The New Sudoku Players' Forum

[JoWovrin]

Code: Select all

+-------+-------+-------+
! . . 6 ! 7 . 9 ! . . . !
! . . . ! . 8 . ! . . . !
! 4 . . ! . . . ! 5 . . !
+-------+-------+-------+
! . 3 . ! . . 6 ! . 9 . !
! 2 . . ! . 1 . ! . . 8 !
! . 1 . ! . . . ! . 7 . !
+-------+-------+-------+
! . . 5 ! . . . ! . . 6 !
! . 9 . ! . 2 . ! . . . !
! . . . ! 1 . 3 ! 4 . . !
+-------+-------+-------+
..67.9.......8....4.....5...3...6.9.2...1...8.1.....7...5.....6.9..2.......1.34..
SE Rating 8.5


This is my first post on this forum, let me know if I screwed something up!
Should be almost one-step require only one tough step, this is SE SKFR 8.5 because the intended step is a weird one

[P.O.]

Hi JoWovrin, here the solution i found: three chains in the first state of the grid then a single and two intersections; but probably not the solution you were thinking of.

Code: Select all

1358    258        6       7       345     9       1238    12348   1234             
d1357-9  257        12379   23456   8       1245   c12367+9 12346   123479           
 4       278        123789  236     36      12      5       12368   12379           
 578     3          478     2458    457     6       12      9       1245             
 2     ea±4+6×(57)  479     3459    1       457     36      3456    8               
d568+9   1          489     234589  3459    2458    236     7       2345             
 1378   a2+478      5      b4(89)  b4(79)  b4(78)  c12378-9 1238    6               
 13678   9          13478   4568    2       4578    1378    1358    1357             
 678     2678       278     1       5679    3       4       258     2579             

c2n4{r5 r7} - r7{c4c5c6}{n7n8n9} - c7n9{r7 r2} - c1n9{r2 r6} - b4n6{r6c1 r5c2} => r5c2 <> 5,7

  1358       258     6       7       345     9       1238    12348   1234             
 a1357+9     257     12379   23456   8       1245   b12367-9 12346   123479           
  4          278     123789  236     36      12      5       12368   12379           
  578        3       478     2458    457     6       12      9       1245             
  2         d+4567   479     3459    1       457     36      3456    8               
ea+6±9×(58)  1       489     234589  3459    2458    236     7       2345             
  1378      d2-478   5      c(48)9  c(47)9  c(478)  b12378+9 1238    6               
  13678      9       13478   4568    2       4578    1378    1358    1357             
  678        2678    278     1       5679    3       4       258     2579       

c1n9{r6 r2} - c7n9{r2 r7} - r7{c4c5c6}{n4n7n8} - c2n4{r7 r5} - b4n6{r5c2 r6c1} => r6c1 <> 5,8

1358    258       6       7       345     9       1238    12348   1234             
13579   257       12379   23456   8       1245    123679  12346   123479           
4       278      c12378-9 236     36      12      5       12368  c1237+9           
578     3        b4(78)   2458    457     6       12      9       1245             
2      a+4567    b4(79)   3459    1       457     36      3456    8               
5689    1        b4(89)   234589  3459    2458    236     7       2345             
1378   a2±4×(78)  5      e(48)9  e(47)9  e(478)   123789  1238    6               
13678   9         13478   4568    2       4578    1378    1358    1357             
678     2678      278     1      d567+9   3       4       258    d257-9             

c2n4{r7 r5} - c3{r4r5r6}{n7n8n9} - r3n9{c3 c9} - r9n9{c9 c5} - r7{c4c5c6}{n4n7n8} => r7c2 <> 7,8

single: n5r4c1
c3n7{r4 r5} => r2c3 r3c3 r8c3 r9c3 <> 7
c3n8{r4 r6} => r3c3 r8c3 r9c3 <> 8
ste.



[denis_berthier]

.
Hi JoWovrin
welcome on this forum

Code: Select all

Resolution state after Singles (and whips[1]):
   +----------------------+----------------------+----------------------+
   ! 1358   258    6      ! 7      345    9      ! 1238   12348  1234   !
   ! 13579  257    12379  ! 23456  8      1245   ! 123679 12346  123479 !
   ! 4      278    123789 ! 236    36     12     ! 5      12368  12379  !
   +----------------------+----------------------+----------------------+
   ! 578    3      478    ! 2458   457    6      ! 12     9      1245   !
   ! 2      4567   479    ! 3459   1      457    ! 36     3456   8      !
   ! 5689   1      489    ! 234589 3459   2458   ! 236    7      2345   !
   +----------------------+----------------------+----------------------+
   ! 1378   2478   5      ! 489    479    478    ! 123789 1238   6      !
   ! 13678  9      13478  ! 4568   2      4578   ! 1378   1358   1357   !
   ! 678    2678   278    ! 1      5679   3      ! 4      258    2579   !
   +----------------------+----------------------+----------------------+
233 candidates.

The puzzle is in W5.

