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19 November 2009 @ 11:52 pm
Friday Puzzle #24 - Multi-Operation Calcu-doku  
Last week I posted a Calcu-doku variant that I thought was pretty cool. The sudden motivation to explore this concept, which I'd been holding onto for awhile, was the discovery of a hilarious error with some official KENKEN(R) puzzles that couldn't even be corrected right. While I loved the text of my entry, in the rush to make a puzzle that fit a #23 theme I cut some corners and added in an extra constraint to the first 23-only grid I found to make it solvable; to restate your comments on this "fix" succinctly: the shaded cells were not appreciated.

Well, the very first Number Place puzzle had four circled cells that clued a small subset of numbers for those squares. We can agree that the proper form of a sudoku does not have circled cells just as the proper form of these calcu-doku should not have any extra constraints in shaded cells even if the first attempt at such a puzzle had this weakness. Since I really think Multi-Operation Calcu-doku offers some good challenges, I've tried to write some "proper" puzzles this week to reintroduce the concept. While "Parquet" should be rather approachable, the larger "Double Trouble" puzzle has some really fun deductions necessary to solve it.

18 = ((1+5)*3) or 1+5 ->6 *3-> 18

Rules: In each n x n grid, fill each cell with a number from 1 to n so that each number appears exactly once in each row and column. Each grid also contains several rectangular cages whose cells are labeled with either a number or a mathematical operation. Proceeding from the cell with the numerical value and going through the connected cells in order, performing operations as they are encountered, the digits placed inside the cells will evaluate to the indicated value (as in the example cage above).

Mike Selinkerselinker on November 20th, 2009 09:51 am (UTC)
You know what makes that bug even more hilarious? The page describes it affecting seven puzzles, and the page shows eight. So the bad arithmetic bug reaches out and affects its own description.
motrismotris on November 20th, 2009 04:38 pm (UTC)
Yes - the "seven" puzzles being wrong is the particular secondary error that seals the story for me. Makes you wonder how "limited" the wireless carriers with problems are.
Mike Selinkerselinker on November 20th, 2009 05:22 pm (UTC)
I'm gonna have to call that "Genius Level."
(Anonymous) on November 20th, 2009 03:31 pm (UTC)
Both puzzles were pretty straightforward, but enjoyable and had nice structural conceits. I think that as with killer sudoku, the logic will get far more interesting and involved with longer chains that don't follow the rows and columns. Even in the larger puzzle there were a lot of tight restrictions right from the start that led to a pretty clear solving path.
standupphilosopherstandupcanada on November 20th, 2009 03:44 pm (UTC)
6:30 for the pair which isn't remarkable either way, however the fact that 4 minutes + of it was for the first (completely missed the easier breakins whereas in #2 I looked in the right spot first and it was just a case of filling in numbers all the way through) got me thinking about the sudoku editor posts. Assuming you had 1000 editors (or 100 or a dozen) rating the puzzles based on the deviation of the solving times could certainly guide you to which ones would be the best for use in competition. I'd be interested in seeing which of the required solving strategies leads to the biggest variations - and by interested I mean can someone else plug in all the data and let me know how it turns out.
motrismotris on November 20th, 2009 04:48 pm (UTC)
The challenge is not knowing which solving strategies necessarily lead to the biggest variations, but stratifying a few of the well-known solving strategies into different classes based on the "obviousness" of spotting a certain step. Naked singles (only one choice of number left for a cell) are my favorite "basic" strategy to consider in this kind of discussion and the first place where incorrectly rated puzzles pop up. Its obvious to a computer when a move is a naked single and it does them immediately. To a human solver, who does not see all the candidates immediately, there will be a much greater variation in when these get spotted and candidate-based versus candidate-free solvers will also vary in their times for this kind of step compared to puzzles that resolve with just hidden singles/pairs.
jdyer on November 20th, 2009 07:27 pm (UTC)
I'm still feeling a bit funny with the notation. I think that's not so much that the value it equals is at the beginning (I can just think of it as 21 = etc....) but that when following the trail vertically, visually the operation displays after the number, kind of like postfix notation.

I'm not sure how to fix this other than putting the operations on the edges somehow, but I can't think of any elegant way of drawing that.
motrismotris on November 20th, 2009 07:29 pm (UTC)
I also had the operation on edge idea, but not yet a simple template to use to implement it. I do think you've hit on a problem with the format with upper-left operations when reading to the left or up.
thesubro on November 20th, 2009 10:32 pm (UTC)
Notation Schmotation
The simple fact is that these are novel variations of sudoku and KenKen and offer the opportunity for SOME decent puzzlemaking and solving. No notation here will be perfect or easy (how about a, b, c, d, ... on the corners so the order is clear; how about inkblot resultant numbers in fuzzy font in the background and/or the operands on the lines between the squares). It doesnt really matter. The solver will get it eventually.

I like the variation better than simple KenKen and completely addition KenKen Jr. (otherwise known as Killer Sudoku). I fear that the lack of constraints without gimmicky steps (circled 2s,3s; or side by side multiples of 7 and/or 5) will tax the creators to only allow for so many solvable and yet enjoyable puzzles of variety. Time (and Tom) will tell.

Thanks for the puzzles.

motrismotris on November 20th, 2009 11:32 pm (UTC)
Re: Notation Schmotation
Well, the crazy eventual point (since I don't think KenKen with operations is interesting or very deep) is something akin to operationless multioperation puzzles. But maybe this might be too much. Something imbetween would be to not give the operations, but to limit a particular puzzle to a subset of the space. So in this grid you are making 25 with x and + in some order, with x and - in this other puzzle. Cage size (my average was too high on #23, maybe too low here) would matter. Cage bending is also critical and I chose to not do it here for my "cutesy" double trouble theme but there should be some space to explore.

Another notation (for another variant of this puzzle) could be something like [25,+,*] marked as usual in just the topleft-most cell of a cage. The clue tells you that the three cells, in some order, equal 25 using addition once and multiplication once. That could free up the approach of thinking without an ordering constraint while making the presentation cleaner.

I'd frankly, in this case, almost want random computer generation for awhile to see the standard solving space before varying things too much. There are some valid riffs to try out, and then some convergence to what feels like the right kind of solve, with neither trivial nor impossible steps to see the finish.