dailysudoku.com

[someone_somewhere]

Hello,
I found in the Sunday Time Magazine Sudoku 8:

500000000
400070006
908405000
010003090
005209600
040800020
000604503
700020004
000000009

could solved it after finding "hidden pair in row", "X-wing on column" and "XY-wing". It looks to be a very nice one!

can someone do it without advanced techniques?

see u,

[David Bryant]

I have solved this puzzle. I'm not sure if I used an "advanced technique," or not.

I'll just describe the position I reached in general terms for now. After about 12 moves (I'm not sure exactly how many -- I'll have to go back and retrace the early steps) I reached a position that had three noteable characteristics:

1. the only possibilities at r4c4 were {5, 7};
2. there were several columns and rows where "9" could only appear in two places; and
3. the set {2, 6, 8} already appeared in column 4.

What I noticed at this point was that placing a "5" in r4c4 made it impossible to complete the top middle 3x3 box, from which I inferred that r4c4 = 7 -- the rest of the puzzle was relatively straightforward. dcb

[someone_somewhere]

David, I suppose that you did it!

Here to compare it with a "classic" way of solving:

5 in r2c8 9 in r6c3 7 in r7c8 4 in r9c3 - Unique Horizontal
2 in r9c7 - Unique in 3x3 block
1 not in r7c3, it is in r7c1 or r9c1 (Column on 3x3 Block interaction)
1 not in r8c3, it is in r7c1 or r9c1 (Column on 3x3 Block interaction)
2 in r7c3 - Sole Candidate
2 in r4c1 - Unique Horizontal
8 not in r5c8, it is in r4c7 or r4c9 (Row on 3x3 Block interaction)
8 not in r5c9, it is in r4c7 or r4c9 (Row on 3x3 Block interaction)
1 not in r8c4, Hidden Pair 5 9 in r8c2 and r8c4 (in Row)
3 not in r8c2, Hidden Pair 5 9 in r8c2 and r8c4 (in Row)
3 not in r8c4, Hidden Pair 5 9 in r8c2 and r8c4 (in Row)
6 not in r8c2, Hidden Pair 5 9 in r8c2 and r8c4 (in Row)
8 not in r8c2, Hidden Pair 5 9 in r8c2 and r8c4 (in Row)
1 not in r8c8, Nacked Pair 1 8 in r8c6 and r8c7 (same Row)
8 not in r8c8, Nacked Pair 1 8 in r8c6 and r8c7 (same Row)
6 in r8c8 - Sole Candidate
3 in r8c3 - Sole Candidate
1 in r2c3 - Sole Candidate
3 not in r5c2, it is in r5c1 or r6c1 (Column on 3x3 Block interaction)
8 not in r1c6, it is in r2c6 r2c7 r8c6 r8c7 (X-Wing on Column)
8 not in r1c7, it is in r2c6 r2c7 r8c6 r8c7 (X-Wing on Column)
8 not in r4c7, it is in r2c6 r2c7 r8c6 r8c7 (X-Wing on Column)
8 not in r9c6, it is in r2c6 r2c7 r8c6 r8c7 (X-Wing on Column)
8 in r4c9 - Unique Horizontal
5 in r6c9 - Unique Vertical
4 not in r4c5, XY-Wing-2 X=1 Y=7 in r5c9 X=1 Z=4 in r5c5 Y=7 Z=4 in r4c7
4 in r4c7 4 in r5c5 - Unique Horizontal
4 in r1c8 - Unique Horizontal
8 in r1c5 8 in r2c7 8 in r8c6 - Unique Horizontal
9 in r2c4 1 in r8c7 9 in r8c2 - Unique Horizontal
9 in r1c7 3 in r2c2 9 in r7c5 5 in r8c4 5 in r9c2 - Unique Horizontal
3 in r1c4 2 in r2c6 5 in r4c5 1 in r7c1 3 in r9c5 6 in r9c1 - Unique Horizontal
6 in r4c3 8 in r7c2 8 in r9c8 - Unique Horizontal
7 in r4c4 8 in r5c1 7 in r6c7 7 in r9c6 - Unique Horizontal
3 in r5c8 7 in r5c2 3 in r6c1 1 in r9c4 - Unique Horizontal
3 in r3c7 7 in r3c9 1 in r5c9 - Unique Horizontal
1 in r1c6 7 in r1c3 1 in r3c8 2 in r3c2 1 in r6c5 - Unique Horizontal
2 in r1c9 6 in r1c2 6 in r3c5 6 in r6c6 - Unique Horizontal

Final SuDoku Table

5 6 7 3 8 1 9 4 2
4 3 1 9 7 2 8 5 6
9 2 8 4 6 5 3 1 7
2 1 6 7 5 3 4 9 8
8 7 5 2 4 9 6 3 1
3 4 9 8 1 6 7 2 5
1 8 2 6 9 4 5 7 3
7 9 3 5 2 8 1 6 4
6 5 4 1 3 7 2 8 9

[David Bryant]

I've gone back and retraced the early moves I made on this puzzle. Here's what it looked like to me.

