## "Only couples" solving strategy?

Advanced methods and approaches for solving Sudoku puzzles

### "Only couples" solving strategy?

Hello everyone!

I'm pretty new to the world of sudokus, solved my first one a week ago or so.. I read some basic stuff on the net, and then I more or less have been using my own method and it seems it allows me to solve every sudoku so far without trouble.
Basically, instead of noting every possiblity for numbers in each 3x3 square, I note them only if there are just exactly 2 possiblities, and using an array of logical deducing techniques after that (but nothing like "hidden triplets" or whatever, since I never note all the options for numbers in a square), I've always managed to solve even difficult sudokus.

A bit lower I've detailed my strategy and techniques used step by step for solving "AI Escargot", about which I had found an article presenting it as particularly difficult. It took me about an hour at a peaceful rythm with this method, and I really haven't practiced much so far..

Mostly, I wanted to know if there are sudokus that I won't be able to solve at all that way, and that will really force me to note all options? (If so can you please give me one!).
Or is it faster to use complete possibilities notation and advanced techniques (all these X-wing and stuff that I haven't looked much into so far)?

Thanks!

AI escargot :
http://img135.imageshack.us/my.php?image=aiescargotgj0.jpg

step 1: I make a quick "balayage " not sure of the english term, swapping? and get this :
http://img152.imageshack.us/my.php?image=step1ub7.jpg

step2 :
the central square has a 5 on the bottom, so I can place a couple of 5 at the top of middle right square. In that square the top 2 open sqaures have a 3 and a 5, so the bottom 3 have 678. That allows me to place a couple of 8 in the central quare and the middle left square, as well as a couple of 6 in the central square. The 3 square on rank 5 have a 68 and 2, so I can place a couple of 2 (and deduce where the 8 is, he can only be on r5c6).

http://img135.imageshack.us/my.php?image=step2gf9.jpg

step 3 :
just a bit more "balayage"
http://img152.imageshack.us/my.php?image=step3st2.jpg

step4 :
same thing
http://img340.imageshack.us/my.php?image=step4xk4.jpg

step5 :
In the bottom central square I have a 2 a 4 and a 5, I can place a couple of 2, and the presence of the 5 allows me to place a 5 in the bottom left square.
http://img152.imageshack.us/my.php?image=step5vs4.jpg

step 6 :
I can place a couple of 9 in the bottom left square. This leaves only 1 and 2 on rank 9 giving me 2 other couples in the bottom right square. So knowing there is a 2 in the rank 9 right square, this gives me a couple of 2 in the bottom left square (actually I could even already place the 2 exactly, since I have a 2 in the rank 8 central square, but I hadn t noticed).
The rank 8 has 245 in the center, and a 8 on the right. So r1c1 has either a 3 or a 6. there is a 3 on c1, so it s a 6. This gives a couple of 3 in the bottom right square. I also mistakenly placed a couple of 5 in the central bottom square (or I don't see how I deducted that? but I think it's a mistake) but I didn't use that information later on at all.
http://img293.imageshack.us/my.php?image=step6hp7.jpg

step7 :
I place the 2 and the 3 in the bottom left square, giving me a few more couples.
Rank 8 has a 2, and it s not in the middle right square who has a 2 already. So that gives me the 2 in the top right square.
Or sorry, simpler, just "balayage" : the 2 in the middle right sqaure gives me the 2 and 1 in the bottom right, which gives me a couple of 1 and the 2 in the top right.
http://img293.imageshack.us/my.php?image=step7sl9.jpg

step8 :
rank 4, I know the 3 and 5 are on the right, so the 6 8 and 9 are on the left. this gives me a couple of 6, from which I deduce where the 9 is.
http://img216.imageshack.us/my.php?image=step8qn4.jpg

step9 :
more obvious balayage, fill in the 1 and 2 in middle left and the 1 in top left.
http://img293.imageshack.us/my.php?image=step9th8.jpg

step10 :
I get the 1 in the top right, wich gives me the 1 in the centre top, and also the 7 there. I can place couples of 9 in the central square and the top left square.
http://img83.imageshack.us/my.php?image=step10uq2.jpg

step11 :
I have the 9 in the centre top, which allows me to completely fill the top right square.
http://img83.imageshack.us/my.php?image=step11zl4.jpg

step12 :
I can also fill in the middle and bottom left squares, and I also place a 7 in the top right.
http://img253.imageshack.us/my.php?image=step12xw3.jpg

step13 :
I can place the 7 and a couple of 6 and 8 in the middle right square.
On column 7, the 6 can't be on r3c7 or on r8c7 since both ranks have a 6 already. r4c7 has a 3 or 5, so the 6 is on r7c7. I place it. "Hard" part is over.
http://img253.imageshack.us/my.php?image=step13xt2.jpg

step14 :
I place the 5 in bottom right, a couple of 3 in middle top, a couple of 6 in top right. This couple of 6 gives alows me to place the 6 and the 8 in the middle right.
http://img83.imageshack.us/my.php?image=step14nw6.jpg

step 15 : the couple of 3 in middle top give me the 3 in central square, and everything just fills up, the 9 and 5 in centre square, a couple of 5 in middle top, the 5 in top right..
http://img253.imageshack.us/my.php?image=step15ou9.jpg

step16 : more filling : the 3 and 5 in middle right, the 3 and 8 in bottom right, the 8 in top right, the 3 on r3c4, therefore the 6 on r1c4.. etc.. puzzle over.
http://img253.imageshack.us/my.php?image=step16mx7.jpg

Edit : the img balise is not working? :/
P.S : I think there is only one other "technique" that I've had to use so far besides the ones shown in this example. It's for instance if I get 2 couples 2&4 in c1r4 and c1r5 and 2 couples 2 & 8 in c5r4 and c6r5, then I know the 2 is in rank 6 in the middle right box.
Cashane

Posts: 3
Joined: 01 November 2008

I got completely stuck on this one :
http://img45.imageshack.us/my.php?image=stuckue4.jpg
going deep into considerations to find that C6R8 was either a 5 or a 6, that if C8R8 was a 8 then C8R2 was a 1, etc... but geting no real progress.
While a complete filling would have immediately given me the 2 on C2R7 which was quite hard to notice with my partial filling .
Cashane

Posts: 3
Joined: 01 November 2008

### Re: "Only couples" solving strategy?

The puzzle you show is a very simple one (and so is your second puzzle, needing only pairs). This is AI Escargot (http://forum.enjoysudoku.com/viewtopic.php?p=37328#p37328)
Code: Select all
`+-------+-------+-------+| 1 . . | . . 7 | . 9 . || . 3 . | . 2 . | . . 8 || . . 9 | 6 . . | 5 . . |+-------+-------+-------+| . . 5 | 3 . . | 9 . . || . 1 . | . 8 . | . . 2 || 6 . . | . . 4 | . . . |+-------+-------+-------+| 3 . . | . . . | . 1 . || . 4 . | . . . | . . 7 || . . 7 | . . . | 3 . . |+-------+-------+-------+`

And many other puzzles are looked at being much harder now. See this thread: http://forum.enjoysudoku.com/viewtopic.php?t=4212&start=0&postdays=0&postorder=asc&highlight=

If you want help for the second puzzle, post it on the "Help with particular puzzles forum": http://forum.enjoysudoku.com/posting.php?mode=newtopic&f=17
eleven

Posts: 1846
Joined: 10 February 2008

Oh my..