The New Sudoku Players' Forum

[jovi_al01]

hello all! this puzzle is one i've spent the last few days working on. i'm quite happy with it!

Code: Select all

.-------.-------.-------.
| . . 2 | 3 . . | 5 . . |
| . 1 . | . 4 . | . 9 . |
| . . . | 5 . . | . . 6 |
+-------+-------+-------+
| . 7 6 | . . . | . . . |
| 8 . . | . 2 . | . 4 . |
| 9 . . | . . . | 8 . 3 |
+-------+-------+-------+
| . . . | . . 5 | . . 2 |
| . . . | . . 6 | . 1 . |
| . . . | 8 7 . | . . . |
'-------'-------'-------'

very interested to see your solutions!

[shye]

this one is an absolute gem to me! very familiar patterns

Code: Select all

.---------------------------.----------------------.--------------------.
| 467      4689     2       | 3      1689   1789   | 5      78    14    |
| 3567     1        3578    | 267    4      278    | 23     9     78    |
| 347      3489     34789   | 5      189    12789  | 14     23    6     |
:---------------------------+----------------------+--------------------:
|#1234-5   7        6       |*149   *13589 #34-189 | 129    25    159   |
| 8        35       135     | 1679   2     *1379   | 1679   4     1579  |
| 9        245      145     | 167-4  156   *147    | 8      2567  3     |
:---------------------------+----------------------+--------------------:
|*13467    34689    34789-1 | 149    139    5      | 34679  3678  2     |
|*23457    34589-2  345789  | 249    39     6      | 3479   1     45789 |
|#12-3456 *234569  *13459   | 8      7     #1234-9 | 3469   356   459   |
'---------------------------'----------------------'--------------------'

8 Truths = {34R4 12R9 12C1 34C6}
8 Links = {49n1 49n6 34b5 12b7}
-189r4c6 -3456r9c1 -1r7c3 -2r8c2 -4r6c4 -5r4c1 -9r9c6
stte

decided to use xsudo for this one, slowly learning how to work with it ヽ(´▽`)/

[jovi_al01]

that's my solution too, shye! (i think-- i don't understand the notation all that well, but it looks like you got the same eliminations i did )
this one was inspired by some of your recent work! thanks for being a wonderful muse and thank you for the kind words!

[shye]

a less intimidating looking solution, which does the same thing:

unorthodox quadruple
at least one of r4c1, r9c1 & r9c6 must be a 1 (else repeat 1 in b7)
at least one of r4c1, r9c1 & r9c6 must be a 2 (else repeat 2 in b7)
at least one of r4c1, r4c6 & r9c6 must be a 3 (else repeat 3 in b5)
at least one of r4c1, r4c6 & r9c6 must be a 4 (you get the picture)
4 cells for 4 candidates, all others removed

[Cenoman]

this puzzle is one i've spent the last few days working on. i'm quite happy with it!

Thanks for sharing !

a less intimidating looking solution, which does the same thing:

unorthodox quadruple
at least one of r4c1, r9c1 & r9c6 must be a 1 (else repeat 1 in b7)
at least one of r4c1, r9c1 & r9c6 must be a 2 (else repeat 2 in b7)
at least one of r4c1, r4c6 & r9c6 must be a 3 (else repeat 3 in b5)
at least one of r4c1, r4c6 & r9c6 must be a 4 (you get the picture)
4 cells for 4 candidates, all others removed

Awsome !

Here is a "classical" solution in four steps (much less attractive )

Code: Select all

 +-----------------------------+-------------------------+-------------------------+
 |  467      4689     2        |  3    Dd1689    1789    |  5       78     14      |
 |Bb56-73    1      Ab35-78    |Cc267    4       278     | a23      9      78      |
 |  347      3489     34789    |  5      189     12789   |  14     g23     6       |
 +-----------------------------+-------------------------+-------------------------+
 | F1234-5   7        6        |  149  Ef13589  E13489   |  129    g25     19-5    |
 |  8       G35       13-5     |  1679   2       1379    |  1679    4      1579    |
 |  9        245      145      |  1467 Ee56-1    147     |  8       567-2  3       |
 +-----------------------------+-------------------------+-------------------------+
 |  13467    34689    134789   |  149    139     5       |  34679   3678   2       |
 |  23457    234589   345789   |  249    39      6       |  3479    1      45789   |
 |  123456   234569   13459    |  8      7       12349   |  3469    356    459     |
 +-----------------------------+-------------------------+-------------------------+

