## Hard Puzzle : can it be solved without assuming a number?

Post the puzzle or solving technique that's causing you trouble and someone will help
Tracy, I said that colouring sounds like trial and error to me because if you give the colour blue to a cell, and green to the other cell, this is the same than assuming the number is in the blue cell, and not in the green cell, or the other way round.

I see it as a "disguised" trial and error

However, the advantage of colouring is that you don't have to put your number and see what you get, you just use colours instead ;-)

Marjorie
Marjorie

Posts: 3
Joined: 07 February 2006

Marjorie,

The logic behind the turbot fish (finned x-wing) is the same as that behind colouring is the same as that behind x-wing. The pattern of a turbot fish or an x-wing is fairly easy to spot (though I've never spotted a turbot fish on my own) and use, but we do so without thought of the logic behind it because we've already accepted the logic, so it's not really thought about in terms of conjugate links, weak links or strong links, even though that's all it is. Colouring is merely pattern recognition that isn't common enough to become a named pattern. I'm not questioning your choice to not use it but, to say you don't like it because it seems like trial & error, when you do use other techniques that rely on the same logic merely because they have a common pattern, is disingenious.

If every single possible pattern of conjugate links had a distinctive name would that make it seem less like trial & error? To me, much of the appeal of using colouring is in the fact that each pattern may be unique but I figured it out and knew how to use it, when so many of the techniques we use have been discovered and proved by others so we use them without thinking about the logic behind them. In effect, I'm using the logic to prove that particular pattern, not the pattern with no thought to the logic.

Tracy
TKiel

Posts: 209
Joined: 05 January 2006

Marjorie wrote:... if you give the colour blue to a cell, and green to the other cell, this is the same than assuming the number is in the blue cell, and not in the green cell, or the other way round.

Exactly! You can only use colouring on conjugate pairs i.e. where you know that one of two cells in a row, column or box contains the candidate value but not which one at that point. This knowledge can be used logically to make exclusions in other cells when combined with other (strongly or weakly) linked conjugate pairs.

It's taken me a while to get my head round what I thought was a relatively straightforward technique but thanks to Tracy and others on this forum I think I'm getting there. There is no guessing involved.
CathyW

Posts: 316
Joined: 20 June 2005

As TKiel implies, the only difference between using a naked pair versus coloring to make an exclusion is degree. If you think of one as T&E in disguise, then they both are -- and everything else is as well.

A simple naked pair:

Code: Select all
`[12][12][123]`

The first two cells must be ...

Code: Select all
`[1.][.2][123]`

... or ...

Code: Select all
`[.2][1.][123]`

... we don't know which.

Either way, the third cell cannot be 1 or 2.

A simple coloring exclusion. The 5s in this grid mark the only cells that can still contain a 5:

Code: Select all
`  .   +5    .  |  .   -5    .  |  .    .    .   -5    .    .  |  .    .    .  |  .   +5    .    .    .    .  |  .   +5    .  | x5    .    .  ---------------+---------------+--------------- +5    .    .  |  .    .    .  | -5    .    .    .    .    .  |  .    .    5  |  .    .    .    .   -5    .  |  .    .    .  |  5   x5   .  ---------------+---------------+---------------  .    .    .  |  .    .    .  |  5    5    .    .    .    5  |  .    .    .  |  .    .    .    .    .    .  |  5    .    .  |  .    .    .  `

All the cells marked PLUS must have the same value -- '5' or 'not 5'. All cells marked MINUS must have the same value. MINUS cells must have opposite value that the PLUS cells have.

The fives must be ...

Code: Select all
`  .  [+5]   .  |  .    .    .  |  .    .    .    .    .    .  |  .    .    .  |  .  [+5]   .    .    .    .  |  .  [+5]   .  | x5    .    .  ---------------+---------------+---------------[+5]   .    .  |  .    .    .  |  .    .    .    .    .    .  |  .    .    .  |  .    .    .    .    .    .  |  .    .    .  |  .   x5    .  ---------------+---------------+---------------  .    .    .  |  .    .    .  |  .    .    .    .    .    .  |  .    .    .  |  .    .    .    .    .    .  |  .    .    .  |  .    .    .  `

... or ...

Code: Select all
`  .    .    .  |  .  [-5]   .  |  .    .    .  [-5]   .    .  |  .    .    .  |  .    .    .    .    .    .  |  .    .    .  | x5    .    .  ---------------+---------------+---------------  .    .    .  |  .    .    .  |[-5]   .    .    .    .    .  |  .    .    .  |  .    .    .    .  [-5]   .  |  .    .    .  |  .   x5    .  ---------------+---------------+---------------  .    .    .  |  .    .    .  |  .    .    .    .    .    .  |  .    .    .  |  .    .    .    .    .    .  |  .    .    .  |  .    .    . `

... we don't know which.

Either way, r3c7<>5 and r6c8<>5.
tso

Posts: 798
Joined: 22 June 2005

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