The New Sudoku Players' Forum

[icecream17]

On the Andrew Stuart solver I clicked on "Solution count" and the solver said "Too few clues/solutions, normal sudokus have 17 minimum"

Normal sudokus? Hmm...

After overthinking this, I present... a sudoku with 0 givens!!!!

(454 candidates possible, 275 candidates removed)

Code: Select all

+-------------------------------+-------------------------+--------------------------------+
| 348       14689     24569     | 245789  125689  12568   | 123456789 236789    12345689   |
| 123456789 123456789 124689    | 47      123569  123459  | 3468      12489     478        |
| 123467    1234689   13456789  | 12359   2358    1357    | 24567     689       45789      |
+-------------------------------+-------------------------+--------------------------------+
| 12357     1235789   12369     | 13579   1456789 12457   | 12467     123458    2346789    |
| 1235      13567     235678    | 2346789 2456789 234567  | 135678    145689    123689     |
| 14789     13569     236789    | 345678  145789  12347   | 123456789 235689    25679      |
+-------------------------------+-------------------------+--------------------------------+
| 23458     46789     124567    | 56789   23589   1246    | 16789     123456789 12346789   |
| 246       135678    39        | 134578  59      235689  | 12347     1389      1789       |
| 156789    28        1348      | 2346789 23568   23469   | 123456789 123456789 123456789  |
+-------------------------------+-------------------------+--------------------------------+


Remember how the minimum sudoku has 17 clues?

I wonder: what's the minimum amount of (eliminated) candidates needed to make a valid sudoku?

_________
Postscript:
I just realized that 17 cell sudokus only need 17*9 = 153 candidate eliminations

So here's an improved to (617 possible, 112 eliminated)

Code: Select all

+--------------------------------+--------------------------------+--------------------------------+
| 123456789 123456789 123456789  | 123456789 145       1          | 123456789 123456789 23456789   |
| 123456789 46        123456789  | 123456789 123456789 123456789  | 236       123456789 123456789  |
| 123456789 123456789 123456789  | 123456789 123456789 123456789  | 123456789 123456789 123456789  |
+--------------------------------+--------------------------------+--------------------------------+
| 23567     2467      123456789  | 56        123456789 123456789  | 123456789 123456789 123456789  |
| 123456789 123456789 123456789  | 123456789 145       123456789  | 123456789 14        1          |
| 57        123456789 123456789  | 123456789 123456789 123456789  | 123456789 123456789 123456789  |
+--------------------------------+--------------------------------+--------------------------------+
| 123456789 123456789 123456789  | 26        123456789 123456789  | 23        123456789 123456789  |
| 123456789 145       1458       | 123456789 123456789 123456789  | 123456789 123456789 123456789  |
| 15        123456789 1          | 123456789 123456789 123456789  | 123456789 123456789 123456789  |
+--------------------------------+--------------------------------+--------------------------------+


[Mathimagics]

Hello icecream17!

I am sorry for the delay responding to your post, it kind of slipped past me ...

These puzzles are called "Sukaku" or "PencilMark Sudoku" ... not my area of expertise, but I seem to recall that valid puzzles exist with just 86 clues (that is, 86 eliminated candidates).

You might like to check out this thread: http://forum.enjoysudoku.com/pencilmark-sudoku-t36694.html

Cheers
MM

[1to9only]

There is also the thread started by Ruud in 2016: http://forum.enjoysudoku.com/pencilmark-only-sudoku-t4929.html

[denis_berthier]

.
One point not to forget is, some sukakus cannot be obtained by partially solving a sudoku and can be much harder than any known sudoku.
Apart from this, they have to satisfy the same constraints and the same resolution rules apply to them - which implies they are not in and of themselves a topic of interest for puzzle solvers. But they may be a topic for other studies.

The number of clues has a slight impact on the mean complexity of Sudoku puzzles (see [PBCS] for details). In particular, 17-clue puzzles are significantly easier in the mean.
It may be the case that the same is true for the number of remaining candidates wrt Sukakus - or not.
I've come to think that the number of clues (or the number of initial candidates) is not very important. What may be more meaningful is the number of candidates after Singles (or after Singles and whips[1]).


For fun, I tried your examples. SudoRules allows to do this easily:

Code: Select all

(solve-sukaku-grid
   +-------------------------------+-------------------------+--------------------------------+
   ! 348       14689     24569     ! 245789  125689  12568   ! 123456789 236789    12345689   !
   ! 123456789 123456789 124689    ! 47      123569  123459  ! 3468      12489     478        !
   ! 123467    1234689   13456789  ! 12359   2358    1357    ! 24567     689       45789      !
   +-------------------------------+-------------------------+--------------------------------+
   ! 12357     1235789   12369     ! 13579   1456789 12457   ! 12467     123458    2346789    !
   ! 1235      13567     235678    ! 2346789 2456789 234567  ! 135678    145689    123689     !
   ! 14789     13569     236789    ! 345678  145789  12347   ! 123456789 235689    25679      !
   +-------------------------------+-------------------------+--------------------------------+
   ! 23458     46789     124567    ! 56789   23589   1246    ! 16789     123456789 12346789   !
   ! 246       135678    39        ! 134578  59      235689  ! 12347     1389      1789       !
   ! 156789    28        1348      ! 2346789 23568   23469   ! 123456789 123456789 123456789  !
   +-------------------------------+-------------------------+--------------------------------+
)

The solution is in W7, which makes this puzzle quite hard.

Code: Select all

Resolution state after Singles and whips[1]:
   +----------------------------+----------------------------+----------------------------+
   ! 38       14689    24569    ! 2589     125689   12568    ! 1235679  23679    1234569  !
   ! 1235679  1235679  1269     ! 4        123569   12359    ! 36       129      8        !
   ! 1236     1234689  1345689  ! 12359    2358     7        ! 256      69       459      !
   +----------------------------+----------------------------+----------------------------+
   ! 12357    1235789  12369    ! 1359     1456789  125      ! 1267     123458   23679    !
   ! 1235     13567    235678   ! 23689    2456789  2356     ! 135678   145689   12369    !
   ! 4        13569    236789   ! 3568     15789    123      ! 12356789 235689   25679    !
   +----------------------------+----------------------------+----------------------------+
   ! 2358     46789    124567   ! 56789    23589    1246     ! 16789    12356789 123679   !
   ! 26       135678   39       ! 13578    59       235689   ! 4        1389     179      !
   ! 156789   28       1348     ! 236789   23568    23469    ! 12356789 12356789 1235679  !
   +----------------------------+----------------------------+----------------------------+
380 candidates.