1. r2c8 = 5 (because of "5" at r1c1, r3c6, and r7c7 -- sole candidate)
2. r6c3 = 9 (because of "9" at r3c1, r4c8, and r5c6 -- sole candidate)
3. r9c3 = 4 (because of "4" at r2c1, r6c2, and r8c9 -- sole candidate)
4. r9c7 = 2 (because of "2" at r6c8 and r8c5 -- sole candidate)
5. r7c8 = 7 (this is the only cell in row 7 that can contain a "7" -- note r8c1 and r2c5)
6. r7c3 = 2 (sole candidate -- note that "1" must appear at r1c3 or r2c3
7. r4c1 = 2 (this is the only cell in row 4 that can contain a "2" -- note r5c4 and r6c8)

At this point the grid looked like this -- I've only entered the possibilities that I had pencilled in, leaving the more complex possibilities blank. I have also marked all the spots where a "9" can possibly appear with an asterisk ("*").

[Victor]

This IS a tricky sudoku. You can do it by finding pairs, etc. AND by the X-wing that Someone_Somewhere gives: at one stage, 8 can go in rows 2 and 8 in the columns 6 and 7 only. So logically you can have an 8 nowhere else in these columns, which turns out to be enough to solve it all without the need for XY-wing, by later finding sneakily hidden multiples.

[Louise56]

[David Bryant]

[Louise56]

Thanks, David for explaining that to me! I don't see the naked pair in row 8. I have a 1,8 pair in row 8 in r8c6, r8c7 and r8c8. I've been following SomeoneSomewhere's solution and he must have put a 6 in r8c8 in order to get the naked pair. I don't see how the 6 gets there. In box 9 I have a 6 in r8c8 and r9c8.

Thanks again for your response!

[Louise56]

David,

I found the naked pair! I had put a 3 in r8c6 which was a mistake since column 6 already had a 3 in it! It's amazing that one mistake can throw off the whole puzzle! I'll see if I can finish this bad boy, otherwise you may hear from me again! I appreciate your patience and excellent teaching!

[someone_somewhere]

Hi David,

Do you have an example that can be solved with "quadruples" but not with "pairs" or "triples"? Could be in paralel with X-wing, XY-wing, coloring or some more advanced than "quadruples".

Thank you in advance,

see u,

[David Bryant]

[Louise56]

[someone_somewhere]

Hi David,

Thank you for your efforts.
The first one you mentioned, can be solved without "quadruples".
"Hidden pair" is enough:

- 6 - - - 5 - - -
5 - - - 7 - 9 - -
7 4 3 1 6 9 8 - -
- - 4 - 8 1 - - 7
2 - - - 5 - 1 - -
- 1 - - - - - 8 -
1 - - 6 3 4 2 9 8
4 - 6 - 9 - - - 1
- - - 5 1 - - 4 -

2 not in r1c8, it is in r3c8 or r3c9 (Row on 3x3 Block interaction)
2 not in r1c9, it is in r3c8 or r3c9 (Row on 3x3 Block interaction)
2 not in r2c8, it is in r3c8 or r3c9 (Row on 3x3 Block interaction)
2 not in r2c9, it is in r3c8 or r3c9 (Row on 3x3 Block interaction)
5 not in r8c2, it is in r7c2 or r7c3 (Row on 3x3 Block interaction)
7 not in r8c2, it is in r7c2 or r7c3 (Row on 3x3 Block interaction)
7 not in r9c2, it is in r7c2 or r7c3 (Row on 3x3 Block interaction)
7 not in r9c3, it is in r7c2 or r7c3 (Row on 3x3 Block interaction)
3 not in r6c9, Hidden Pair 2 5 in r3c9 and r6c9 (in Column)
4 not in r6c9, Hidden Pair 2 5 in r3c9 and r6c9 (in Column)
6 not in r6c9, Hidden Pair 2 5 in r3c9 and r6c9 (in Column)
9 not in r6c9, Hidden Pair 2 5 in r3c9 and r6c9 (in Column)
9 in r5c9 - Unique Vertical
... (and the rest is no problem)

Now, I will take a look at the second one.

see u,

[someone_somewhere]

Hi,

Second one, I have already analysed. No need for "quadruples".
See the discussion at that point.

So, still I don't have an example (hidden or nacked qadruples) that I am looking for.

Still, thank you for your efforts, and keep your eyes open ...

see u,

[someone_somewhere]

Hi Louise,

The Sudoku from USATODAY is extreme interesting.
I am wondering how you solved it with the X-wing technique.

I could not do it!

