Understanding Swordfish

AndyT · Posted: Fri Jan 27, 2006 4:20 am Post subject: Understanding Swordfish

Guys, I'd appreciate some help understanding the Swordfish technique. I've seen it discussed in a number of places, not least in Angus' excellent program. In fact, that's a great place to start because I don't even follow his explanation in the help file. The demo puzzle looks like this:

However, the explanation:

md68 · Posted: Fri Jan 27, 2006 4:34 am Post subject:

I have problems too to understand it but maybe this explanation helps you out:

http://www.sudokuoftheday.com/pages/techniques-9.php

If you have figured it out then let me know Smile

angusj · Site Admin

AndyT · Posted: Mon Jan 30, 2006 9:08 am Post subject:

Thanks for taking the time, Angus but, even having read the verbose version, I'm baffled. Worse I'm not doing too much better with Colours. This came up as a hint:

Now I have no idea where the colour mapping started but if you end up in the bottom left box, what's the problem? R5C2 and R9C2 and R8C5 are blue so force R8C2 to be green. So that makes R8C1 blue and R7C1 green. So 2 greens in column 1. How does this display lead to the conclusion that blue is wrong for 5s? It also appears sensitive to the starting cell.

angusj · Site Admin

AndyT · Posted: Mon Jan 30, 2006 10:42 am Post subject:

But if I go from R7C5 left to R7C2, that cell gets coloured green.

If I go down from R4C1 green, that makes R7C1 blue and the cell beneath it green thus column 1 has 2 green cells and green is false.

I appear to be able to make either colour false.

angusj · Site Admin

AndyT · Posted: Mon Jan 30, 2006 11:09 am Post subject:

Yes. Why are all four 5s in the bottom left box not candidates?

angusj · Site Admin

AndyT · Posted: Mon Jan 30, 2006 2:06 pm Post subject:

Angus, I appreciate both your time and your frustration but I've done enough teaching (in the air) in my life to know that things can be really obscure until just the right explanation hits you.

I may be getting there - standby!

Henk · Posted: Mon Jan 30, 2006 4:08 pm Post subject:

I have also written an explanation of Colors and Swordfish. The images maybe help you understand it. It is not very well written, but it might help you in combination with the writing of angusj.

http://www.intosudoku.com/Doc/Colors.html
http://www.intosudoku.com/Doc/MultiColors.html
http://www.intosudoku.com/Doc/SwordFish.html
http://www.intosudoku.com/Doc/ForcingChain.html
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AndyT · Posted: Tue Jan 31, 2006 6:41 am Post subject:

OK, guys, for the last time then I can go and quietly shoot myself! Here's a final example from one of Angus' puzzles that lends itself nicely to colours but - to me - is critical of order:

The plan is to identify spurious 9s. So I started at R6C1 and made that blue. Thus
R4C3 green
R3C3 blue
R2C1 green
R3C4 green
R3C5 blue (!)
R2C9 blue
R1C7 green
R1C5 blue
hence R3C5 green ... but it's already blue!

This suggests to me that this "build" placed 2 blue cells in row 3 - thus blue is not 9, hence R3C4 green is 9. Wrong.

Clearly you have a neat algorithm in your code that deduces the outcome. However, there still seems to be a line missing from the verbal Rules of Colours that I can't see.

Where is this logic flawed?

Thanks, guys!

Ruud · Site Admin

Hi Andy,

unfortunately, you cannot assign a color to R3C5, because it is not a conjugate of any of the other colors you identified.

In this situation, you cannot proceed with coloring.

However, you can spot an XY-Wing in the following cells:
R4C7 {5,9}
R4C6 {5,3} = 3 when R4C7 = 5
R6C8 {9,3} = 3 when R4C7 = 9
R4C8 {-3} (eliminated)

I shall not even attempt to explain this technique... Wink

But it does break the puzzle.

Ruud.
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AndyT · Posted: Tue Jan 31, 2006 8:32 am Post subject:

But Angus' program offers Colors as a hint here and proceeds to remove the 9 from R3C4.

Thank you for not explaining XY!! You may have saved my sanity.

angusj · Site Admin