resolution path in W7: Show

finned-x-wing-in-columns: n9{c1 c6}{r2 r9} ==> r9c4 ≠ 9
finned-x-wing-in-columns: n8{c6 c1}{r1 r8} ==> r8c2 ≠ 8
whip[2]: r8n2{c1 c6} - b5n2{r4c6 .} ==> r5c1 ≠ 2
biv-chain[3]: r9c2{n8 n2} - r8n2{c1 c6} - c6n8{r8 r1} ==> r1c2 ≠ 8
z-chain[4]: r8n2{c1 c6} - c6n8{r8 r1} - c1n8{r1 r9} - r9c2{n8 .} ==> r7c1 ≠ 2
z-chain[4]: c1n8{r9 r1} - c6n8{r1 r8} - r8n2{c6 c1} - r9c2{n2 .} ==> r7c2 ≠ 8
z-chain[4]: c1n8{r9 r1} - c6n8{r1 r8} - r8n2{c6 c1} - r9c2{n2 .} ==> r9c3 ≠ 8
t-whip[4]: r9c2{n2 n8} - c1n8{r9 r1} - c6n8{r1 r8} - r8n2{c6 .} ==> r7c3 ≠ 2
t-whip[4]: r8c3{n3 n9} - c1n9{r9 r2} - c6n9{r2 r9} - r9n4{c6 .} ==> r9c3 ≠ 3
biv-chain[3]: r9c3{n1 n4} - c6n4{r9 r7} - b8n1{r7c6 r8c4} ==> r8c2 ≠ 1
z-chain[3]: b7n3{r8c3 r7c1} - r1c1{n3 n8} - c6n8{r1 .} ==> r8c6 ≠ 3
z-chain[4]: r9c3{n1 n4} - c6n4{r9 r7} - b8n1{r7c6 r8c4} - r3n1{c4 .} ==> r2c3 ≠ 1
t-whip[4]: r8n2{c6 c1} - r9c2{n2 n8} - c1n8{r9 r1} - c6n8{r1 .} ==> r8c6 ≠ 5, r8c6 ≠ 9
x-wing-in-columns: n9{c1 c6}{r2 r9} ==> r9c9 ≠ 9, r9c8 ≠ 9, r9c7 ≠ 9, r2c8 ≠ 9, r2c5 ≠ 9, r2c3 ≠ 9, r2c2 ≠ 9
biv-chain[4]: b8n1{r8c4 r7c6} - b8n4{r7c6 r9c6} - r9n9{c6 c1} - r8c3{n9 n3} ==> r8c4 ≠ 3
t-whip[4]: r8c1{n6 n2} - r9c2{n2 n8} - c1n8{r9 r1} - c6n8{r1 .} ==> r8c6 ≠ 6
whip[1]: r8n6{c2 .} ==> r7c2 ≠ 6, r7c3 ≠ 6, r9c1 ≠ 6
t-whip[3]: r2c3{n2 n6} - c1n6{r3 r8} - r8n2{c1 .} ==> r2c6 ≠ 2
t-whip[3]: r2c3{n2 n6} - c1n6{r3 r8} - b7n2{r8c1 .} ==> r3c2 ≠ 2, r2c2 ≠ 2
biv-chain[2]: r8n2{c6 c1} - c2n2{r9 r4} ==> r4c6 ≠ 2
z-chain[3]: b5n2{r5c6 r6c6} - r8n2{c6 c1} - c2n2{r9 .} ==> r5c3 ≠ 2
t-whip[4]: c6n8{r1 r8} - r8n2{c6 c1} - r9c2{n2 n8} - c1n8{r9 .} ==> r1c4 ≠ 8, r1c5 ≠ 8
z-chain[5]: r9n9{c1 c6} - c6n4{r9 r7} - r7c2{n4 n7} - r2n7{c2 c1} - c1n9{r2 .} ==> r8c3 ≠ 9
naked-single ==> r8c3 = 3
t-whip[5]: r2c7{n6 n3} - r1n3{c9 c1} - r1n8{c1 c6} - r8c6{n8 n2} - r8c1{n2 .} ==> r2c1 ≠ 6
biv-chain[4]: c1n6{r3 r8} - r8n2{c1 c6} - c6n8{r8 r1} - r1c1{n8 n3} ==> r3c1 ≠ 3
whip[5]: r4n4{c5 c8} - r4n8{c8 c2} - c3n8{r6 r3} - r1n8{c1 c6} - b2n6{r1c6 .} ==> r4c5 ≠ 6
whip[5]: c6n9{r2 r9} - c1n9{r9 r2} - r2n7{c1 c2} - r2n5{c2 c5} - r8c5{n5 .} ==> r2c6 ≠ 3
whip[5]: c6n9{r2 r9} - c1n9{r9 r2} - r2n7{c1 c2} - r2n5{c2 c5} - r8c5{n5 .} ==> r2c6 ≠ 1
z-chain[4]: b7n1{r9c3 r9c1} - c1n9{r9 r2} - r2c6{n9 n5} - r4c6{n5 .} ==> r4c3 ≠ 1
z-chain[6]: r7c1{n5 n8} - r9c2{n8 n2} - r8c1{n2 n6} - r8c2{n6 n7} - r2n7{c2 c1} - c1n9{r2 .} ==> r9c1 ≠ 5
t-whip[6]: c6n8{r1 r8} - r8n2{c6 c1} - c1n6{r8 r3} - r3c8{n6 n9} - r8c8{n9 n1} - b8n1{r8c4 .} ==> r1c6 ≠ 1
whip[6]: r8n2{c6 c1} - c1n6{r8 r3} - r3c8{n6 n9} - r8c8{n9 n1} - r2c8{n1 n2} - r2c3{n2 .} ==> r8c6 ≠ 8
6 singles
whip[1]: b2n6{r2c5 .} ==> r5c5 ≠ 6, r9c5 ≠ 6
whip[1]: b5n2{r5c5 .} ==> r5c9 ≠ 2
biv-chain[3]: r8c2{n7 n5} - r8c5{n5 n9} - r9n9{c6 c1} ==> r9c1 ≠ 7
z-chain[3]: c6n5{r5 r2} - c6n9{r2 r9} - r8c5{n9 .} ==> r4c5 ≠ 5
z-chain[3]: c6n5{r5 r2} - c6n9{r2 r9} - r8c5{n9 .} ==> r5c5 ≠ 5
z-chain[3]: c6n5{r5 r2} - c6n9{r2 r9} - r8c5{n9 .} ==> r6c5 ≠ 5
biv-chain[4]: c6n9{r2 r9} - r8c5{n9 n5} - r8c2{n5 n7} - b1n7{r2c2 r2c1} ==> r2c1 ≠ 9
3 singles
whip[1]: c6n5{r5 .} ==> r4c4 ≠ 5, r6c4 ≠ 5
whip[1]: b7n1{r9c3 .} ==> r3c3 ≠ 1
z-chain[3]: c1n5{r5 r2} - r2n7{c1 c2} - r8c2{n7 .} ==> r4c2 ≠ 5
z-chain[3]: c1n5{r5 r2} - r2n7{c1 c2} - r8c2{n7 .} ==> r5c2 ≠ 5
z-chain[3]: c1n5{r5 r2} - r2n7{c1 c2} - r8c2{n7 .} ==> r6c2 ≠ 5
whip[1]: r6n5{c9 .} ==> r4c8 ≠ 5, r5c7 ≠ 5, r5c8 ≠ 5
z-chain[4]: r1c4{n5 n2} - r3c5{n2 n3} - r7c5{n3 n9} - r8c5{n9 .} ==> r2c5 ≠ 5
whip[1]: r2n5{c2 .} ==> r1c3 ≠ 5, r3c3 ≠ 5
hidden-pairs-in-a-block: b1{n5 n7}{r2c1 r2c2} ==> r2c2 ≠ 6, r2c2 ≠ 1, r2c1 ≠ 2, r2c1 ≠ 1
naked-pairs-in-a-column: c2{r2 r8}{n5 n7} ==> r7c2 ≠ 7, r5c2 ≠ 7, r4c2 ≠ 7
naked-single ==> r7c2 = 4
naked-single ==> r9c3 = 1
hidden-single-in-a-block ==> r9c6 = 4
whip[1]: c6n3{r6 .} ==> r4c4 ≠ 3, r5c4 ≠ 3, r6c4 ≠ 3
biv-chain[3]: r6c4{n8 n6} - c6n6{r5 r7} - b8n1{r7c6 r8c4} ==> r8c4 ≠ 8
hidden-single-in-a-row ==> r8c8 = 8
biv-chain[3]: r4c4{n9 n1} - r8n1{c4 c9} - r8n9{c9 c5} ==> r4c5 ≠ 9, r5c5 ≠ 9, r6c5 ≠ 9, r7c4 ≠ 9
