Colouring (trap)

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Colouring (trap)

Postby Sudoku123456789 » Tue Oct 31, 2017 12:21 am

Regarding the colouring technique, all conjugate pairs 'should' labeled.
In this example (extracted my puzzle to the solver of the Sudoku Joy app) the conjugate pairs 9 in R4 & C4 are not labeled.

Could anybody explain why this is the case/this is wrong?

Besides that, what is your opinion on using the colouring technique? When a function in the app would be available to label/when I would make the puzzle with pen & paper this would be easily applicable, but when this is not the case the technique would be (extremely) hard to apply since I would have to remember which cell would be green/yellow and so on.
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Re: Colouring (trap)

Postby Leren » Tue Oct 31, 2017 2:23 am

Code: Select all
*---------------------------------------*
| 9   1   3 | 8    5   6  | 7   2   4   |
| 6   8   7 | 2    3   4  |Y59  1  G59  |
| 2   5   4 | 7    1   9  | 3   8   6   |
|-----------+-------------+-------------|
| 35  37  8 | 569  2   1  | 4   36  79  |
| 1   6   2 | 4    7-9 3  | 8  G59  579 |
| 345 347 9 | 56   678 58 | 2   36  1   |
|-----------+-------------+-------------|
| 34  349 5 | 369  69  2  | 1   7   8   |
| 7   2   6 | 1   Y89  58 |G59  4   3   |
| 8   39  1 | 359  4   7  | 6  Y59  2   |
*---------------------------------------*

My solver came up with the following simple colouring move : Since r5c5 can see both G in r5c8 and Y in r8c5 it can't be 5 and this is enough to solve the puzzle. It's also solvable with two Kites.

Personally, I hate colouring. There are always other ways to come to the same eliminations, and its one of those moves where, even when the solver points it out to you, you sometimes have to stare at the grid for ages until you understand all of the colourings. Medusa colouring is even worse.

PS

I think that r4c4, r5c5 and r7c4 are not coloured because this is a Trap move (an uncoloured cell can see both colours). If they were coloured you would have a Contradiction move, where yellow some yellow coloured cells can see each other, proving that the yellow parity cells are all not 9 and the green parity cells are all 9. This would solve the puzzle, but maybe the solver uses Trap moves before Contradiction moves, and since the Trap move solves the puzzle, the extra colouring is not necessary. Who really knows ? Just another example of why colouring moves are only really partly documented.

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Re: Colouring (trap)

Postby David P Bird » Tue Oct 31, 2017 10:06 am

The short answer is that digit colouring techniques only give opposite colours to candidates that are conjugately linked. This means that although r4c9 - r4c4 - r5c5 form another conjugate path, it would need to use a different pair of colours as none of these cells is conjugate to any of the green and yellow ones.
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Re: Colouring (trap)

Postby Leren » Tue Oct 31, 2017 10:28 am

I think David is right, I missed the 9 in r5c9. I haven't thought much about colouring for years, so I am a bit rusty. I'd stick to the two Kites.

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Re: Colouring (trap)

Postby Sudoku123456789 » Tue Oct 31, 2017 2:41 pm

Your answer makes a lot of sense, David.
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Re: Colouring (trap)

Postby eleven » Wed Nov 01, 2017 1:07 am

Leren wrote:It's also solvable with two Kites.

Or one: 9r5c8=r9c8-r8c7=r8c5 => r5c5<>9
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