The New Sudoku Players' Forum

[shye]

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+-------+-------+-------+
| . 4 2 | . . 6 | 5 . . |
| 6 . . | 9 4 . | . 7 . |
| 7 . . | . . . | . . 6 |
+-------+-------+-------+
| . 3 . | . . 9 | . . 7 |
| . 8 . | . 1 . | . 9 . |
| 2 . . | 8 . . | . 6 . |
+-------+-------+-------+
| 3 . . | . . . | . . 2 |
| . 2 . | . 5 8 | . . 3 |
| . . 4 | 3 . . | 7 5 . |
+-------+-------+-------+
.42..65..6..94..7.7.......6.3...9..7.8..1..9.2..8...6.3.......2.2..58..3..43..75.

estimated rating: 7.2
made with help from SCLT, i havent seen a lot of puzzles that do stuff like this ヽ(´▽`)/

[eleven]

2 steps:

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 *--------------------------------------------------------------------*
 |e#189   4       2     |  17     378   6      |  5     138    #189   |
 |  6    d15     d358   |  9      4     1235   |  128   7      c18    |
 |  7     159    d358   |  125    238   1235   | c49    12348   6     |
 |----------------------+----------------------+----------------------|
 |  45    3       16    |  45     26    9      |  128   128     7     |
 |  45    8       67    |  267    1     237    |  23    9       45    |
 |  2     179     179   |  8      37    45     |  13    6       45    |
 |----------------------+----------------------+----------------------|
 |  3     15679   58    |  1467   679   147    |  469   148     2     |
 | #19    2       179   |  1467   5     8      |  469   14      3     |
 |a*189  #169     4     |  3     *269   12     |  7     5     b#189   |
 *--------------------------------------------------------------------*

Broken wing 9r1c19,r8c1,r9c19, guardians 9r9c15
8r9c1 = r9c9 - (8=1)r2c9 - (1=538)b1p569 => -8r1c1
=> 8r9c1, 9r9c5

[jovi_al01]

beautiful puzzle, shye and SCLT!

my solution:
because of GSP, r1c1, r1c9, r9c1, and r9c9 form an interesting pattern. because 8 and 9 must not map to themselves after the rotation is applied, we create an x-wing on 1s in r1 and r9, reducing the puzzle to singles.

[eleven]

Oh my dear, i did not see, that the puzzle has rotational digit symmetry - what a shame !

[denis_berthier]

.

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Resolution state after Singles and whips[1]:
   +-------------------+-------------------+-------------------+
   ! 189   4     2     ! 17    378   6     ! 5     138   189   !
   ! 6     15    1358  ! 9     4     1235  ! 128   7     18    !
   ! 7     159   13589 ! 125   238   1235  ! 12489 12348 6     !
   +-------------------+-------------------+-------------------+
   ! 145   3     16    ! 2456  26    9     ! 128   128   7     !
   ! 45    8     67    ! 24567 1     23457 ! 23    9     45    !
   ! 2     179   179   ! 8     37    3457  ! 13    6     145   !
   +-------------------+-------------------+-------------------+
   ! 3     15679 15789 ! 1467  679   147   ! 14689 148   2     !
   ! 19    2     179   ! 1467  5     8     ! 1469  14    3     !
   ! 189   169   4     ! 3     269   12    ! 7     5     189   !
   +-------------------+-------------------+-------------------+

Two solutions in two non-W1 steps in BC4:

Code: Select all

biv-chain[4]: r8c1{n9 n1} - r8c8{n1 n4} - b3n4{r3c8 r3c7} - b3n9{r3c7 r1c9} ==> r1c1≠9
hidden-single-in-a-row ==> r1c9=9
whip[1]: c1n9{r9 .} ==> r7c2≠9, r7c3≠9, r8c3≠9, r9c2≠9
biv-chain[3]: r1c1{n1 n8} - r9n8{c1 c9} - r2c9{n8 n1} ==> r2c2≠1, r2c3≠1, r1c8≠1
stte

Code: Select all

biv-chain[4]: r1n9{c9 c1} - r8c1{n9 n1} - r8c8{n1 n4} - b3n4{r3c8 r3c7} ==> r3c7≠9
hidden-single-in-a-block ==> r1c9=9
whip[1]: c1n9{r9 .} ==> r7c2≠9, r7c3≠9, r8c3≠9, r9c2≠9
biv-chain[3]: r1c1{n1 n8} - r9n8{c1 c9} - r2c9{n8 n1} ==> r2c2≠1, r2c3≠1, r1c8≠1
stte

[Ngisa]

