did not contain duplicates - they almost always did...), but finally I hit upon a formation that worked - and which went on to become the final image hidden in the puzzle - albeit requiring the use of a 3x3 'period' in place of one 4x4 shaded square to prevent the 13th and 16th columns requiring two '4' clues (see the top right corner of the final puzzle diagram). However, this brought another issue to resolve...
- How to use the same number in the sudoku puzzle for more than one purpose? It was obvious from the nonogram clues that in some 4x4 squares the same number was going to need to be used as both a row clue and a column clue:
Figure 4: Final nonogram enumeration and required letter indices (listed from top-left corner of their respective 4x4 boxes).
Take the letter T in the third 4x4 box on the top row, for example. In this particular box, not only does every row require a '1' clue, but every column requires a '1' clue and the number '1' in this particular box would also need to act as an index for the first letter in the sentence "THIS IS A NONODOKU." Three uses for the same number! A little thought meant that this obstacle could be overcome by using two different primary colours to indicate whether a number was needed as a row clue or a column clue (I settled on the alliterative 'red for rows', with blue for columns, since blue showed up better than yellow), permitting the use of the two primary colours' common secondary colour (in this case, purple) to indicate numbers required in both its row and its column's clues. Then to avoid any further colour-related complications or confusion, I opted to augment the numbers required for indexing with a symbol - in this case, a circle. Thus a purple '1' in a circle indicated that the '1' was required as a row clue, a column clue, and as the index for that letter in the final name resolution.
Now that colour featured so prominently in the puzzle there was one final aesthetic consideration to take into account:
- Making the puzzle solvable for people with colour-blindness: In one of my previous puzzles I had been contacted by a puzzler after publishing to ask if the puzzle - which was entirely dependent on the use of colour - was available in an annotated form, since he had trouble telling apart the colours I had chosen so carefully for aesthetic reasons, but completely oblivious to the needs of those who might not be able to differentiate between them. This struck me pretty hard, as I have tended to be more aware of this need in presentations and reports throughout my life, as my own brother has a particularly severe form of colour-blindness. To this end, I ensured that I would make a second version of the image available, with all red areas marked by an asterisk in the bottom left corner, all blue areas marked by an asterisk in the top right corner, and all purple areas marked with an asterisk in both.
Finally (and briefly), the last two main obstacles of the creation process:
How to fit all the required nonogram clue numbers into the sudoku grid in a valid formation? Quite simply, more trial and error! A pretty long and painful process which I shan't chart in full here, but involved lots of swaps and double-checking all numbers 'worked'. Using conditional formatting in Excel to highlight all cells containing the same number was useful for double-checking the sea of numbers met all of sudoku's uniqueness constraints.
Removing enough numbers from the completed sudoku grid to make sure the sudoku was solvable but not trivial: Generally, this involved removing one of each number from each row and column, then seeing which other numbers could be deduced if removed, and continuing this process until roughly half of the numbers remained and no individual 4x4 box was almost completely full.
The final puzzle was then ready!
Figure 5: The final puzzle, complete with aids for colour-blindness.
The entire puzzle was prepared and created in Microsoft Excel. To pick out one helpful tip here for creating puzzles (and solutions) in Excel, which I wish more people knew and used: It is possible to remove the background gridlines from your finished grid, thereby ensuring only the content you want to show is actually displayed.
Just navigate to the View tab, and in the 'Show' sub-menu uncheck the Gridlines checkbox. Voila! A lovely neat-looking piece of work!
Figure 6: In Excel 2016, toggle gridlines on and off using the Gridlines checkbox in the Show sub-menu of the View tab.
The puzzle was solved six-and-a-half hours after publish by @JoeyDionne without the need for any hints to be provided or any edits to be made. This was especially satisfying! Plus it was fantastic to watch the community discussing the puzzle in comments and in The Sphinx's Lair chatroom and providing feedback with the upvote button (and one via the downvote button without ever explaining why - but hey, that's the way things go). At the time of writing (at +74) it is the third-highest ranked grid-deduction question on the site and the second-highest ranked in both sudoku and reverse-puzzling - truly I never anticipated it would be this well-received and I would like to thank all the puzzlers who interacted with it, attempted it, and appreciated it.
Plus the process gave me plenty of ideas for other ways to create hybrid sudoku and grid-deduction puzzles, thereby spawning the "This new puzzle type needs a name" series! I hope you've enjoyed discovering and solving these puzzles as much as I've loved making them - they're a lot of work, and a lot of trial and error, but boy is it worth it at the end!
Thanks for reading :)