biv-chain[4]: b5n9{r4c4 r5c4} - b5n2{r5c4 r5c5} - c5n4{r5 r4} - r4n8{c5 c2} ==> r4c2 ≠ 9
z-chain[4]: r1c4{n5 n2} - r3c5{n2 n3} - r7c5{n3 n9} - r8c5{n9 .} ==> r1c5 ≠ 5
t-whip[4]: c5n6{r1 r2} - r2c3{n6 n2} - r3c1{n2 n1} - b2n1{r3c4 .} ==> r1c5 ≠ 2
z-chain[5]: r7c3{n5 n7} - r7c4{n7 n6} - r6c4{n6 n8} - r9n8{c4 c5} - r9n5{c5 .} ==> r7c8 ≠ 5
whip[1]: b9n5{r9c9 .} ==> r9c5 ≠ 5
z-chain[5]: c6n6{r5 r7} - b8n1{r7c6 r8c4} - r4c4{n1 n9} - r4c3{n9 n2} - r2c3{n2 .} ==> r5c3 ≠ 6
whip[5]: r4n8{c2 c5} - c5n4{r4 r5} - c5n7{r5 r6} - c3n7{r6 r7} - c3n5{r7 .} ==> r5c3 ≠ 8
naked-pairs-in-a-column: c3{r5 r7}{n5 n7} ==> r6c3 ≠ 7
t-whip[6]: b4n2{r4c3 r6c3} - r2c3{n2 n6} - r4c3{n6 n9} - c4n9{r4 r5} - r5n2{c4 c5} - r2n2{c5 .} ==> r4c8 ≠ 2
whip[6]: c1n2{r4 r3} - c7n2{r3 r1} - c4n2{r1 r5} - c4n9{r5 r4} - r4c3{n9 n6} - r2c3{n6 .} ==> r4c9 ≠ 2
z-chain[7]: c3n8{r3 r6} - r6c4{n8 n6} - c6n6{r5 r7} - b8n1{r7c6 r8c4} - r4c4{n1 n9} - r4c3{n9 n2} - r2c3{n2 .} ==> r3c3 ≠ 6
t-whip[7]: b1n4{r1c3 r3c3} - c3n8{r3 r6} - r4n8{c2 c5} - c5n4{r4 r5} - r5n2{c5 c4} - c4n9{r5 r4} - c3n9{r4 .} ==> r1c3 ≠ 6, r1c3 ≠ 2
t-whip[4]: r2c8{n1 n2} - r1n2{c9 c4} - r5n2{c4 c5} - r5n4{c5 .} ==> r5c8 ≠ 1
whip[5]: r5n9{c9 c4} - r4c4{n9 n1} - r8n1{c4 c9} - b6n1{r5c9 r5c7} - c7n8{r5 .} ==> r6c7 ≠ 9
whip[7]: r4c4{n9 n1} - r8n1{c4 c9} - r7n1{c7 c6} - c6n6{r7 r5} - r5c9{n6 n3} - r4c8{n3 n4} - r5c8{n4 .} ==> r4c9 ≠ 9
whip[7]: r4c4{n9 n1} - r8n1{c4 c9} - r7n1{c7 c6} - c6n6{r7 r5} - r5c9{n6 n3} - r4c8{n3 n4} - r5c8{n4 .} ==> r5c4 ≠ 9
hidden-single-in-a-block ==> r4c4 = 9
whip[1]: b4n9{r6c3 .} ==> r6c8 ≠ 9, r6c9 ≠ 9
naked-pairs-in-a-column: c3{r2 r4}{n2 n6} ==> r6c3 ≠ 6, r6c3 ≠ 2
whip[1]: r6n2{c9 .} ==> r4c7 ≠ 2
biv-chain[3]: c4n3{r9 r3} - c4n1{r3 r8} - r7c6{n1 n6} ==> r9c4 ≠ 6
whip[1]: r9n6{c9 .} ==> r7c7 ≠ 6, r7c8 ≠ 6, r7c9 ≠ 6
z-chain[3]: c4n1{r8 r3} - r3n3{c4 c5} - c5n5{r3 .} ==> r8c4 ≠ 5
biv-chain[5]: b3n7{r1c8 r1c7} - c7n9{r1 r7} - r8n9{c9 c5} - r8n5{c5 c2} - b7n7{r8c2 r7c3} ==> r7c8 ≠ 7
z-chain[5]: r5c1{n1 n5} - b5n5{r5c6 r4c6} - c6n1{r4 r7} - c4n1{r8 r3} - c1n1{r3 .} ==> r6c2 ≠ 1
z-chain[5]: r7c3{n7 n5} - r7c4{n5 n6} - r7c6{n6 n1} - r8c4{n1 n7} - b7n7{r8c2 .} ==> r7c7 ≠ 7
biv-chain[5]: r7c7{n1 n9} - r8n9{c9 c5} - r8n5{c5 c2} - c3n5{r7 r5} - r5c1{n5 n1} ==> r5c7 ≠ 1
z-chain[5]: r7c3{n7 n5} - r7c4{n5 n6} - r7c6{n6 n1} - r8c4{n1 n7} - b7n7{r8c2 .} ==> r7c9 ≠ 7
z-chain[6]: b5n5{r4c6 r5c6} - c3n5{r5 r7} - r8n5{c2 c5} - c5n9{r8 r7} - r7c7{n9 n1} - r6n1{c7 .} ==> r4c6 ≠ 1
naked-single ==> r4c6 = 5
z-chain[4]: r5c6{n3 n6} - r6c4{n6 n8} - b4n8{r6c3 r4c2} - r4n3{c2 .} ==> r5c9 ≠ 3
whip[5]: b4n8{r4c2 r6c3} - r6n9{c3 c2} - c2n3{r6 r5} - r5c6{n3 n6} - r6c4{n6 .} ==> r4c2 ≠ 1
whip[6]: b6n9{r5c8 r5c9} - b3n9{r1c9 r1c7} - r7c7{n9 n1} - c9n1{r7 r1} - r1c5{n1 n6} - r1c2{n6 .} ==> r7c8 ≠ 9
whip[6]: r6c6{n1 n3} - r5c6{n3 n6} - r5c9{n6 n9} - r5c8{n9 n4} - c5n4{r5 r4} - b5n1{r4c5 .} ==> r6c7 ≠ 1
whip[1]: r6n1{c6 .} ==> r4c5 ≠ 1
z-chain[7]: b6n9{r5c8 r5c9} - r8n9{c9 c5} - r8n5{c5 c2} - c3n5{r7 r5} - b4n7{r5c3 r4c1} - r4n2{c1 c3} - r4n6{c3 .} ==> r5c8 ≠ 6
t-whip[6]: r3n4{c9 c3} - b1n8{r3c3 r3c2} - r4n8{c2 c5} - c5n4{r4 r5} - r5c8{n4 n9} - r3n9{c8 .} ==> r3c9 ≠ 5
whip[7]: r2c8{n1 n2} - r1n2{c9 c4} - r3n2{c4 c1} - r4c1{n2 n7} - r4c7{n7 n6} - r3c7{n6 n5} - b2n5{r3c4 .} ==> r4c8 ≠ 1
t-whip[5]: r7c7{n9 n1} - r4n1{c7 c1} - c1n7{r4 r2} - c2n7{r2 r8} - r8c9{n7 .} ==> r7c9 ≠ 9
biv-chain[6]: b6n1{r5c9 r4c7} - r7c7{n1 n9} - r8n9{c9 c5} - r8n5{c5 c2} - c3n5{r7 r5} - r5c1{n5 n1} ==> r5c2 ≠ 1
whip[1]: c2n1{r3 .} ==> r3c1 ≠ 1
4 singles
whip[1]: r4n6{c9 .} ==> r5c7 ≠ 6, r5c9 ≠ 6, r6c7 ≠ 6, r6c8 ≠ 6, r6c9 ≠ 6
naked-pairs-in-a-row: r5{c2 c6}{n3 n6} ==> r5c4 ≠ 6
naked-triplets-in-a-column: c5{r3 r7 r8}{n5 n3 n9} ==> r9c5 ≠ 3
6 singles
whip[1]: r4n3{c9 .} ==> r6c8 ≠ 3
swordfish-in-columns: n1{c5 c6 c8}{r2 r6 r7} ==> r7c9 ≠ 1, r7c7 ≠ 1
15 singles
naked-pairs-in-a-column: c8{r2 r7}{n1 n2} ==> r6c8 ≠ 2, r1c8 ≠ 2
naked-single ==> r6c8 = 5
hidden-triplets-in-a-column: c4{n1 n3 n7}{r8 r3 r9} ==> r3c4 ≠ 5
biv-chain[3]: b3n1{r1c9 r2c8} - r2c5{n1 n2} - r1c4{n2 n5} ==> r1c9 ≠ 5
stte