1. (3)r2c7 = (35-6)r2c13 = r2c4 - r1c5 = (6-5)r6c5 = r4c5 - (5=23)r34c8 loop => -7 r2c13, -8r2c3, -1 r6c5, -5 r4c19, -2 r6c8
2. (5)r2c3 = (5-*6)r2c1 = r2c4 - r1c5 = (658-3)b5p238 = r4c1* - (3=5)r5c2 => -5 r5c3, -3r2c1*

Code: Select all

 +------------------------------+-------------------------+-------------------------+
 |    467      4689    2        |  3      1689    1789    |  5       78     14      |
 |    56       1       5-3      |  267    4       278     | f23      9      78      |
 |    347      3489    34789    |  5      189     12789   |  14      23     6       |
 +------------------------------+-------------------------+-------------------------+
 |   E134      7       6        |De149    13589 Cd13489   | e129     25   De19      |
 |    8        35    Fa13       |  1679   2       1379    |  1679    4      1579    |
 |    9        2      F145      |  1467   56    Cd147     |  8       567    3       |
 +------------------------------+-------------------------+-------------------------+
 |    13467    34689   134789   |  149    139     5       |  34679   3678   2       |
 |    23457    34589   345789   |  249    39      6       |  3479    1      45789   |
 | HAc12346-5  34569 Gb13459    |  8      7    HBc12349   |  3469    356    459     |
 +------------------------------+-------------------------+-------------------------+

3. (3=1)r5c3-r9c3=(12-4)r9c16=r46c6-(4=192)r4c479-(2=3)r2c7 =>-3r2c3
4. (2)r9c1=(2-4)r9c6=r46c6-(4=91)r4c49-r4c1=r56c3-r9c3=(12)r9c16 =>-5r9c1; ste

[eleven]

unorthodox quadruple

Great solution !

Here is a complex alternative:
Note the ALS's 12349 in r78c45 (#) and 1259 in r4c789 (@).

Code: Select all

 *---------------------------------------------------------------------------------*
 |  467      4689     2        |  3      1689    1789    |  5       78     14      |
 |  3567     1        3578     |  267    4       278     |  23      9      78      |
 |  347      3489     34789    |  5      189     12789   |  14      23     6       |
 |-----------------------------+-------------------------+-------------------------|
 | B1234-5   7        6        | A149    8-1359  348-19  | @129    @25    @159     |
 |  8        35       135      |  1679   2       1379    |  1679    4      1579    |
 |  9        245      145      |  167-4  156     147     |  8       2567   3       |
 |-----------------------------+-------------------------+-------------------------|
 | x13467    34689    134789   | #149   #139     5       |  34679   3678   2       |
 | y23457    234589   345789   | #249   #39      6       |  3479    1      45789   |
 | *123456   234569   13459    |  8      7       1249-3  |  3469    356    459     |
 *---------------------------------------------------------------------------------*

If 4 in #, then (19 in r4c4) 1259 in r4c4789 and 12 (not in r5c1) in r789c1: one of them missing in # -> 3r78c5
If 4 not in #, but 1239 => (hidden pair) 12r59c1 -> 1259 in r4c1789 and 3r78c5, 4r4c4
=> -1359r4c5, -19r4c6, -5r5c1, -4r6c4, -3r9c6; stte

[Edit:] Cenoman pointed out, that these elimantions are not enough for ste or bte, thanks.

However this can be repaired:
In the first case 12 are in r789c1, and not both can be in r78c1 (leaving only 3 digits in #), so we get 12r9c1
In the second case we have the hidden pair 12r59c1.
So also 3456r9c1 can be eliminated.

