houzi's very hard puzzle

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houzi's very hard puzzle

Postby houzi » Thu Jun 16, 2005 7:40 am

Hi, I'm new here, hope I'm creating this message properly. I've been doing sudoku for several days, got my own techniques down, read up on other techniques, etc. Now I'm working on a "very hard" puzzle from www.dailysudoku.co.uk/sudoku (the May 28 one), and got stuck. None of the other techniques I read about (swordfish, x-wing, etc.) seem to help, and my methods also seem to be at a dead-end. So I'd like to find out what ideas I'm missing that will work on this one.

Here is where I've gotten:

.3. 2.. 781
..8 ... 3.4
.74 .3. 96.

Last time I got horribly stuck, a day later I found something obvious staring me in the face that I'd missed. Maybe that's the case here, but I don't see it. And I hope maybe there is some new technique I can learn.

I've narrowed down the possibilities for all the sites to the following (no pretty way to draw this I guess, so it's gonna be ugly -- here it is, one row at a time):

(5,6) 3 (5,6,9) 2 (4,5,9) (4,6) 7 8 1
(1,2,5,6) (2,5,6,9) 8 (5,7,9) (5,9) (1,6,7) 3 (2,5) 4
(1,2,5) 7 4 (5,8) 3 (1,8) 9 6 (2,5)
(3,4,5) (5,9) (3,5,9) 1 8 (2,4) 6 (2,5) 7
(4,5) 1 7 6 (2,4) 9 (2,5) 3 8
8 (2,6) (2,6) 3 7 5 1 4 9
(2,3,5) 4 1 (5,7) 6 (2,7) 8 9 (2,3,5)
7 (2,5,6) (2,3,5,6) (5,8,9) (2,5,9) (2,8) 4 1 (2,3,5,6)
9 8 (2,5,6) 4 1 3 (2,5) 7 (2,5,6)

Thanks for any help! My girlfriend is obsessed with these, she keeps printing out more and more to bring home and do together with me. She gets a huge feeling of satisfaction seeing the cascades of cells getting filled in.:D
Posts: 3
Joined: 15 June 2005

Postby Animator » Thu Jun 16, 2005 10:41 am

First: where can the number 6 go in column 1?

In what box is that? Right. Update your pencil marks.

Then look at row 2.
Posts: 469
Joined: 08 April 2005

Postby houzi » Thu Jun 16, 2005 1:24 pm

Thanks for that suggestion. After I posted my message I had come up with a more complicated way to take that same step -- noticing that in columns two and three, each of the lower two blocks needed to have a 6, even though I didn't know which block needed the 6 in which column, but it meant the top block needed its 6 to be in the first column. Then I did recognize the (1,6) pair in row 2, and things fell into place pretty quickly after that. But your way is more direct.

I've found that I tend to work "out" from particular cells, seeing what other things place restrictions on it -- basically using what I think people are calling "pencil marks" quite a lot. Usually it works well for me on some hard puzzles, but there are some times where I miss things which would be obvious if I worked "in" from the more global perspective.

I am not at all surprised by that fact, given my personality -- usually more thinking down in the finer microscopic details, rather than about the "grand picture".

Somebody could rig a psychological profiler program up to sudoku to tell you something about your personality based on the way you solve these things.:D E.g. do you eliminate candidates from cells you are focusing on, or instead do you eliminate some numbers from the set of cells you are not focusing on? Is the row half empty or half full?
Posts: 3
Joined: 15 June 2005

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