Code: Select all

(solve-sukaku-grid
   +--------------------------------+--------------------------------+--------------------------------+
   ! 123456789 123456789 123456789  ! 123456789 145       1          ! 123456789 123456789 23456789   !
   ! 123456789 46        123456789  ! 123456789 123456789 123456789  ! 236       123456789 123456789  !
   ! 123456789 123456789 123456789  ! 123456789 123456789 123456789  ! 123456789 123456789 123456789  !
   +--------------------------------+--------------------------------+--------------------------------+
   ! 23567     2467      123456789  ! 56        123456789 123456789  ! 123456789 123456789 123456789  !
   ! 123456789 123456789 123456789  ! 123456789 145       123456789  ! 123456789 14        1          !
   ! 57        123456789 123456789  ! 123456789 123456789 123456789  ! 123456789 123456789 123456789  !
   +--------------------------------+--------------------------------+--------------------------------+
   ! 123456789 123456789 123456789  ! 26        123456789 123456789  ! 23        123456789 123456789  !
   ! 123456789 145       1458       ! 123456789 123456789 123456789  ! 123456789 123456789 123456789  !
   ! 15        123456789 1          ! 123456789 123456789 123456789  ! 123456789 123456789 123456789  !
   +--------------------------------+--------------------------------+--------------------------------+
)

It solves with singles.

[Leren]

Code: Select all

*-------------------------------------------------------------------------------------------*
| 123456789 123456789 123456789 123456789 123456789 123456789 123456789 123456789 ......... |
| 123456789 ......... 123456789 123456789 123456789 123456789 ......... 123456789 123456789 |
| 123456789 123456789 123456789 ......... 123456789 123456789 123456789 123456789 123456789 |
| ......... 123456789 123456789 123456789 123456789 123456789 123456789 123456789 123456789 |
| 123456789 123456789 ......... 123456789 123456789 123456789 123456789 123456789 123456789 |
| 123456789 123456789 12.456789 123456789 ......... 123456789 123456789 123456789 123456789 |
| 123456789 ......... 123456789 123456789 123456789 123456789 ......... 123456789 123456789 |
| 123456789 123456789 123456789 ......... 123456789 123456789 123456789 123456789 ......... |
| ......... 123456789 123456789 123456789 123456789 ......... 123456789 123456789 123456789 |
*-------------------------------------------------------------------------------------------*

Couldn't resist creating a variant of Str8ts - Str8tsKaku ? This one has 13 black cells (the ones with no candidates) and all other 68 white cells have all 9 candidates except r6c3 has 8 candidates.