So we have
- 4r78c4, 1259 r4c4789, 3r78c5, 12r9c1 or
- 12r59c1, 1259 r4c1789, 4r4c4, 3r78c5

[jovi_al01]

beautiful solution as well! thank you for spending time on this )

[denis_berthier]

.
SER = 8.5

Code: Select all

Resolution state after Singles and whips[1]:
   +----------------------+----------------------+----------------------+
   ! 467    4689   2      ! 3      1689   1789   ! 5      78     1478   !
   ! 3567   1      3578   ! 267    4      278    ! 237    9      78     !
   ! 347    3489   34789  ! 5      189    12789  ! 12347  2378   6      !
   +----------------------+----------------------+----------------------+
   ! 12345  7      6      ! 149    13589  13489  ! 129    25     159    !
   ! 8      35     135    ! 1679   2      1379   ! 1679   4      1579   !
   ! 9      245    145    ! 1467   156    147    ! 8      2567   3      !
   +----------------------+----------------------+----------------------+
   ! 13467  34689  134789 ! 149    139    5      ! 34679  3678   2      !
   ! 23457  234589 345789 ! 249    39     6      ! 3479   1      45789  !
   ! 123456 234569 13459  ! 8      7      12349  ! 3469   356    459    !
   +----------------------+----------------------+----------------------+

1) simplest-first solution, in S+W6: Show

naked-pairs-in-a-block: b3{r1c8 r2c9}{n7 n8} ==> r3c8≠8, r3c8≠7, r3c7≠7, r2c7≠7, r1c9≠8, r1c9≠7
naked-pairs-in-a-block: b3{r2c7 r3c8}{n2 n3} ==> r3c7≠3, r3c7≠2
finned-swordfish-in-columns: n2{c7 c4 c1}{r4 r2 r8} ==> r8c2≠2
biv-chain[3]: r6n2{c2 c8} - r4c8{n2 n5} - b5n5{r4c5 r6c5} ==> r6c2≠5
z-chain[3]: c4n7{r6 r2} - b3n7{r2c9 r1c8} - r6n7{c8 .} ==> r5c6≠7
t-whip[4]: c5n5{r6 r4} - r4n8{c5 c6} - r4n3{c6 c1} - r5c2{n3 .} ==> r6c3≠5
t-whip[5]: r2n6{c1 c4} - c5n6{r1 r6} - c5n5{r6 r4} - r4n8{c5 c6} - r4n3{c6 .} ==> r2c1≠3
biv-chain[4]: r4c8{n5 n2} - b3n2{r3c8 r2c7} - r2n3{c7 c3} - b1n5{r2c3 r2c1} ==> r4c1≠5
whip[1]: b4n5{r5c3 .} ==> r5c9≠5
whip[5]: r4n8{c5 c6} - b5n3{r4c6 r5c6} - r5c2{n3 n5} - r5c3{n5 n1} - b6n1{r5c7 .} ==> r4c5≠1
whip[5]: r4n8{c6 c5} - b5n3{r4c5 r5c6} - r5c2{n3 n5} - r5c3{n5 n1} - b6n1{r5c7 .} ==> r4c6≠1
biv-chain[6]: r3c8{n2 n3} - r2n3{c7 c3} - b1n5{r2c3 r2c1} - r2n6{c1 c4} - c5n6{r1 r6} - r6n5{c5 c8} ==> r6c8≠2
hidden-single-in-a-row ==> r6c2=2
biv-chain[3]: c1n2{r9 r8} - c4n2{r8 r2} - r2n6{c4 c1} ==> r9c1≠6
t-whip[4]: c1n2{r9 r8} - c4n2{r8 r2} - r2n6{c4 c1} - c1n5{r2 .} ==> r9c1≠4, r9c1≠3, r9c1≠1
finned-x-wing-in-rows: n1{r9 r6}{c3 c6} ==> r5c6≠1
z-chain[3]: r6c3{n4 n1} - r9n1{c3 c6} - c6n4{r9 .} ==> r6c4≠4
t-whip[4]: r5c6{n9 n3} - r4n3{c6 c1} - c1n1{r4 r7} - b8n1{r7c4 .} ==> r9c6≠9
t-whip[4]: r6c3{n4 n1} - r9n1{c3 c6} - b8n2{r9c6 r8c4} - b8n4{r8c4 .} ==> r7c3≠4
z-chain[5]: r5c6{n9 n3} - r4n3{c6 c1} - c1n1{r4 r7} - r7c5{n1 n3} - r8c5{n3 .} ==> r4c5≠9
z-chain[5]: r9n1{c6 c3} - r6c3{n1 n4} - c6n4{r6 r4} - r4n8{c6 c5} - c5n3{r4 .} ==> r9c6≠3
whip[1]: c6n3{r5 .} ==> r4c5≠3
z-chain[5]: c5n5{r6 r4} - r4n8{c5 c6} - r4n3{c6 c1} - c1n1{r4 r7} - c4n1{r7 .} ==> r6c5≠1
t-whip[5]: b8n2{r8c4 r9c6} - r9n1{c6 c3} - b4n1{r5c3 r4c1} - r4n3{c1 c6} - r4n4{c6 .} ==> r8c4≠4
t-whip[5]: r4n3{c6 c1} - c1n1{r4 r7} - b8n1{r7c4 r9c6} - b8n4{r9c6 r7c4} - r4n4{c4 .} ==> r4c6≠9, r4c6≠8
singles ==> r4c5=8, r6c5=5, r1c5=6, r2c1=6, r2c3=5, r2c7=3, r3c8=2, r4c8=5, r4c7=2, r5c2=5
hidden-pairs-in-a-block: b7{n2 n5}{r8c1 r9c1} ==> r8c1≠7, r8c1≠4, r8c1≠3
finned-swordfish-in-columns: n1{c5 c7 c1}{r7 r3 r5} ==> r5c3≠1
stte

