How a human beeing thinks

Advanced methods and approaches for solving Sudoku puzzles

Re: Simpler solutions? Remote Pairs vs Simple Colouring

Postby ravel » Fri May 12, 2006 7:25 am

chrisr wrote:Hmm, that's something to get my head around. But I can't see how that's simpler than "simple colouring" in this case.

Its just easier to spot. The pairs jump into your eyes.
And you will have them as pencilmarks very early.
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Postby Pyrrhon » Fri May 12, 2006 1:37 pm

The idea what is simpler is different for humans and computer programs.

From a human point of view simple is what is easy to spot, from a computational point of view what can be recognized with a simple algorithm. A human seems to use more simple tasks.
I've never seen that a sudoku program spots a Turbot fish. Humans seems to have more line-box interaction then computers ...

The tendency is that a human goes through the houses and looks whether there is a symptom that a technique can be used. The computer (at least in the moment) takes a technique and looks after this whether there is a place to use this.

What is easy to spot for a human depends to different things like the culture of the solver, the use of pencilmarks, the stage of a sudoku solving process, the symptoms of for a technique ... For a program this seems not to be.

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Postby re'born » Fri May 12, 2006 6:29 pm

Pyrrhon wrote:I've never seen that a sudoku program spots a Turbot fish.


I believe Simple Sudoku, Sudoku Susser, SudoCue and Sudoku Assistenten all spot Turbot fish. They use different names (e.g., fishy cycles, skyscrapers, 2 string kites, multicoloring,...) but they all have techniques that will catch Turbot fish (as well as other related patterns).
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Susser's Fishy Cycles

Postby keith » Fri May 12, 2006 8:19 pm

I can test this further if someone wants. First, a question:

We know that if there is a fishy pattern, e.g. an X-wing on the columns (say), there will be a complementary pattern (maybe a swordfish) on the rows which makes the same exclusions.

I think this means that a Turbot fish (5 sides) cannot coexist with an X-wing (4), swordfish (6), jellyfish (8), etc. Correct?

Susser does find 2n fish when they coexist: For example, an X-wing in <1> and a swordfish on <2>, and will identify them at the same time.

It does find 2n+1 fish (like a Turbot), but it will not show them until the 2n fishes have been eliminated.

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Postby MrHamilton » Sun May 14, 2006 6:09 pm

R3C9=5
R2C1=8
R1C6=9
Exclude 4 from R1C1 and R3C1
R4C2=8
R5C5=8
Traveling pairs are present in the top stack. 5 travels neither with 8 nor 9, therefore squares R2C3 and R1C5 contain travelers.
Since neither 5 nor 8 travels with 7, exclude 7 from R2C3.
Naked triple in C5, so R1C5=4 establishing that 4 travels with 9, therefore R2C9=4.
R3C4=1
8 travels with 3, therefore R2C3=3.
R1C1=1
R3C2=4
R1C3=7
R9C9=9
R6C1=9
R4C4=9
R7C8=4
R5C4=4
R9C2=3
R7C1=7 (remote pairs)
R8C1=4
R9C7=7
Naked triple in C7, therefore R1C7=8, R1C8=3.
R9C8=8
R4C9=7
R8C6=5
R8C9=1
R9C5=1
Naked pair in C5 excludes 6 in R4C6, R6C4, R6C6
X-wing excludes 5 in R4C3
R5C1=5
R9C3=5
R5C6=3 (X-wing, 2's)
The rest are naked singles.
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Human vs Computer "simple"

Postby chrisr » Sun May 14, 2006 10:38 pm

Pyrrhon wrote:The idea what is simpler is different for humans and computer programs.

From a human point of view simple is what is easy to spot, from a computational point of view what can be recognized with a simple algorithm.


Yes, but in my personal experience, "simple colouring" is still a lot easier for a human to apply than it is to program, particularly the "2 cells of the same colour sharing the same unit" bit, which just leaps out at a human solver after a small amount of work with them coloured crayons...:) .

However, with "remote pairs", it looks as if even after you have identified all your candidate cells, you still need to find the correct chain of them that will let you make an elimination.
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