The number of candidates is 611. The puzzle solves with the Str8ts equivalent of basics.

Leren

[creint]

Leren, can you provide the solution? My solver gives invalid solution.

[Leren]

Oops, I had to draw the PM by hand and accidentally included a non-existent 10th column - fixed. Try it now.

Leren

[m_b_metcalf]

These puzzles are called "Sukaku" or "PencilMark Sudoku" ...

And, as always, I for one appreciate their being published also in the 729 line format, like this:

Code: Select all

123456789020006000123456789000456000123456789123456789000050009123456789123456789123456789123456789123000000123456789100006000123456789003400000123456789020000080003006000000050700123456789123456789123456789000400009123456789000000789123456789123456789123456789003050000020006000123456789020000080123456789123456789123000000123456789020400000123456789123456789123456789123456789123456789020000700123456789000456000123456789123456789000406000123456789000400080003050000123456789123456789123456789123000000123456789100000009123456789123456789123456789020000009100050000003400000123456789000050009123456789000006080123456789000456000123456789123456789123456789123456789100000700123456789123456789000000789123456789000400080123456789


[yzfwsf]

Leren, can you provide the solution? My solver gives invalid solution.

Hidden Text: Show

Code: Select all

Naked Quad: in r4c4,r4c6,r6c4,r6c6 => r4c5<>2468,r5c4<>2468,r5c5<>2468,r5c6<>2468,r6c5<>2468,
Locked Candidates 1 (Pointing): 2 in b5 => r4c1<>2,r4c2<>2,r4c7<>2,r4c8<>2,r4c9<>2
Locked Candidates 1 (Pointing): 4 in b5 => r6c1<>4,r6c2<>4,r6c3<>4,r6c8<>4,r6c9<>4
Locked Candidates 1 (Pointing): 6 in b5 => r1c4<>6,r2c4<>6,r3c4<>6,r8c4<>6,r9c4<>6
Locked Candidates 1 (Pointing): 8 in b5 => r1c6<>8,r2c6<>8,r7c6<>8,r8c6<>8,r9c6<>8
XY-Wing: 459 in r1c4 r1c7 r3c6 => r3c789,r1c56 <> 9
XY-Wing: 278 in r3c8 r5c8 r2c9 => r12c8,r56c9 <> 2
XY-Wing: 135 in r4c9 r4c3 r7c9 => r7c3 <> 5
XY-Wing: 135 in r4c9 r7c9 r6c7 => r789c7,r56c9 <> 5
XY-Wing: 356 in r6c1 r6c7 r3c1 => r3c7 <> 3
XY-Wing: 356 in r6c1 r3c1 r4c3 => r123c3,r45c1 <> 3
Grouped W-Wing: 34 in r2c7,r8c1 connected by 3b1 => r2c1,r8c7<>4
Naked Single: r8c7=6
Naked Single: r8c5=8
XY-Wing: 126 in r2c3 r2c5 r1c2 => r1c56,r2c12 <> 6
XY-Wing: 456 in r6c4 r6c1 r1c4 => r1c1 <> 5
XY-Wing: 179 in r9c6 r9c3 r7c4 => r7c123,r9c45 <> 1
XY-Wing: 236 in r1c2 r7c2 r3c1 => r789c1,r2c2 <> 3
Naked Single: r8c1=4
WXYZ-Wing: 3456 in r6c147,r2c7,Pivot Cell Is r6c7 => r2c4<>4
XY-Chain: (6=2)r1c2 - (2=1)r2c3 - (1=7)r9c3 - (7=9)r9c6 - (9=4)r3c6 - (4=8)r6c6 - (8=2)r4c6 - (2=6)r4c4 => r4c2<>6
XY-Chain: (5=4)r1c4 - (4=6)r6c4 - (6=5)r6c1 - (5=3)r6c7 - (3=1)r4c9 - (1=5)r7c9 => r1c9<>5
XY-Chain: (5=4)r1c4 - (4=9)r3c6 - (9=7)r9c6 - (7=1)r9c3 - (1=2)r2c3 - (2=8)r2c9 - (8=7)r3c8 - (7=5)r3c2 => r1c3<>5 r3c4<>5 r3c5<>5
XY-Chain: (9=5)r1c7 - (5=4)r1c4 - (4=9)r3c6 - (9=7)r9c6 - (7=1)r9c3 - (1=2)r2c3 - (2=8)r2c9 - (8=7)r3c8 - (7=2)r5c8 - (2=9)r7c8 => r1c8<>9 r2c8<>9 r7c7<>9 r9c7<>9
Locked Candidates 1 (Pointing): 9 in b3 => r1c1<>9,r1c3<>9
XY-Chain: (1=2)r2c3 - (2=8)r2c9 - (8=7)r3c8 - (7=2)r5c8 - (2=9)r7c8 - (9=1)r7c4 => r2c4<>1
XY-Chain: (2=1)r2c3 - (1=7)r9c3 - (7=9)r9c6 - (9=4)r3c6 - (4=8)r6c6 - (8=2)r4c6 => r2c6<>2
XY-Chain: (8=2)r2c9 - (2=1)r2c3 - (1=7)r9c3 - (7=9)r9c6 - (9=4)r3c6 - (4=8)r6c6 => r6c9<>8
XY-Chain: (5=7)r3c2 - (7=8)r3c8 - (8=2)r2c9 - (2=1)r2c3 - (1=7)r9c3 - (7=9)r9c6 - (9=1)r7c4 - (1=5)r7c9 => r3c9<>5
