## question about tough sample sudoku in "solving sudoku&q

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r.e.s wrote:The "therefore ..." is yours, not bennys', which is what I was commenting about; i.e., you said "well done" immediately after quoting this:
bennys wrote:A can't be 4 [...] So F is 4 and then you get that E is 8 [...]
that is, he was concluding that r7c1=8 (rather than r7c1=4).
Sorry, I made a mistake when I was trying to lift F to row 7 in the grid, ended up messing up the positions of E & F altogether.
Jeff

Posts: 708
Joined: 01 August 2005

### Re: Thanks Jeff

Jeff wrote:
bennys wrote:I couldn't see it (maybe i looked at the wrong place?)
In this case, do you want me to list my chains. Not to speak for bennys, of course, but I would like to see them (if it's not too much trouble). I think the chains you find are often very instructive.

BTW, you may like to know that the latest version of SS at http://www.angusj.com/sudoku/ now saves images directly to png files -- typically less than 10KB per image, it seems. I mention this because some of the images you've posted recently seem really obese. (I'm a slowpoke still using dialup, so it's very noticable when I read a page that has four images totalling about 260KB!)
r.e.s.

Posts: 337
Joined: 31 August 2005

Hi r.e.s., Thanks for the advice on file size, but angus' images don't show any links and labels.

Here are the chains:

Chain 1: Starting [r7c9]-4-[r7c1]=4=[r1c1]-4-[r2c2]=4=[r2c9]-4-[r7c9] => r7c9<>4
Chain 2: Starting [r7c1]=4=[r1c1]=3=[r1c5]=2=[r5c5]-2-[r4c4]=2=[r7c4]-2-[r7c1] => r7c1<>2
Chain 3: Starting [r7c1]=4=[r1c1]=3=[r3c1]-3-[r3c6]-2-[r3c9]=2=[r2c9]=4=[r9c9]=1=[r9c8]=8=[r7c8]-8-[r7c1] => r7c1<>8
Chain 4: Starting [r7c8]-4-[r7c1]=4=[r1c1]=3=[r3c1]-3-[r3c6]-2-[r3c9]=2=[r2c9]=4=[r9c9]=1=[r9c8]=8=[r7c8] => r7c8<>4

Where '=x=' is a conjugate link and '-x-' is an unconditional link.

Chain 3 and 4 are pretty long. You may be able to find shorter ones. I hope the chain notation above is self-explanatory. Let me know if you need any proofs, though I don't think so.
Jeff

Posts: 708
Joined: 01 August 2005

Jeff,

It's interesting to compare your four chains to the eleven that rubylips' online program (at http://act365.com/sudoku/) uses to solve this puzzle. Here are the eleven (in notation similar to yours), omitting the explanations of each chain and the various cells that are solved by simple moves between chains:
(7,1)-4-(1,1)~4~(1,8)-4-(2,9)~4~(7,9) => (7,9)<>4.
(3,2)-8-(3,1)-3-(1,1)-4-(7,1)~4~(7,8)~8~(7,2) => (7,2)<>8.
(5,9)~3~(5,5)-2-(1,5)-2-(3,6)~2~(8,6)-2-(7,4)-3-(7,9) => (5,9)<>3.
(4,6)~8~(4,7)-8-(5,7)-3-(5,5)~3~(6,6) and (4,6)-8-(6,6) => (6,6)<>3.
(6,4)-3-(6,9)-3-(7,9)-3-(7,4) => (9,4)<>3.
(3,2)~2~(3,6)-2-(8,6)-2-(7,4)-2-(7,2) => (3,2)<>2.
(7,2)-2-(7,4)-2-(4,4)-2-(4,1)~2~(8,1) => (8,1)<>2.
(1,2)-2-(1,5)-2-(5,5)-2-(4,4)-2-(7,4)-2-(7,2) => (2,2<>2.
(1,2)-5-(3,2)-8-(3,1)-3-(3,6)-2-(1,5) and (1,2)-2-(1,5) => (1,5)=2.
Rubylips' solver is the only one I know of that can solve this puzzle by "pattern searching" for nothing more complex than forcing chains (e.g. not the Susser's "tabling" method).

PS: I mentioned the png-saving ability of Simple Sudoku in the hope that it would encourage the use of pngs, which tend to be highly efficient for such simple pictures. As you probably know, the key for compression when modifying them is to use no more than 8-bit color depth (256 colors) -- the images I was griping about use more than 20000 colors.

PPS: If you have access to Excel, you can simply paste the image from Simple Sudoku into Excel, draw the desired lines, arrows, labels, etc, and then Save as Web Page, with the setting Tools/Compress Pics/Web-Screen -- the result is a png file typically <10KB (instead of >50KB).
r.e.s.

Posts: 337
Joined: 31 August 2005

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