It has a solution with "only one hard step" in gW6:

Code: Select all

g-whip[6]: c2n4{r7 r5} - b4n6{r5c2 r6c1} - b4n5{r6c1 r4c1} - b4n8{r4c1 r456c3} - r9c3{n8 n7} - b4n7{r4c3 .} ==> r7c2≠2
whip[1]: r7n2{c8 .} ==> r9c8≠2, r9c9≠2
hidden-triplets-in-a-row: r7{n1 n2 n3}{c1 c7 c8} ==> r7c7≠9, r7c8≠8, r7c7≠8, r7c7≠7, r7c1≠8, r7c1≠7
stte


Is that the one you expected?

[Cenoman]

Code: Select all

 +--------------------------+-------------------------+----------------------------+
 |  1358    258    6        |  7        345    9      |  1238     12348   1234     |
 |  13579   257   c12379    |  23456    8      1245   |  123679   12346   123479   |
 |  4       278   c123789   |  236      36     12     |  5        12368   12379    |
 +--------------------------+-------------------------+----------------------------+
 |  578     3      478      |  2458     457    6      |  12       9       1245     |
 |  2       4567   479      |  3459     1      457    |  36       3456    8        |
 |  5689    1      489      |  234589   3459   2458   |  236      7       2345     |
 +--------------------------+-------------------------+----------------------------+
 |  1378  eb478-2  5        |ea48+9   ea47+9 ea478    |  123789   1238    6        |
 |  13678   9     c13478    |  4568     2      4578   |  1378     1358    1357     |
 |  678     2678  d278      |  1        5679   3      |  4        258     2579     |
 +--------------------------+-------------------------+----------------------------+

There is a very simple chain (using one AHS in c3), solving the puzzle with lclste finish:
(4)r7c2 = (413-2)r238c3 = (2)r9c3 => -2 r7c2; lclste
Variants with ALS'S

Hidden Text: Show

(4)r7c2 = r5c2 - (4=7892)r4569c3 => -2 r7c2; lclste
...up to the ugly ALS XZ rule: (2=56784)r12359c2 - (4=7892)r4569c3 => -2 r7c2; lclste

For ste finish, the above AIC can be extended each side with overlapping ALS's (tagged a, e)
(9=784)r7c456 - r7c2 = (413-2)r238c3 = r9c3 - (2=4789)r7c2456 => +9 r7c45; ste (-9 r7c7)
Variants:

Hidden Text: Show

- with AHS's only:
(1234)r7c1278 = (413-2)r238c3 = r9c3 - r7c2 = (213)r7c178 => -9 r7c7; ste
- with ALS's
(9=784)r7c456 - r7c2 = r5c2 - (4=7892)r4569c3 - (2=4789)r7c2456 => -9 r7c7; ste

[AnotherLife]

Hi JoWovrin,
This puzzle has a nice solution based on a continuous nice loop with almost locked sets. The first move leads to 24 eliminations and a sequence of singles.

Code: Select all

.-------------------------.-----------------------.------------------------.
| 1358   258     6        | 7       345     9     | 1238    12348  1234    |
| 13579  257     123-79   | 23456   8       1245  | 123679  12346  12347-9 |
| 4      278     e1239-78 | 236     36      12    | 5       12368  f12379  |
:-------------------------+-----------------------+------------------------:
| 5-78   3       d478     | 2458    457     6     | 12      9      1245    |
| 2      c456-7  d479     | 3459    1       457   | 36      3456   8       |
| 569-8  1       d489     | 234589  3459    2458  | 236     7      2345    |
:-------------------------+-----------------------+------------------------:
| 13-78  b24-78  5        | a489    a479    a478  | 1239-78 123-8  6       |
| 13678  9       134-78   | 456-8   2       45-78 | 1378    1358   1357    |
| 678    2678    2-78     | 1       h569-7  3     | 4       258    g2579   |
'-------------------------'-----------------------'------------------------'


Continuous nice loop with two ALS's:
(9=4)r7c456 - r7c2 = r5c2 - (4=9)r456c3 - r3c3 = r3c9 - r9c9 = r9c5 - (9=4)r7c456 => -78 r7c127, r8c6, -8 r7c8, r8c4, -7 r9c5 (because 7&8 are locked in ALS r7c456); -78 r389c3, -7 r2c3, -78 r4c1, -7 r5c2, -8 r6c1 (because 7&8 are locked in ALS r456c3); -9 r2c3, -9 r2c9; ste

_____________________________________________
EDIT
I added some more eliminations by the above step.

[JoWovrin]

Hi JoWovrin, here the solution i found: three chains in the first state of the grid then a single and two intersections; but probably not the solution you were thinking of.

That was not what I was thinking of, I like the chains though.

Is that the one you expected?

That was also not what I was thinking of.

There is a very simple chain (using one AHS in c3), solving the puzzle with lclste finish:
(4)r7c2 = (413-2)r238c3 = (2)r9c3 => -2 r7c2; lclste

I found a similar chain later after sharing the puzzle, not what I initially intended though.

I am unsure how to properly notate my intended step , so I will just explain it in words.