Locked Candidates 2 (Claiming): 5 in c9 => r8c8<>5
XY-Chain: (7=8)r3c8 - (8=2)r2c9 - (2=1)r2c3 - (1=7)r9c3 => r3c3<>7
AIC Type 2: (1=9)r7c4 - (9=2)r7c8 - (2=7)r5c8 - (7=8)r3c8 - (8=2)r2c9 - (2=1)r2c3 - (1=7)r9c3 - (7=9)r9c6 => r7c4<>9
Naked Single: r7c4=1
Naked Single: r7c9=5
XY-Chain: (9=2)r7c8 - (2=7)r5c8 - (7=8)r3c8 - (8=2)r2c9 - (2=1)r2c3 - (1=7)r9c3 - (7=9)r9c6 => r7c5<>9 r7c6<>9 r9c9<>9
AIC Type 2: 8r3c4 = r2c4 - (8=2)r2c9 - (2=1)r2c3 - (1=7)r9c3 - (7=9)r9c6 - (9=4)r3c6 => r3c4<>4
Grouped AIC Type 2: (1=3)r4c9 - (3=5)r6c7 - (5=6)r6c1 - r5c13 = 6r5c9 => r5c9<>1
Grouped AIC Type 2: 6r5c9 = r5c13 - (6=5)r6c1 - (5=3)r6c7 => r5c9<>3
Death Blossom Complex Type 1: Set have degrees of freedom of 3-123456789{r123569c3} => r4c2<>3
6r13c3-(6=23){r17c2}
5r356c3-(5=13){r4c39}
9r356c3-(9=35){r48c3}
6r56c3-(6=35){r4c3,r6c1}
Death Blossom Complex Type 1: Set have degrees of freedom of 3-123456789{r123569c3} => r6c2<>3
6r13c3-(6=23){r17c2}
5r35c3,9r356c3-(59=3){r48c3}
5r6c3,6r56c3-(56=3){r6c17}
Locked Candidates 2 (Claiming): 3 in c2 => r7c3<>3
Death Blossom Complex Type 2: Set have degrees of freedom of 3-23478{r27c7} => r9c4<>4
3r27c7-(3=456){r6c147}
2r7c7,7r7c7,8r7c7-(278=3469){r7c123568}
Region Forcing Chain: Each 4 in c3 true in turn will all lead r1c3<>1
(4-1)r1c3
4r3c3 - (4=9)r3c6 - (9=7)r9c6 - (7=1)r9c3 - 1r1c3
4r5c3 - (4=2)r5c2 - (2=7)r5c8 - (7=8)r3c8 - (8=2)r2c9 - (2=1)r2c3 - 1r1c3
Region Forcing Chain: Each 4 in c3 true in turn will all lead r1c3<>6
(4-6)r1c3
4r3c3 - (4=9)r3c6 - (9=7)r9c6 - (7=1)r9c3 - (1=2)r2c3 - (2=6)r1c2 - 6r1c3
4r5c3 - (4=2)r5c2 - (2=6)r1c2 - 6r1c3
Cell Forcing Chain: Each candidate in  r3c9 true in turn will all lead r2c1<>5
1r3c9 - (1=3)r4c9 - (3=5)r6c7 - r3c7 = r3c23 - 5r2c1
2r3c9 - (2=8)r2c9 - (8=7)r3c8 - (7=5)r3c2 - 5r2c1
3r3c9 - (3=6)r3c1 - (6=5)r6c1 - 5r2c1
4r3c9 - (4=3)r2c7 - (3=5)r6c7 - r3c7 = r3c23 - 5r2c1
6r3c9 - r5c9 = r5c13 - (6=5)r6c1 - 5r2c1
7r3c9 - (7=5)r3c2 - 5r2c1
8r3c9 - (8=7)r3c8 - (7=5)r3c2 - 5r2c1
Region Forcing Chain: Each 6 in r3 true in turn will all lead r2c2<>4
6r3c1 - (6=2)r1c2 - (2=4)r5c2 - 4r2c2
6r3c3 - (6=2)r1c2 - (2=4)r5c2 - 4r2c2
6r3c5 - (6=1)r2c5 - (1=2)r2c3 - (2=8)r2c9 - (8=7)r3c8 - (7=2)r5c8 - (2=4)r5c2 - 4r2c2
6r3c9 - r5c9 = r5c13 - (6=5)r6c1 - (5=3)r6c7 - (3=4)r2c7 - 4r2c2
Locked Candidates 2 (Claiming): 4 in c2 => r5c3<>4
AIC Type 2: 4r1c3 = r3c3 - (4=9)r3c6 - (9=7)r9c6 - (7=1)r9c3 - (1=2)r2c3 => r1c3<>2
Region Forcing Chain: Each 6 in r9 true in turn will all lead r1c8<>4
6r9c1 - (6=5)r6c1 - (5=3)r6c7 - (3=4)r2c7 - 4r1c8
6r9c2 - (6=2)r1c2 - (2=1)r2c3 - (1=7)r9c3 - (7=9)r9c6 - (9=4)r3c6 - r2c6 = r2c78 - 4r1c8
6r9c5 - r7c6 = (6-4)r2c6 = r2c78 - 4r1c8
Region Forcing Chain: Each 4 in c9 true in turn will all lead r1c8<>7
4r1c9 - r1c3 = r3c3 - (4=9)r3c6 - (9=7)r9c6 - (7=1)r9c3 - (1=2)r2c3 - (2=8)r2c9 - (8=7)r3c8 - 7r1c8
4r3c9 - (4=9)r3c6 - (9=7)r9c6 - (7=1)r9c3 - (1=2)r2c3 - (2=8)r2c9 - (8=7)r3c8 - 7r1c8
4r5c9 - (4=2)r5c2 - (2=7)r5c8 - 7r1c8
4r9c9 - (4=8)r9c8 - (8=7)r3c8 - 7r1c8
Region Forcing Chain: Each 4 in c9 true in turn will all lead r1c8<>8
4r1c9 - r1c3 = r3c3 - (4=9)r3c6 - (9=7)r9c6 - (7=1)r9c3 - (1=2)r2c3 - (2=8)r2c9 - 8r1c8
4r3c9 - (4=9)r3c6 - (9=7)r9c6 - (7=1)r9c3 - (1=2)r2c3 - (2=8)r2c9 - 8r1c8
4r5c9 - (4=2)r5c2 - (2=7)r5c8 - (7=8)r3c8 - 8r1c8
4r9c9 - (4=8)r9c8 - 8r1c8
Region Forcing Chain: Each 6 in r9 true in turn will all lead r1c9<>4
6r9c1 - (6=5)r6c1 - (5=3)r6c7 - (3=4)r2c7 - 4r1c9
