Friday Puzzle #15 - (Not So?) Grate Calcudoku
When writing a lot of puzzles, there are several ways to get some that are unexpectedly hard. Using a computer to strictly tell you there is 1 answer (without checking a solution path yourself) is a good way to get some really bad outliers. I'll almost never encounter this problem in my designs, but I encounter it all the time with work by other designers. Trying to make very minimal designs, or artistic designs with very specific constraints, is another way to get a puzzle that is too hard. In some designs, you might have a hard time just filling a valid grid with digits and so considerations of difficulty don't come into mind until you reach an answer and experiment with how to clue a puzzle to reach it. Finally, you can run into non-uniqueness at the end of a construction, requiring some digit tweaking which can compromise intended work-ins and possibly making the puzzle much easier or much harder than expected. The puzzle here is primarily a result of the last case.
In my forthcoming book of hand-crafted calcudoku puzzles there will be an 8x8 grid called "A Grate Puzzle" (yes, I'm shameless when it comes to titling sometimes). Anyway, the puzzle below was a first attempt to use the same theme (shape of cages plus geometric isolation of each of the four operations to one quadrant) but simply is "too hard to be published" in my opinion and got a full rewrite for the book. However, one thing I realize is that I have very little sense of what is or is not hard for my (blog) audience. So, to those who would take up this gauntlet, here is a puzzle that I could eventually solve in around twenty minutes (I wasn't timing but this seems about right), that has 2 or 3 solid chunks of progress that follow much longer periods of staring.
Note: As always, although it is brought up each and every time by solvers of those other computer-generated puzzles, multi-cell subtraction and division starts with the largest value with all digits subtracted/divided from it. A cage with 1, 4, 2 and - is 4-2-1=1 or the same digits with / is 4/2/1=2.