Hidden Text: Show

In r7 and c3 there have to be 6 instances of {123} total, since r7c3 is a given 5. There are also 6 instances of {789} in r3 and c7 total. There are 12 instances total of {123789} yet to be found in r37 and c37. Box 7 can only take a maximum of 3 instances of {123} and box 3 can only take a maximum of 3 instances of {789}. The remaining 6 cells in r37 and c37 (r2c3, r3c2 r3c3, r7c7 r7c8, r8c7) can only take a total of 6 instances of {123789}, therefore we can conclude that all three instances of {123} in box 7 are in r7/c3, and all three instances of {789} in box 3 are in r3/c7. This gives a naked 678 tripple in box 7, after singles in b7 one last tripple in r7c456 makes it ste.

Note that there are some more eliminations this pattern makes, which are not needed to solve it (like r3c2 and r8c7 being {78}).

[JoWovrin]

(9=4)r7c456 - r7c2 = r5c2 - (4=9)r456c3 - r3c3 = r3c9 - r9c9 = r9c5 - (9=4)r7c456 => -78 r7c127, -8 r7c8 (7&8 are locked in ALS r7c456); -78 r389c3, -7 r2c3, -78 r4c1, -7 r5c2, -8 r6c1 (7&8 are locked in ALS r456c3); -9 r2c3, -9 r2c9; ste

That's a really cool loop, nice spot!

[eleven]

Similar to Cenoman for ste:

Code: Select all

+-----------+-----------+-----------+
!  .  .  6  !  7  .  9  !  .  .  .  !
!  .  .  y  !  .  8  .  !  .  .  .  !
!  4  .  y  !  .  .  .  !  5  .  .  !
+-----------+-----------+-----------+
!  . *3  .  !  .  .  6  !  .  9  .  !
! *2  .  .  !  .  1  .  !  .  .  8  !
!  . *1  .  !  .  .  .  !  .  7  .  !
+-----------+-----------+-----------+
!  x  -  5  !  .  .  .  !  x  x  6  !
!  .  9  y  !  . *2  .  !  .  .  .  !
!  .  .  -  ! *1  . *3  !  4  .  .  !
+-----------+-----------+-----------+

123r7c178 = 2r7c2 - r9c3 = (123-4)r238c4 = (4-2)r7c2 = 123r7c178 => -2r7c2, -789r7c178, stte

[marek stefanik]

Hi JoWovrin,

Welcome to the forum!

My solution was very similar to what others have found, so I'll at least add a few eliminations.

Code: Select all

.---------------------.--------------------.-----------------------.
| 1358   258   6      | 7       345   9    | 1238    1234–8 1234   |
| 13579  257  #123–79 | 23456   8     1245 | 123679  12346  1234–79|
| 4     #78–2 #1239–78| 236     36    12   | 5       12368  12379  |
:---------------------+--------------------+-----------------------:
| 578    3     478    | 2458    457   6    | 12      9      1245   |
| 2      4567  479    | 3459    1     457  | 36      3456   8      |
| 5689   1     489    | 234589  3459  2458 | 236     7      2345   |
:---------------------+--------------------+-----------------------:
| 1378   2478  5      | 489     479   478  |#1239–78#123–8  6      |
| 678–13 9     13478  | 4568    2     4578 |#78–13   1358   1357   |
| 678    678–2 278    | 1       5679  3    | 4       258    2579   |
'---------------------'--------------------'-----------------------'

#-marked cells must contain each of 123789 at least once (123r7c3\b7, 789r3c7\b3) => remote sextuple, remote pair 78r3c2 r8c7, eliminations in b37

Marek

[JoWovrin]

Thank you everyone for the many slightly different ways of solving this, I found all of them interesting!

#-marked cells must contain each of 123789 at least once (123r7c3\b7, 789r3c7\b3) => remote sextuple, remote pair 78r3c2 r8c7, eliminations in b37

This was what I tried building this puzzle around

[marek stefanik]

I missed the explanation above.

You can use Xsudo's notation for this one, but it is difficult to read for many people.

The idea is (exactly as you described it) that 123r7 123c3 789r3 789c7 (the truths) can be entirely covered by 123b7 789b3 and the cells (the links).
Since the number of truths is the same as the number of links, you can eliminate all candidates covered by the links that aren't part of the truths (basically the same as base\cover sets of fish).

12 Truths = {123R7 123C3 789R3 789C7}
12 Links = {123b7 789b3 2n3 3n23 7n78 8n7}
(xny means rxcy)

If you paste it in Xsudo, you'll see that it also finds the eliminations in r3c3 and r7c7, even though the logic I described doesn't work for them (it uses brute-force to find the eliminations).
In this case you can just split the pattern in two:

8 Truths = {123R7 123C3 9R3 9C7}
8 Links = {123b7 9b3 23n3 7n78}

And after that:

4 Truths = {78R3 78C7}
4 Links = {78b3 3n2 8n7}

Now every elimination is justified.

Marek

[eleven]

(xny means rxcy)

Thanks for the hint, at least i can read the notation now.
However i saw the eliminations without it: since each digit must be in the 6 cells (123 in r23c3 and r7c78, 789 in r3c23 and r78c7), you can eliminate all, which would force 2 of them there.