6r9c2 - (6=2)r1c2 - (2=1)r2c3 - (1=7)r9c3 - (7=9)r9c6 - (9=4)r3c6 - r2c6 = r2c78 - 4r1c9
6r9c5 - r7c6 = (6-4)r2c6 = r2c78 - 4r1c9
Cell Forcing Chain: Each candidate in  r3c3 true in turn will all lead r2c6<>4
1r3c3 - (1=7)r9c3 - (7=9)r9c6 - (9=4)r3c6 - 4r2c6
2r3c3 - (2=1)r2c3 - (1=7)r9c3 - (7=9)r9c6 - (9=4)r3c6 - 4r2c6
4r3c3 - r3c79 = r2c78 - 4r2c6
5r3c3 - (5=7)r3c2 - (7=8)r3c8 - (8=2)r2c9 - (2=1)r2c3 - (1=7)r9c3 - (7=9)r9c6 - (9=4)r3c6 - 4r2c6
6r3c3 - (6=2)r1c2 - (2=1)r2c3 - (1=7)r9c3 - (7=9)r9c6 - (9=4)r3c6 - 4r2c6
8r3c3 - r3c4 = r2c4 - (8=2)r2c9 - (2=1)r2c3 - (1=7)r9c3 - (7=9)r9c6 - (9=4)r3c6 - 4r2c6
9r3c3 - (9=4)r3c6 - 4r2c6
Locked Candidates 2 (Claiming): 4 in r2 => r3c7<>4,r3c9<>4
AIC Type 1: 8r2c4 = r3c4 - (8=7)r3c8 - (7=2)r5c8 - (2=4)r5c2 - r5c9 = r9c9 - (4=8)r9c8 => r2c8<>8
AIC Type 1: 4r2c7 = r2c8 - (4=8)r9c8 - (8=7)r3c8 - (7=2)r5c8 - (2=4)r5c2 => r5c7<>4
AIC Type 1: 4r2c7 = r2c8 - (4=8)r9c8 - (8=7)r3c8 - (7=2)r5c8 - (2=4)r5c2 - r5c9 = 4r9c9 => r7c7<>4 r9c7<>4
Locked Candidates 2 (Claiming): 4 in r7 => r9c5<>4
AIC Type 2: (2=8)r2c9 - (8=7)r3c8 - (7=2)r5c8 - (2=4)r5c2 - r5c9 = 4r9c9 => r9c9<>2
AIC Type 2: (5=7)r3c2 - (7=8)r3c8 - (8=4)r9c8 - r9c9 = r5c9 - r5c2 = 4r4c2 => r4c2<>5
AIC Type 1: (7=8)r3c8 - (8=4)r9c8 - r9c9 = r5c9 - (4=2)r5c2 - (2=7)r5c8 => r2c8<>7 r4c8<>7 r6c8<>7 r8c8<>7
Empty Rectangle : 7 in b5 connected by c8 => r3c5 <> 7
AIC Type 1: (8=7)r3c8 - (7=2)r5c8 - (2=4)r5c2 - r5c9 = r9c9 - (4=8)r9c8 => r4c8<>8 r6c8<>8
AIC Type 1: (2=4)r5c2 - r5c9 = r9c9 - (4=8)r9c8 - (8=7)r3c8 - (7=2)r5c8 => r5c1<>2 r5c3<>2 r5c7<>2
Locked Candidates 1 (Pointing): 2 in b6 => r7c8<>2,r8c8<>2
Naked Single: r7c8=9
AIC Type 2: 4r7c5 = r7c6 - (4=9)r3c6 - (9=7)r9c6 => r7c5<>7
AIC Type 2: (7=1)r9c3 - (1=2)r2c3 - (2=8)r2c9 - r3c8 = (8-4)r9c8 = 4r9c9 => r9c9<>7
Grouped AIC Type 1: (5=7)r3c2 - r3c8 = (7-2)r5c8 = (2-4)r5c2 = (4-6)r5c9 = r5c13 - (6=5)r6c1 => r6c2<>5
Grouped AIC Type 2: (1=3)r4c9 - (3=5)r6c7 - (5=6)r6c1 - r5c13 = (6-4)r5c9 = 4r9c9 => r9c9<>1
Grouped AIC Type 2: (3=2)r7c2 - r79c1 = r12c1 - (2=1)r2c3 - (1=6)r2c5 - r2c6 = 6r7c6 => r7c6<>3
Grouped AIC Type 2: (3=2)r7c2 - r79c1 = r12c1 - (2=1)r2c3 - (1=6)r2c5 - r2c6 = (6-4)r7c6 = 4r7c5 => r7c5<>3
Almost Locked Set XY-Wing: A=r9c12345678{123456789}, B=r123468c9{1236789}, C=r1234568c8{12345678}, X,Y=4, 8, Z=3 =>  r9c9<>3
Locked Pair: in r9c8,r9c9 => r7c7<>8,r9c7<>8,r9c1<>8,r9c2<>8,r9c7<>8,
Death Blossom Complex Type 2: Set have degrees of freedom of 6-123456789{r45c9,r6c8} => r4c1<>6,r6c2<>6,r6c3<>6
3r4c9,r6c8,5r6c8-(35=6){r6c17}
4r5c9-(4=12356789){r5c12345678}
7r5c9,8r5c9,9r5c9-(789=1356){r5c134567}
2r6c8-(2=1356789){r5c1345678}
Cell Forcing Chain: Each candidate in  r6c8 true in turn will all lead r1c4<>4
1r6c8 - (1=3)r4c9 - (3=5)r6c7 - (5=6)r6c1 - (6=4)r6c4 - 4r1c4
2r6c8 - (2=7)r5c8 - (7=8)r3c8 - (8=2)r2c9 - (2=1)r2c3 - (1=7)r9c3 - (7=9)r9c6 - (9=4)r3c6 - 4r1c4
3r6c8 - (3=5)r6c7 - (5=6)r6c1 - (6=4)r6c4 - 4r1c4
5r6c8 - (5=6)r6c1 - (6=4)r6c4 - 4r1c4
6r6c8 - (6=4)r6c4 - 4r1c4
Hidden Single: 4 in c4 => r6c4=4
Hidden Single: 6 in b5 => r4c4=6
Hidden Single: 2 in b5 => r4c6=2
Hidden Single: 8 in b5 => r6c6=8
Naked Single: r1c4=5
Naked Single: r1c7=9
AIC Type 2: 8r2c2 = (8-4)r4c2 = (4-2)r5c2 = (2-7)r5c8 = r3c8 - (7=5)r3c2 => r2c2<>5
Hidden Single: 5 in r2 => r2c8=5
Hidden Single: 4 in b3 => r2c7=4
Locked Candidates 2 (Claiming): 6 in r2 => r3c5<>6
Grouped W-Wing: 13 in r4c9,r8c8 connected by 3b3 => r46c8,r8c9<>1
