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11 February 2011 @ 12:15 am
Friday Puzzle #88 - Chaotic Calcu-doku  
Of the many complaints I hear about other sources of Calcu-doku puzzles (too easy/repetitive, too many clues/too many small cages, poor use of subtraction/division, ...), one frequent comment is that the default 1-N number sets used in the puzzle eventually get boring. Once you've learned all the basics for the most common sets like 1-5 and 1-6, there isn't much room for the puzzle to grow in difficulty without apparently needing to grow in size.

There are some simple fixes to this problem. First, there is no reason to use 1-N all the time. From introducing 0 as the first number, having different number sets, or even having completely unknown number sets, there is plenty of room to change the flavor of a puzzle with a unique set of numbers that isn't 1-N. One of my favorite special number sets, used in my book TomTom Puzzles, was the first 6 Fibonacci numbers where having two 1's in the set of possible numbers led to a lot of unusual possibilities compared to the standard puzzle.

But even then, the fact that a certain set of numbers must appear once in every row and column still constrains the puzzle a lot so that after getting a few numbers in, the values of the remaining cages are no longer as crucial compared to doing "sudoku-like" elimination steps. I've often wondered if using more open number sets would contain an interesting puzzle space, and some experimentation in this direction is the subject of this week's puzzles.

In Chaotic Calcu-doku, a range of numbers is defined with more possible members than cells in each row or column. While the normal rule that "no number repeats in a row/column" is maintained, there is not the same certainly that the last number must be X, because there will be more options for that last number. In the first 5x5 puzzle below, any number from 1-6 can be put into a cell, with an unknown quantity of each number used (there could be zero 6's, resulting in a standard calcu-doku, or there could be one, two, three, four, or even five 6's - you don't know). In the second 6x6 puzzle, exactly four instances of each number from 1-9 must appear, obeying all other rules. Both puzzles should offer quite different challenges than standard calcu-doku puzzles. Enjoy!

Rules: Enter (the indicated quantity of) numbers from the given range into the grid so that each cell contains a number and no number repeats in any row or column. The sum or product of the numbers in each cage must match the indicated value given in the upper-left corner of the cage.

MellowMelonMellowMelon [wordpress.com] on February 11th, 2011 07:48 am (UTC)
They really are a lot more fun this way... saying this as someone not too fond of Sudoku. The first one was fairly smooth. I'm not entirely sure how much I followed the intended path on the second one. Started with some involved logic about where the four 7s could go, and it didn't get too much simpler from there. I did finish it though. Given how many times I used every constraint, it seems like it would be extremely difficult to construct.
(Anonymous) on February 11th, 2011 01:14 pm (UTC)
easier break-in
I got in via the 15s and 25s: If the bottom right 25 can't have a 9, else it must also have an 8 or 7 on the bottom row, leaving the 15s with no options. After that, I made a lucky wrong deduction, so can't say how it would realistically have gone from there.


(Anonymous) on February 11th, 2011 05:39 pm (UTC)
Re: easier break-in
The top left "5" (as constrained by the other nearby 5) makes a very good break-in point. After that there are so few places you can put the remaining 1's in the puzzle that it cracks quite a bit open. (the 25's and 15's as mentioned and the 7-counting being other good early starts, of course). After that flurry of early stuff, I found simply keeping track of how many of everything I had used (I just wrote digits off to the side like a battleship fleet and crossed them off) resolved all the ambiguities in a nice smooth logical flow.

Very elegantly constructed puzzle with some nice "rhyming" structures.
motrismotris on February 11th, 2011 04:31 pm (UTC)
Standard calcu-doku are very easy to construct (easier than any other puzzle I've played with in terms of getting a theme or good solve). These were much more challenging, but fun to think about entries. In the second puzzle, I intended the two three-cell corners to be the break-ins, and then you can isolate the 4th instance of the most important digits. Going after the 7's is a reasonable alternative but not what I did.
(Anonymous) on February 11th, 2011 10:57 am (UTC)
Very nice.
I happen to use these number sets in Skyscraper puzzles frequently, so I was happy to see them in a Calcu-Doku. I particularly enjoy the 4x9 variation since the global number constraints allow some nice arguments which are not available in most other number sets.
motrismotris on February 11th, 2011 04:28 pm (UTC)
Right. I'd noticed your recent weekly "chaotic skyscraper" puzzle which is why I used this particular name.

I'd thought of the 4 each of 1-9 constraint two years ago in response to zundevil in one of the linked entries before I'd seen your puzzle (not sure if you originated the concept or saw it somewhere else too), but that number set in a 6x6 puzzle is a really nice variant on Latin Squares with new global constraints.