Two steps

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+--------------------+-------------------+---------------------+
| 18-9   4       2   | 17     378   6    | 5       138     189 |
| 6      15      358 | 9      4     1235 | 128     7       18  |
| 7     e159     358 | 125    238   1235 |d12489  c12348   6   |
+--------------------+-------------------+---------------------+
| 45     3       16  | 45     26    9    | 128     128     7   |
| 45     8       67  | 267    1     237  | 23      9       45  |
| 2      179     179 | 8      37    45   | 13      6       45  |
+--------------------+-------------------+---------------------+
| 3      1567-9  58  | 1467   679   147  | 14689   148     2   |
|a19     2       179 | 1467   5     8    | 1469   b14      3   |
| 189   16-9     4   | 3      269   12   | 7       5       189 |
+--------------------+-------------------+---------------------+


Step 1: (9=1)r8c1 - (1=4)r8c8 - r3c8 = (4-9)r3c7 = (9)r3c2 => - 9r1c1,r79c2

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[code]
+--------------------+-------------------+-----------------+
|e1-8     4      2   | 17     378   6    | 5     138    9  |
| 6      d15     358 | 9      4     1235 | 128   7     c18 |
| 7       9      358 | 125    238   1235 | 4     1238   6  |
+--------------------+-------------------+-----------------+
| 45      3      16  | 45     26    9    | 128   128    7  |
| 45      8      67  | 267    1     237  | 23    9      45 |
| 2       17     9   | 8      37    45   | 13    6      45 |
+--------------------+-------------------+-----------------+
| 3       1567   58  | 1467   679   147  | 69    148    2  |
| 19      2      17  | 1467   5     8    | 69    14     3  |
|a189     16     4   | 3      269   12   | 7     5     b18 |
+--------------------+-------------------+-----------------+


Step 2: (8)r9c1 = r9c9 - (8=1)r2c9 - r2c2 = (1)r1c1 => - 8r1c1; stte

Clement

[shye]

because of GSP, r1c1, r1c9, r9c1, and r9c9 form an interesting pattern. because 8 and 9 must not map to themselves after the rotation is applied, we create an x-wing on 1s in r1 and r9, reducing the puzzle to singles.

matched my solution! i was fascinated by this deduction using gsp for slightly more advanced logic and wanted to see what else could be made from it

i'd describe it like this, slightly more longform compared to jovi's:
due to gsp there are two states for the corner pairs [r1c1 & r9c9] and [r1c9 & r9c1]. its not possible for both corner pairs to be the same state, since each value sees the other corners (this would be true no matter what sets were in the corners, as long as they are the same two sets), so one set must be an 89 pair and the other double 1s. common eliminations are -1r1c48, -1r2c9, -1r8c2, -1r9c26

and here is my attempt to notate that, notating gsp pairs is quite difficult it turns out!! if anyone has a better way to write it out do let me know
(xy: 89)
(1r1c1 & 1r9c9) = (xr1c1 & yr9c9) - (x|yr1c9 & x|yr9c1) = (1r1c9 & 1r9c1)

Broken wing 9r1c19,r8c1,r9c19, guardians 9r9c15

i think there are missing guardians? 9r7c2 and 9r8c3. it would still be valid to deduce -9r9c2, but not as helpful >_>
however just applying your second deduction and then using gsp for -9r9c9 brings the puzzle down to singles so

[yzfwsf]

I think it might be like this (11=89)r1c1r9c9-(89=11)r1c9r9c1 => -1r1c48,r9c26,r48c1,r26c9.

[marek stefanik]

You might also call them a 1189 quadruple, since 89 can only appear once each, but I don't know how to notate then more explicitly (which in this case would be required).

Marek

[Cenoman]

Edit: comment re-organised and modified (Sept. 28)

Nice puzzle and nice solution. Thank you, shye for sharing !

(11=89)r1c1r9c9-(89=11)r1c9r9c1 => -1r1c48,r9c26,r48c1,r26c9.

Nice condensed writing !
There no ambiguity about (89)r1c1r9c9: both possible configurations are dealt with. (11)r1c1r9c9 is unusual, and I'd use a comma:
(1,1=89)r1c1r9c9-(89=1,1)r1c9r9c1, to focus on the distribution of digits in the set of cells. Just my own style.

shye's uncondensed writing is closer to the logic,

Hidden Text: Show

but I guess the medium term (x|yr1c9 & x|yr9c1) should read (x|y)r1c9|r9c1 (The "&" logical operand is inappropriate)

First additional minor comment: there is no reason to write an assymmetric chain.
In the first version of my comment, I focused on the central weak link of the chain. My mistake! The concern is on the side strong links:
for (xr1c1 & yr9c9) to be True, 1r1c1 AND 1r9c9 must be False, but in a non-symmetric puzzle, this is not equivalent to (1r1c1 & 1r9c9) = False. It is the same in the reverse direction: for (1r1c1 & 1r9c9) to be True, xr1c1 AND yr9c9 must be False. This condition also is met thanks to the symmetry.

