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[Mogulmeister]

[Mogulmeister]

[TomC]

r3c7 <> 8 as then r1c3=8 and r2c5=8 leaving no <8> in row 5

[Mogulmeister]

A nice ALS

Set A is Yellow {2,4,8}
Set B is Purple {2,3,4,8}

Restricted common is 8

Common candidate 4 is eliminated from r5c5.

[ZeroAssoluto]

Hi everyone,

W-Wing 2,8 in r4c2,r6c4 SL with number 8 in r5c35 and -2 in r4c6,r6c2
or
Finned X-Wing with number 8 in r25c35 finned in r2c2 and -8 in r13c3
or
Finned Swordfish with number 8 in r135c357 finned in r3c4 and -8 in r2c5

Ciao Gianni

[TomC]

Nice solutions all

Gianni, what would you describe my solution above as?

[ZeroAssoluto]

[TomC]

Well Gianni, when I look for a solution one way I do it is to look at the whole of the puzzle to find patterns to help me solve.

Sometimes you need several of these patterns to combine to find the solution (like clues to solve a crime)

As it happens <8> was the clue to the pattern, as it was in your three solutions

Firstly, row 5 only contains two <8>'s in c3 and c5

Secondly, if you look at r3c7, if it is <8> then follow it left x2 up x1 and you get r2c5=8, follow it again left x2 up x1 and you get r1c3=8 (like a little <8> snake)

Thirdly, when these <8>'s drop down they knock out the <8>'s in row 5 (maybe like a skyscraper)

So r3c7 can't be an <8>

I've been doing sudoku for such a long time that this seems to be the best way to describe it to you

You could maybe say that if I see a pattern which will solve (that is no 8's in row 5) then I look for another pattern which will force the situation

Hope this helps
Tom

[TomC]

This method I used in the recent VH 111821 in other puzzles

[Mogulmeister]

Your method Tom is essentially contradiction based. The art of the impossible.Proof by negative assertion.

By plugging in a value you propagate changes in the fabric of a puzzle that might breakdown into impossibilities or contradictions. If your mind works that way the contradictions can be quickly seen. With me it is ALS. Both techniques mean looking at the structure of the puzzle first rather than applying a pattern.

This can be multichained although you only really need to have one of them to get your answer. This is how dongrave's long contradiction chains work. Very powerful because if your start point is a bivalue (2 digits in square) and you prove one leads to contradiction then the correct value is the other one on the square. Make it into a loop and the contradictions can be sometimes found at the start.

This is called a discontinuous nice loop.

Let's start one off with the above puzzle by sticking 8 in r3c7.

(2=8) r3c7-(8=7)r1c7-(7=1)r1c9-(1=8)r1c3-r5c3=r5c5-(8)r23c5=r3c4-(8)r3c7

Plug 8 into r3c7 and the loop creates a contradiction which you can see in two ways:

a)The loop puts an 8 in r3c4 and there is also an 8 in r3c7 - Contradiction can't have two 8s in a row.

b)If the loop is followed all the way round it removes the 8 at the starting point of the loop so it must be false. The 8 removes itself.

However you view it r3c7 < > 8

There are at least 6 different types of contradictions (sometimes called logical absurdities)

1)Put too many of the same numbers into a house (row, column or box)
2)Remove a number totally from a house
3)Create a loop where the starting number is removed
4)Create a loop where a number is forced in even when removed at the start
5)Create multiple numbers in the same square location as the answer
6)Remove all numbers so the a square is vacant

[Mogulmeister]

Another wrinkle on this is one where you have a start cell with 2 or 3 candidates in it and a target cell which always reduces to the same value whatever candidate you choose to start with.

In this case you can do nothing about the start cell but you do now know the value of the target cell.

[TomC]

You know my methods, Mogulmeister.

When you have eliminated the impossible, whatever remains, however improbable, must be the truth?

[Mogulmeister]

Always.