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### Re: Another Solution

Carcul wrote:but this cannot be, because now we have an incompatible pattern of “5s” in cells {r1c24|r3c25|r5c24|r7c45}.

Carcul, even after your editing, it still doesn't make sense to me...
Code: Select all
` *-----------------------------------------------------------* | 6    *15    2     |*15    9     8     | 3     7     4     | | 358   1358  589   | 4     7     135   | 58    2     6     | | 4    *358   7     | 2    *35    6     |*58    1     9     | |-------------------+-------------------+-------------------| | 2     7     4     | 6     358   35    | 1     9     58    | | 1    *58    6     |*58    2     9     | 4     3     7     | | 358   9     58    | 1578  4     135   | 2     6     58    | |-------------------+-------------------+-------------------| | 9     2     1     |*58   *58    7     | 6     4     3     | | 7     6     58    | 3     1     4     | 9     58    2     | | 58    4     3     | 9     6     2     | 7     58    1     | *-----------------------------------------------------------*`

You see, after carrying out your steps, the grid becomes as above...

5s can be in cells {r1c24|r3c257|r5c24|r7c45}, and the pattern is not incompatible because of r3c7...

So perhaps you need to elaborate a bit more...

[Edited] Imexplicable typo fixed...
Last edited by udosuk on Sat Feb 17, 2007 12:53 am, edited 1 time in total.
udosuk

Posts: 2698
Joined: 17 July 2005

Udosuk wrote:Carcul, even after your editing, it still doesn't make sense to me...(...)You see, after carrying out your steps, the grid becomes as above...(...)So perhaps you need to elaborate a bit more...

You have the answer in front of your eyes. The correct cells are marked in your grid (r3c7 isn't needed).

Udosuk wrote:and the pattern is not incompatible because of r3c8...

The pattern is incompatible because of its implications in the cells marked. Start with the X-Wing in cells r15c24 and see the "circle" of implications that follow.

Carcul
Carcul

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Joined: 04 November 2005

Carcul, thanks for the effort to try to explain it, but still it's not clear at all...

I take it when you said "we have an incompatible pattern of 5s", you meant that there was no way to place all the 5s in the state at that point. But from the position I displayed above, it is possible to place all the 5s, such as:
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`.5.|...|......|..5|......|...|5..---+---+---...|...|..5...|5..|...5..|...|...---+---+---...|.5.|.....5|...|......|...|.5....|5..|.....5|...|......|...|5..---+---+---...|..5|....5.|...|......|...|..5---+---+---...|.5.|......|...|.5.5..|...|...`

There are many other possible patterns...

So, you cannot conclude the contradiction solely from the pattern of 5s... You must have considered other candidates (such as 8)... And for me (1) it should have been pointed out specifically, and (2) it's not a proper way to end a forcing chain if you need to consider 2 or more candidates for "incompatible patterns"...
udosuk

Posts: 2698
Joined: 17 July 2005

### Re: Another Solution

Carcul wrote:[r8c3]=9=[r7c1](-9-[r7c7]-6-[r7c45])-9-[r1c1]=9=[r1c5]-9-[r2c6]=9=
=[r5c6]=2=[r9c6]=6=[r9c5]-6-[r9c1]=6=[r8c2](-6-[r1c2])-6-[r3c2]=6=
=[r3c56]-6-[r1c4]=6=[r4c4]=7=[r4c2]-7-[r3c2]=7=[r3c3],

but this cannot be, because now we have an incompatible pattern of “5s” in cells {r1c24|r3c25|r5c24|r7c45}.

So, r8c3 must be “9” and the puzzle is solved.

Setting r8c3=9 at the identical pencilmarks of your post, Simple Sudoku still gets stuck ... so how is it solved?
ronk
2012 Supporter

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Location: Southeastern USA

Ronk wrote:Setting r8c3=9 at the identical pencilmarks of your post, Simple Sudoku still gets stuck ... so how is it solved?

In my opinion, a type-1 UR is as trivial as a naked pair. It just happens that SS doesn't have URs implemented.

