Sunday, February 17, 2008

sudoku strategies

First, since it comes from a shortening (the Japanese people love shortening words - it's like some sort of abbr. obsession) of the phrase "数字は独身に限る" into "数独", can we please use the correct romanization of "sudoku"? It's not that hard, and yes, correct spelling and grammar do improve readability. Also, using non-convoluted sentence structure and refraining from using long words. See "Consequences of erudite vernacular utilized irrespective of necessity: problems with using long words needlessly".

Now that Tom Snyder is putting up videos of both his solving and discussion of various sudoku, the issue of sudoku strategies has resurfaced to my attention. For a while, I had been plugging away at the sudoku in various books. But after watching some of Tom's videos, I seem to be doing slightly better. I'm not sure that I got any really useful advice from the videos, since they are not geared towards the difficulty level I am working at, but I think it has allowed me to make more use of geometry that I hadn't really thought of before.

I do find it amusing that there are all these videos and websites about sudoku strategies, that are really sort-of brute-force:
here are a list of strategies that may be used under very specific and complicated circumstances, when in doubt, just cycle through them until you find one that works.

However, I think Tom has hit the nail on the head by outlining some key principles to "good" sudoku solving:

1. each number written down provides information that may lead to the next number:
- that digit can no longer be present in that row, box, or column
- there is less space for the remaining digits in that row, box, or column

2. fast notation can help immensely (this seems to be quite useful for me)
- marking cells in a box when a single digit can only be present in two or three cells doesn't help immediately, but it can under the following cases:
- filling in the same digit elsewhere narrows down the choices
- noting that another digit or two must be in the same set of cells "traps" those digits to those cells. often this allows one to bruteforce the remaining digits in the cell by comparing across rows or columns

3. flexibility is key
- switching from strategy to strategy speeds up solving immensely, but requires that one be able to recognize a viable angle of attack that may yield good results

I think my math team training is fairly useful for 3, as time constraints on problems forces the development of rapid analysis of what strategies to pursue next and when brute force should be used to open up new angles of attack.

Anyway, one of these days, I will probably develop a better discussion of sudoku strategies in my editorials section. I think it could be useful to formalize strategies (and not just for sudoku; I seem to have improved a lot with killer, wacky, and diagonal variations recently, too.)

Not that I think I will ever be good enough to make the US team or anything, but I would like to think I'm improving overall. After last year's debacle with the US puzzle championship, I'm hoping for a stronger showing this year. Don't forget to register! Techers represent! (Wei-hwa and Tom are both caltech alums)



Anonymous cathy said...

I started Sudoku in Jauary 2005, when I could only find it in the London Times and print out a pussle a day. It is just applied logic. I go through it the first few times in numerical order and then, maybe, have to guess. But only the 50-50 ones at first. Since I also play chess, I can see moves a few ahead of time and know if my guess is correct or not. The nine by nine Sudoku really is not that difficult for me. The 16 x16 (add A-F) is more of a challenge, if for no other reason than it takes longer to go through it in order. I was kind of sad to see it showing up here everywhere.

February 22, 2008 at 12:12 PM  

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