The New Sudoku Players' Forum

[sag]

First, the puzzle:

Code: Select all

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

I got this far:

Code: Select all

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

Thanks in advance!

[angusj]

Look for an X-wing and an XY-wing.

[sag]

Thank you for the hint. I had already found the X-wing, but this was the first puzzle I've encountered that contained an XY-wing, so now I know what that is!

[sag]

Ok, here's another puzzle

Code: Select all

 *-----------*
 |693|241|587|
 |.84|3.5|2..|
 |52.|...|43.|
 |---+---+---|
 |.7.|...|.54|
 |...|657|...|
 |2.5|..4|71.|
 |---+---+---|
 |...|...|.45|
 |..8|5.3|17.|
 |.5.|4..|8.3|
 *-----------*


 *-----------*
 |693|241|587|
 |.84|3.5|2..|
 |52.|...|43.|
 |---+---+---|
 |.7.|...|.54|
 |...|657|...|
 |2.5|..4|71.|
 |---+---+---|
 |...|...|.45|
 |..8|5.3|17.|
 |.5.|4..|8.3|
 *-----------*

 
 *-----------------------------------------------------------------------------*
 | 6       9       3       | 2       4       1       | 5       8       7       |
 | 17      8       4       | 3       679     5       | 2       69      169     |
 | 5       2       17      | 789     6789    689     | 4       3       169     |
 |-------------------------+-------------------------+-------------------------|
 | 389     7       69      | 189     12389   289     | 369     5       4       |
 | 13489   134     19      | 6       5       7       | 39      29      289     |
 | 2       36      5       | 89      389     4       | 7       1       689     |
 |-------------------------+-------------------------+-------------------------|
 | 139     13      12679   | 1789    126789  2689    | 69      4       5       |
 | 49      46      8       | 5       269     3       | 1       7       269     |
 | 179     5       12679   | 4       12679   269     | 8       269     3       |
 *-----------------------------------------------------------------------------*


Simple Sudoku gave a couple of hints involving colors, but after that no further hints were available. Thanks.

[rubylips]

Here's how you could solve the puzzle with forcing chains, though somebody else might be able to spot something simpler:

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1. Consider the chain r4c5-3-r6c5-3-r6c2-6-r4c3-6-r4c7.
When the cell r4c7 contains the value 3, some other value must occupy the cell r4c5, which means that the value 6 must occupy the cell r4c7 - a contradiction.
Therefore, the cell r4c7 cannot contain the value 3.
- The move r4c7:=3 has been eliminated.
The cell r5c7 is the only candidate for the value 3 in Column 7.
2. The values 1, 2, 3 and 8 occupy the cells r4c1, r4c4, r4c5 and r4c6 in some order.
- The moves r4c1:=9, r4c4:=9, r4c5:=9 and r4c6:=9 have been eliminated.
The value 9 in Row 6 must lie in Box 5.
- The move r6c9:=9 has been eliminated.
Consider the chain r5c1-8-r4c1-3-r6c2-6-r8c2-4-r8c1.
When the cell r5c1 contains the value 4, so does the cell r8c1 - a contradiction.
Therefore, the cell r5c1 cannot contain the value 4.
- The move r5c1:=4 has been eliminated.
The cell r5c2 is the only candidate for the value 4 in Row 5.


[sag]

Here's how you could solve the puzzle with forcing chains, though somebody else might be able to spot something simpler:

Code: Select all

1. Consider the chain r4c5-3-r6c5-3-r6c2-6-r4c3-6-r4c7.
When the cell r4c7 contains the value 3, some other value must occupy the cell r4c5, which means that the value 6 must occupy the cell r4c7 - a contradiction.
Therefore, the cell r4c7 cannot contain the value 3.
- The move r4c7:=3 has been eliminated.

I don't understand your explanation, but now that you have pointed it out I can see that you are correct in my own way.

Code: Select all

The cell r5c7 is the only candidate for the value 3 in Column 7.
2. The values 1, 2, 3 and 8 occupy the cells r4c1, r4c4, r4c5 and r4c6 in some order.
- The moves r4c1:=9, r4c4:=9, r4c5:=9 and r4c6:=9 have been eliminated.
The value 9 in Row 6 must lie in Box 5.
- The move r6c9:=9 has been eliminated.

I see all that now, and I thank you.

Code: Select all

Consider the chain r5c1-8-r4c1-3-r6c2-6-r8c2-4-r8c1.
When the cell r5c1 contains the value 4, so does the cell r8c1 - a contradiction.
Therefore, the cell r5c1 cannot contain the value 4.
- The move r5c1:=4 has been eliminated.
The cell r5c2 is the only candidate for the value 4 in Row 5.


I don't understand. r8c1's candidates are 1,7,9 so I don't see how r5c1=4 forces the contradiction r8c1=4

[emm]

I don't understand. r8c1's candidates are 1,7,9 so I don't see how r5c1=4 forces the contradiction r8c1=4

r8c1 candidates are 4,9 - but I am confused too

Consider the chain r5c1-8-r4c1-3-r6c2-6-r8c2-4-r8c1.
When the cell r5c1 contains the value 4, so does the cell r8c1 - a contradiction.

but
r5c1=4 => r8c1=9
r5c1=8 => r5c7=3 => r5c2=4 => r8c1=4

[rubylips]

Code: Select all

1. Consider the chain r4c5-3-r6c5-3-r6c2-6-r4c3-6-r4c7.
When the cell r4c7 contains the value 3, some other value must occupy the cell r4c5, which means that the value 6 must occupy the cell r4c7 - a contradiction.
Therefore, the cell r4c7 cannot contain the value 3.
- The move r4c7:=3 has been eliminated.