2) 3-step solution in W8, using my recent fewer steps algorithm (http://forum.enjoysudoku.com/reducing-the-number-of-steps-t39234.html)
This is the first solution it finds [the next 2 solutions in W8 were also 3-step, and I stopped it there]
=====> STEP #1
whip[8]: r4n8{c5 c6} - r4n3{c6 c1} - r4n4{c1 c4} - c6n4{r6 r9} - b8n2{r9c6 r8c4} - c1n2{r8 r9} - r9n1{c1 c3} - b4n1{r5c3 .} ==> r4c5≠5
singles ==> r6c5=5, r1c5=6, r2c1=6, r2c3=5,> r2c7=3
whip[1]: b3n2{r3c8 .} ==> r3c6≠2
=====> STEP #2
hidden-pairs-in-a-block: b3{n1 n4}{r1c9 r3c7} ==> r3c7≠2, r3c7≠7, r1c9≠8, r1c9≠7
singles ==> r3c8=2, r4c8=5, r5c2=5, r4c7=2, r6c2=2
=====> STEP #3
biv-chain[5]: b3n7{r1c8 r2c9} - r2c4{n7 n2} - r8n2{c4 c1} - r8n5{c1 c9} - b9n8{r8c9 r7c8} ==> r7c8≠7, r1c8≠8
stte

[jco]

I found a solution in 3 (non-basic) steps.
It took me a long time to find step 2 (looking carefully at eleven's solution helped).

After basics

Code: Select all

.------------------------------------------------------------------------.
| 467     4689    2      |  3     d1689    1789  |  5       78     14    |
| 3567    1       3578   | e267    4      e278   | f23      9     e78    |
| 347     3489    34789  |  5      189     12789 |  14      23     6     |
|------------------------+-----------------------+-----------------------|
| 1345-2  7       6      |  149   b13589   13489 | g129    a25     159   |
| 8       35      135    |  1679   2       1379  |  1679    4      1579  |
| 9       245     145    |  1467  c156     147   |  8       567-2  3     |
|------------------------+-----------------------+-----------------------|
| 13467   34689   134789 |  149    139     5     |  34679   3678   2     |
| 23457   234589  345789 |  249    39      6     |  3479    1      45789 |
| 123456  234569  13459  |  8      7       12349 |  3469    356    459   |
'------------------------------------------------------------------------'