Carcul
Carcul

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Udosuk wrote:you meant that there was no way to place all the 5s in the state at that point.

Obviously that was not what I meant, because it is rather obvious that there is no contradiction in the "5s" alone. Again:

Carcul wrote:Start with the X-Wing in cells r15c24 and see the "circle" of implications that follow.

Carcul
Carcul

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Carcul wrote:
Ronk wrote:Setting r8c3=9 at the identical pencilmarks of your post, Simple Sudoku still gets stuck ... so how is it solved?

In my opinion, a type-1 UR is as trivial as a naked pair. It just happens that SS doesn't have URs implemented.

In my opinion, your "solved" statement could easily have been something like ... so, r8c3 must be “9” and then a UR solves the puzzle.

Thanks for reminding me why I skim over most of your solutions. However, udosuk is still hanging right in there.
ronk
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Joined: 02 November 2005
Location: Southeastern USA

Ronk wrote:In my opinion, your "solved" statement could easily have been something like ... so, r8c3 must be “9” and then a UR solves the puzzle.

I am just being coherent with myself; otherwise, I would have to write something link "... so rXcY must be "a" and then a naked pair, a naked triple, and several hidden/naked singles solve the puzzle".

I think in everything there is an evolution, and in the present level of development of Sudoku solving techniques, a type-1 UR should be considered as trivial as a naked pair.

Think in the following analogy with the History of Mathematics. Some centuries ago, evaluating the area of the "parabolic segment" (the area between the function f(x) = x^2, x=0, x=1, and y=0) was so hard that the first person who managed to evaluate it (Archimedes, 3rd cent. b.C.) used a method called "method of exhaustion". Nowadays, with the development of mathematical thought, that problem is so easily solved that a student in the 12th year of school can do it in a matter of seconds. In present, the "method of exhaustion" only have some pedagogical value, but no pratical use.

Ronk wrote:Thanks for reminding me why I skim over most of your solutions.

I have never asked you (or anybody) to study any of the solutions I post. If you want to make a critic, then do it directly.

Carcul
Carcul

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Joined: 04 November 2005

Carcul wrote:Start with the X-Wing in cells r15c24 and see the "circle" of implications that follow.

Code: Select all
` *-----------------------------------------------------------* | 6    *15    2     |*15    9     8     | 3     7     4     | | 358   1358  589   | 4     7     135   | 58    2     6     | | 4    *358   7     | 2    *35    6     | 58    1     9     | |-------------------+-------------------+-------------------| | 2     7     4     | 6     358   35    | 1     9     58    | | 1    *58    6     |*58    2     9     | 4     3     7     | | 358   9     58    | 1578  4     135   | 2     6     58    | |-------------------+-------------------+-------------------| | 9     2     1     |*58   *58    7     | 6     4     3     | | 7     6     58    | 3     1     4     | 9     58    2     | | 58    4     3     | 9     6     2     | 7     58    1     | *-----------------------------------------------------------*`

x-wing (r15c24) -> r7c4=8 -> r5c4=5 -> r1c4=1 -> r1c2=5 -> r5c2=8 -> r3c2=3 -> r3c5=5 -> r7c5=8 -> contradiction

IMHO this is not an "incompatible pattern of 5s", but an incompatible pattern of 1,3,5,8...

Carcul wrote:Obviously that was not what I meant, because it is rather obvious that there is no contradiction in the "5s" alone.

Obviously Carcul has a different take on the meaning of the words "obviously" and "obvious" to mine (and many others')...

ronk wrote:Thanks for reminding me why I skim over most of your solutions. However, udosuk is still hanging right in there.

Believe me Ron, I don't think there'll be much "hanging" anymore... Unless I want my hair to be all snowy by the end of the year...

BTW Carcul, I don't think you should take Ron's and my comments as criticisms, but rather as compliments to your uncanny ability to see things "obviously"...
udosuk

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Joined: 17 July 2005

The chains are still mostly outta my league...but great study material! Many thanks to all for your inputs.
Sudtyro

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