I don't understand your explanation, but now that you have pointed it out I can see that you are correct in my own way.

The notation describes the following implication chain:
r4c5<>3 => r6c5=3 => r6c2=6 => r4c3<>6 => r4c7=6
So, when r4c7 contains the value 3, r4c5 doesn't (because the cells are in Row 4) whereupon the chain tells us that r4c7 must contain a 6, which contradicts the original assertion.

Code: Select all

Consider the chain r5c1-8-r4c1-3-r6c2-6-r8c2-4-r8c1.
When the cell r5c1 contains the value 4, so does the cell r8c1 - a contradiction.
Therefore, the cell r5c1 cannot contain the value 4.


The implication chain here is:
r5c1<>8 => r4c1=8 => r6c2=3 => r8c2=6 => r8c1=4
So r5c1=4 => r8c1=4, the necessary contradiction.

r5c1=4 => r8c1=9

This is undoubtedly true but it doesn't allow us to make an inference because, as the logic books tells us, it's possible to prove anything from a false statement. (Of course, at this stage we don't know for sure that the statement is false, but we have no reason to suppose that it is true). The solver is able to make an inference from the initial assumption that r5c1=4 because it goes on to derive a statement that blatantly contradicts that assumption. Since the statement r5c1=4 is false, it will be possible to draw many different contradictory inferences from it.

r5c1=8 => r5c7=3 => r5c2=4 => r8c1=4

Again, this is true. Your assertion r5c1=8 => r8c1=4 could be combined with my assertion r5c1<>8 => r8c1=4 to prove that r8c1=4. (It does, check the solution). However, my Forcing Chains logic misses this argument because your assertion can't be derived just from a true Forcing Chain, where it's only possible to infer a statement from its immediate predecessor in the chain.

[sag]

Thanks, rubylips, I understand this puzzle now. I can't guarantee that I won't need help with next Saturday's 6-star puzzle if it is of the same level of difficulty as this week's.

[emm]

Yes, thanks rubylips, I'm taking a printout of the puzzle to work today - will get back if more questions arise.

[bennys]

I think there is a way to solve in one step.

Code: Select all

+----------------------+----------------------+----------------------+
| 6      9      3      | 2      4      1      | 5      8      7      |
| 17     8      4      | 3      679    5      | 2      69     169    |
| 5      2      17     | 789    6789   689    | 4      3      169    |
+----------------------+----------------------+----------------------+
| 389    7     *69     | 189    12389  289    | 369    5      4      |
| 13489  134   *19     | 6      5      7      |*39    *29    *289    |
| 2      36     5      | 89     389    4      | 7      1     *689    |
+----------------------+----------------------+----------------------+
| 139    13     12679  | 1789   126789 2689   | 69     4      5      |
| 49    *46     8      | 5      269    3      | 1      7      269    |
| 179    5      12679  | 4      12679  269    | 8      269    3      |
+----------------------+----------------------+----------------------+

A = {R8C2}
B = {R5C3,R4C3}
C = {R4C7,R4C8,R4C9,R5C9}

R6C2 = 6 will make A ,B and C locked and then
R5C2 cant be 4 because of A
R5C2 cant be 1 because of B
R5C2 cant be 3 because of C (the only 3 in C is in R5)
So we know that R6C2 = 3
and that solve the puzzle.

[emm]

The implication chain here is:
r5c1<>8 => r4c1=8 => r6c2=3 => r8c2=6 => r8c1=4
So r5c1=4 => r8c1=4, the necessary contradiction.

What confuses me about this, is that my candidates for r5c1 are 1,3,4,8,9 so that while r5c1 might < >8 or 4, it can still = 1 or 9, so I can’t assume the contradiction.

C = R4C7,R4C8,R4C9,R5C9}

bennys, I suppose you mean C = r5c7, r5c8, r5c9, r6c9. There are quite a few chains from r6c2=6 that end up with a contradiction. Did you have any idea to pick r6c2 as the starting cell or did you find it by random testing? Can you relate this to the non-cell contradiction?

[bennys]

Yes it should be C = {R5C7,R5C8,R5C9,R6C9}

Actually I found that R5C2 cant be 3 because then R6C2 = 6 and C is left with only 3 candidates.
but then I noticed that it doesn't totally solve the puzzle so i looked a little more around it.

[rubylips]

The implication chain here is:
r5c1<>8 => r4c1=8 => r6c2=3 => r8c2=6 => r8c1=4
So r5c1=4 => r8c1=4, the necessary contradiction.

What confuses me about this, is that my candidates for r5c1 are 1,3,4,8,9 so that while r5c1 might < >8 or 4, it can still = 1 or 9, so I can’t assume the contradiction.

You're right - when r5c1 contains 1 or 9, r8c1 will contain 4. However, the fact that r8c1 contains 4 doesn't contradict the fact that r5c1 contains 1 - it's quite possible that r5c1 could contain 1 while r8c1 contains 4. However, the fact that r8c1 contains 4 directly contradicts the statement that r4c1 contains 4 as the two cells are in Column 4. Therefore, it's possible to eliminate the value 4 from r5c1.

I'm taking a printout of the puzzle to work today - will get back if more questions arise.

Quiet day at the office today?

[emm]

rubylips, I call it multi-tasking!

The thing is - while r5c1=4 and r8c1=4 is certainly a contradiction, how do you make the leap from there to eliminating the 4 from r5c1 while it still has other possible candidates?

You jumped from the contradiction to "Therefore, the cell r5c1 cannot contain the value 4." I can see the contradiction I just can't see the jump.

Isn't there a world of possibility in bennys' statement - 'so i looked a little more around it'!