So here are my efforts:

Initial Sudoku Table:

123045000
000000000
600700200
070080030
040020060
050010090
009003008
000000000
000290714

3 in r3c5 - Sole Candidate
6 in r2c5 - Sole Candidate
2 in r2c6 - Unique Horizontal
7 not in r2c8, it is in r1c8 or r1c9 (Row on 3x3 Block interaction)
7 not in r2c9, it is in r1c8 or r1c9 (Row on 3x3 Block interaction)
3 not in r8c1, it is in r9c1 or r9c2 (Row on 3x3 Block interaction)
3 not in r8c2, it is in r9c1 or r9c2 (Row on 3x3 Block interaction)
5 not in r7c1, it is in r9c1 or r9c3 (Row on 3x3 Block interaction)
5 not in r8c1, it is in r9c1 or r9c3 (Row on 3x3 Block interaction)
5 not in r8c3, it is in r9c1 or r9c3 (Row on 3x3 Block interaction)
3 in r9c2 7 in r1c8 - Unique Vertical
1 not in r8c3, it is in r7c2 or r8c2 (Column on 3x3 Block interaction)
6 not in r8c3, it is in r7c2 or r8c2 (Column on 3x3 Block interaction)
6 not in r9c3, it is in r7c2 or r8c2 (Column on 3x3 Block interaction)
9 not in r2c1, it is in r2c2 or r3c2 (Column on 3x3 Block interaction)
5 not in r7c4, it is in r7c5 or r8c5 (Column on 3x3 Block interaction)
5 not in r8c4, it is in r7c5 or r8c5 (Column on 3x3 Block interaction)
7 not in r8c6, it is in r7c5 or r8c5 (Column on 3x3 Block interaction)
2 not in r8c9, it is in r7c8 or r8c8 (Column on 3x3 Block interaction)
4 not in r2c7, it is in r2c8 or r3c8 (Column on 3x3 Block interaction)
8 not in r1c7, it is in r2c8 or r3c8 (Column on 3x3 Block interaction)
8 not in r2c7, it is in r2c8 or r3c8 (Column on 3x3 Block interaction)
8 in r1c4 6 in r9c6 - Unique Horizontal
8 in r8c6 - Unique Vertical
1 in r3c6 - Unique Vertical
9 in r2c4 - Unique in 3x3 block
9 in r3c2 - Unique in 3x3 block
8 in r2c2 5 in r3c9 - Sole Candidate
4 in r2c8 4 in r3c3 - Sole Candidate
8 in r3c8 - Sole Candidate
4 not in r4c4, it is in r4c6 or r6c6 (Column on 3x3 Block interaction)
4 not in r6c4, it is in r4c6 or r6c6 (Column on 3x3 Block interaction)
5 not in r7c7, it is in r7c8 or r8c8 (Column on 3x3 Block interaction)
5 not in r8c7, it is in r7c8 or r8c8 (Column on 3x3 Block interaction)
6 in r7c7 - Sole Candidate
9 in r1c7 1 in r7c2 - Sole Candidate
6 in r1c9 4 in r7c4 6 in r8c2 3 in r8c7 - Sole Candidate
1 in r2c7 1 in r8c4 9 in r8c9 - Sole Candidate
3 in r2c9 - Sole Candidate
4 in r8c1 - Unique Horizontal

And now I am stucked at the position:

Final SuDoku Table

1 2 3 8 4 5 9 7 6
- 8 - 9 6 2 1 4 3
6 9 4 7 3 1 2 8 5
- 7 - - 8 - - 3 -
- 4 - - 2 - - 6 -
- 5 - - 1 - - 9 -
- 1 9 4 - 3 6 - 8
4 6 - 1 - 8 3 - 9
- 3 - 2 9 6 7 1 4

or with the exclude table:

1 2 3 8 4 5 9 7 6
57 8 57 9 6 2 1 4 3
6 9 4 7 3 1 2 8 5
29 7 126 56 8 49 45 3 12
389 4 18 35 2 79 58 6 17
238 5 268 36 1 47 48 9 27
27 1 9 4 57 3 6 25 8
4 6 27 1 57 8 3 25 9
58 3 58 2 9 6 7 1 4

From here only some coloring, multicoloring, nisho, etc can help.
Or someone else . . . ?

see u,
Thank you in advance for further hits.

[someone_somewhere]

Hi,
It's me again. From the previous position, I could apply Nishio (limited form of trial and error) and solve it.

I made the assumtion:
2 in r4c1

this leads to 1 in r4c9.

with this 2 followed 2 chains:
- 7 in r5c9, 9 in r5c6, 4 in r4c6 and
- 6 in r4c3, 5 in r4c4, 4 in r4c7

and now I have two "4"s in r4: one in c6 and one in c7.
This implies that my assuption "2 in r4c1" is leading to a conradiction.

The rest is now obvious: 9 in r4c1 !

Has someone a simpler solution?

see u,

[David Bryant]

I haven't tried the puzzle you posted yet, Someone. I visited the USA Today site and got a different one -- must have been the wrong day. Here it is.

[Guest]

Hi,

You should have tried my one!!!
It is identical to your one!!!

As I have posted, I was able to solve it ONLY with a little bit of Nishio.
Just take a look again at my previous postings.

see u,

[David Bryant]

You're right! I guess all the zeroes threw me off ... I didn't notice the three columns filled up in the three middle 3x3 boxes with all those zeroes in there!

I also tried to apply "Nishio", but started from the {1, 8} possibility in r5c3, just because it looked odd. Why did you start from r4c1? dcb

PS So you and I were working on the same puzzle, but are we sure it's the one Louise56 was talking about? Is this the one you were talking about, Louise?

[Louise56]