1. (2=5)r4c8 - r4c5 = (5-6)r6c5 = r1c5 - r12c1 = (65-3)r2c13 = (3-2)r2c7 = r4c7 => -2 r4c1, r6c8 [1 placement]

Code: Select all

.--------------------------------------------------------------------------.
|  467      4689    2      |  3    la189+6   1789  |  5       78     14    |
|  3567     1       3578   |  267    4       278   |  23      9      78    |
|  347      3489    34789  |  5      189     12789 |  14      23     6     |
|--------------------------+-----------------------+-----------------------|
| j1345     7       6      | e149  jc13589  j13489 | d129    d25    d159   |
|  8        35     i135    |  1679   2       1379  |  1679    4      1579  |
|  9        2      i145    |  1467 kb156     147   |  8       567    3     |
|--------------------------+-----------------------+-----------------------|
|  13467    34689   134789 | f149    139     5     |  34679   3678   2     |
|  23457    34589   345789 | f249    39      6     |  3479    1      45789 |
| g123456   34569  h13459  |  8      7      g12349 |  3469    356    459   |
'--------------------------------------------------------------------------'

2. (6)r1c5=(6-5)r6c5=r4c5-(5=219)r4c789-(1|9=4)r4c4-(4)r78c4=(42-1)r9c16=r9c3-r56c3=(138-5)r4c156=(5-6)r6c5=(6)r1c5
=> +6 r1c5 [9 placements and eliminations by HP(25)r89c1]

Code: Select all

.------------------------------------------------------------------.
|  47    489    2      |  3     6     1789  | 5     a7-8     14    |
|  6     1      5      | c27    4     278   | 3      9      b78    |
|  347   3489   34789  |  5     189   1789  | 14     2       6     |
|----------------------+--------------------+----------------------|
|  134   7      6      |  149   1389  13489 | 2      5       19    |
|  8     5      13     |  1679  2     1379  | 1679   4       179   |
|  9     2      14     |  1467  5     147   | 8      67      3     |
|----------------------+--------------------+----------------------|
|  1347  34689  134789 |  149   139   5     | 4679  g368-7   2     |
| e25    3489   34789  | d249   39    6     | 479    1      f45789 |
|  25    3469   1349   |  8     7     12349 | 469    36      459   |
'------------------------------------------------------------------'

3. (7)r1c8 = r2c9 - (7=2)r2c4 - r8c4 = (2-5) r8c1 = (5-8) r8c9 = (8) r7c8 => -7 r7c8, -8 r1c8; ste

Edit: insert explicit mention to my numbering of moves.

[denis_berthier]

I found a solution in 3 steps.
It took me a long time to find step 2 (looking carefully at eleven's solution helped).
After basics

Code: Select all

.------------------------------------------------------------------------.
| 467     4689    2      |  3     d1689    1789  |  5       78     14    |
| 3567    1       3578   | e267    4      e278   | f23      9     e78    |
| 347     3489    34789  |  5      189     12789 |  14      23     6     |
|------------------------+-----------------------+-----------------------|
| 1345-2  7       6      |  149   b13589   13489 | g129    a25     159   |
| 8       35      135    |  1679   2       1379  |  1679    4      1579  |
| 9       245     145    |  1467  c156     147   |  8       567-2  3     |
|------------------------+-----------------------+-----------------------|
| 13467   34689   134789 |  149    139     5     |  34679   3678   2     |
| 23457   234589  345789 |  249    39      6     |  3479    1      45789 |
| 123456  234569  13459  |  8      7       12349 |  3469    356    459   |
'------------------------------------------------------------------------'

Well, not really 3 steps, as two pairs eliminate 6 candidates before the start and you have one more HP after step 2.
So, in my view, that makes 6 steps - including one of length 17.

[jovi_al01]

simon did this puzzle on Cracking The Cryptic!
https://www.youtube.com/watch?v=rxxn0F1TPe0