The chain alone doesn't account for the whole solution. A reference to the GSP is needed. What about:
(1r1c1 & 1r9c9) =* (xr1c1 & yr9c9) - (xr1c9 & yr9c1) =* (1r1c9 & 1r9c1) => -1r1c48,r9c26,r48c1,r26c9 (*central symmetry)

Or Avoiding the x,y substitution, and borrowing yzfwsf's idea:
(1r1c1 & 1r9c9) =* (89)r1c1,r9c9 - (89)r1c9,r9c1 =* (1r1c9 & 1r9c1)=> -1r1c48,r9c26,r48c1,r26c9 (*central symmetry)

Same concern with yzfwsf condensed writing. It works thanks to the symmetry:
(11=*89)r1c1r9c9-(89=*11)r1c9r9c1 => -1r1c48,r9c26,r48c1,r26c9 (*central symmetry)
or consistently with my proposal: (1,1=*89)r1c1r9c9-(89=*1,1)r1c9r9c1 (*central symmetry)

Note: such a reference is not needed if the effects of the central symmetry have been worded before the chain.

[shye]

I think it might be like this (11=89)r1c1r9c9-(89=11)r1c9r9c1 => -1r1c48,r9c26,r48c1,r26c9.

The chain alone doesn't account for the whole solution. A reference to the GSP is needed. What about:
(1r1c1 & 1r9c9) =* (xr1c1 & yr9c9) - (xr1c9 & yr9c1) =* (1r1c9 & 1r9c1) => -1r1c48,r9c26,r48c1,r26c9 (*central symmetry)

Or Avoiding the x,y substitution, and borrowing yzfwsf's idea:
(1r1c1 & 1r9c9) =* (89)r1c1,r9c9 - (89)r1c9,r9c1 =* (1r1c9 & 1r9c1)=> -1r1c48,r9c26,r48c1,r26c9 (*central symmetry)

Same concern with yzfwsf condensed writing. It works thanks to the symmetry:
(11=*89)r1c1r9c9-(89=*11)r1c9r9c1 => -1r1c48,r9c26,r48c1,r26c9 (*central symmetry)
or consistently with my proposal: (1,1=*89)r1c1r9c9-(89=*1,1)r1c9r9c1 (*central symmetry)

awesome! this definitely makes it more digestable, thank you both for the input

how would you guys suppose to write out the deduction in the example i linked to earlier? i think substitution is easiest here, als makes this much more complicated

(x=3y)r4c12 –* (y=1x)r6c89
*central symmetry, (xy: 68)
=> -68r4c8 -68r6c2 stte

my first attempt without substitution doesnt seem sound, but ill share anyway in case it isnt too far off, or if it inspires something:

(6,8=683)r4c12 -* (168=6,8)r6c89
*central symmetry
=> -68r4c8 -68r6c2 stte

[Cenoman]

how would you guys suppose to write out the deduction in the example i linked to earlier? i think substitution is easiest here, als makes this much more complicated

(x=3y)r4c12 –* (y=1x)r6c89
*central symmetry, (xy: 68)
=> -68r4c8 -68r6c2 stte

my first attempt without substitution doesnt seem sound, but ill share anyway in case it isnt too far off, or if it inspires something:

(6,8=683)r4c12 -* (168=6,8)r6c89
*central symmetry
=> -68r4c8 -68r6c2 stte

The deduction in urhegyi's puzzle, found by marek was +7r4c8 (or equivalent: -68r4c8)
marek's solution is a demo by contradiction: (36789) in r4c128, r6c2; if r6c2 is 6, resp. 8, r4c8 is 8, resp. 6 => digit 3 only left for r4c12, contradiction.

To put this into a chain, let's use symmetric cells (as you do in your attempts). Noticing that 3 is locked in r4c12 and 1 is locked in r6c89, for ALS's r4c12 and r6c89 we have: (3x)r4c12 = (3y)r4c12 and (1x)r6c89 = (1y)r6c89.
Now, using the central sysmmetry: (1y)r6c89 is True if and only if (3x)r4c12 is True (and similarly when swapping x <-> y)
So the above ALS strong links can be written: (3xr4c12 & 1yr6c89) =* (3yr4c12 & 1xr6c89) (* central symmetry) => -xy r4c8, r6c2

As the substitution brings no simplification, I'd rather write: (36r4c12 & 18r6c89) =* (38r4c12 & 16r6c89) (* central symmetry) => -68 r4c8, r6c2

[shye]

As the substitution brings no simplification, I'd rather write: (36r4c12 & 18r6c89) =* (38r4c12 & 16r6c89) (* central symmetry) => -68 r4c8, r6c2

wonderful! this is so much clearer, thank you っ´ω`c) simpler than i was making it out to be