XY-Chain: (5=7)r3c2 - (7=8)r3c8 - (8=4)r9c8 - (4=3)r4c8 - (3=5)r4c3 => r3c3<>5
Hidden Single: 5 in b1 => r3c2=5
2-String Kite: 5 in r5c6,r9c1 connected by r8c6,r9c5 => r5c1 <> 5
AIC Type 1: (2=6)r1c2 - r1c8 = (6-2)r6c8 = 2r5c8 => r5c2<>2
Hidden Single: 2 in r5 => r5c8=2
Hidden Single: 7 in c8 => r3c8=7
Hidden Single: 8 in c8 => r9c8=8
Hidden Single: 4 in b9 => r9c9=4
Hidden Single: 4 in b6 => r4c8=4
Hidden Single: 4 in b4 => r5c2=4
Naked Triple: in r6c1,r6c7,r6c8 => r6c3<>35,r6c5<>35,r6c9<>36,
Locked Candidates 2 (Claiming): 3 in r6 => r4c7<>3,r4c9<>3,r5c7<>3
Naked Single: r4c9=1
Dual Empty Rectangle : 5 in b7 connected by r6,c6 => r5c7 <> 5
AIC Type 2: (2=6)r1c2 - r1c8 = (6-3)r6c8 = r6c7 - r7c7 = 3r7c2 => r7c2<>2
Naked Single: r7c2=3
AIC Type 2: (6=1)r2c5 - (1=2)r2c3 - (2=6)r1c2 - r1c8 = r6c8 - (6=5)r6c1 - r9c1 = 5r9c5 => r9c5<>6
Locked Candidates 1 (Pointing): 6 in b8 => r7c1<>6,r7c3<>6
Hidden Pair: 46 in r7c5,r7c6 => r7c5<>2,r7c6<>7
AIC Type 2: (1=2)r2c3 - (2=6)r1c2 - r3c3 = 6r5c3 => r5c3<>1
AIC Type 2: 6r5c3 = r3c3 - (6=2)r1c2 - (2=1)r2c3 - (1=7)r9c3 => r5c3<>7
AIC Type 2: 5r5c6 = r8c6 - r8c3 = (5-6)r9c1 = r9c2 - (6=2)r1c2 - (2=1)r2c3 - (1=7)r9c3 - (7=9)r9c6 => r5c6<>9
AIC Type 2: 6r9c1 = r9c2 - (6=2)r1c2 - (2=1)r2c3 - (1=7)r9c3 => r9c1<>7
AIC Type 2: 6r9c1 = r9c2 - (6=2)r1c2 - (2=1)r2c3 - (1=7)r9c3 - (7=9)r9c6 => r9c1<>9
AIC Type 2: (7=1)r9c3 - (1=2)r2c3 - (2=6)r1c2 - r9c2 = (6-5)r9c1 = 5r9c5 => r9c5<>7
AIC Type 2: 5r9c5 = r9c1 - r6c1 = (5-3)r6c7 = 3r9c7 => r9c5<>3
AIC Type 1: (3=6)r3c1 - r6c1 = (6-3)r6c8 = r6c7 - r9c7 = 3r9c4 => r3c4<>3
AIC Type 2: (7=1)r9c3 - (1=2)r2c3 - (2=6)r1c2 - r1c8 = (6-3)r6c8 = r6c7 - r9c7 = 3r9c4 => r9c4<>7
AIC Type 2: 3r9c4 = r9c7 - r6c7 = (3-6)r6c8 = r1c8 - (6=2)r1c2 - (2=1)r2c3 - (1=7)r9c3 - (7=9)r9c6 => r9c4<>9
AIC Type 2: (2=3)r9c4 - r9c7 = (3-5)r6c7 = r6c1 - r9c1 = 5r9c5 => r9c5<>2
Locked Candidates 1 (Pointing): 2 in b8 => r2c4<>2,r3c4<>2
AIC Type 1: (2=6)r1c2 - r1c8 = (6-3)r6c8 = r6c7 - r9c7 = (3-2)r9c4 = 2r8c4 => r8c2<>2
AIC Type 2: (3=6)r3c1 - (6=2)r1c2 - r1c5 = 2r3c5 => r3c5<>3
AIC Type 2: 8r4c2 = r2c2 - (8=2)r2c9 - r8c9 = r8c4 - (2=3)r9c4 - r9c7 = (3-5)r6c7 = 5r4c7 => r4c7<>8
Locked Candidates 2 (Claiming): 8 in r4 => r5c1<>8,r5c3<>8
AIC Type 2: (3=5)r4c3 - (5=7)r4c7 - (7=2)r7c7 - r8c9 = r8c4 - (2=3)r9c4 - r9c7 = (3-5)r6c7 = 5r6c1 => r4c3<>5
Naked Single: r4c3=3
X-Wing:5c36\r58  => r5c5<>5
AIC Type 2: 5r4c7 = (5-3)r6c7 = r9c7 - (3=2)r9c4 - r8c4 = r8c9 - (2=7)r7c7 => r4c7<>7
Naked Single: r4c7=5
Hidden Single: 5 in b5 => r5c6=5
Hidden Single: 5 in b8 => r9c5=5
Hidden Single: 5 in b7 => r8c3=5
Hidden Single: 5 in b4 => r6c1=5
Hidden Single: 6 in r6 => r6c8=6
Hidden Single: 3 in b6 => r6c7=3
Hidden Single: 3 in r9 => r9c4=3
Hidden Single: 2 in b8 => r8c4=2
Hidden Single: 3 in b5 => r5c5=3
Hidden Single: 1 in b5 => r6c5=1
Hidden Single: 1 in b4 => r5c1=1
Hidden Single: 6 in b4 => r5c3=6
Naked Single: r2c5=6
Hidden Single: 6 in b8 => r7c6=6
Hidden Single: 4 in b8 => r7c5=4
Locked Candidates 1 (Pointing): 9 in b7 => r2c2<>9,r4c2<>9,r6c2<>9
Locked Candidates 1 (Pointing): 7 in b8 => r1c6<>7,r2c6<>7
Locked Candidates 1 (Pointing): 9 in b8 => r2c6<>9,r3c6<>9
Naked Single: r3c6=4
Hidden Single: 4 in b1 => r1c3=4
Locked Candidates 1 (Pointing): 2 in b9 => r3c7<>2
Naked Pair: in r1c6,r1c8 => r1c1<>3,r1c9<>3,
Hidden Pair: 36 in r3c1,r3c9 => r3c9<>28
Skyscraper : 9 in r2c4,r4c5 connected by r24c1 => r3c5,r5c4 <> 9
Hidden Single: 9 in b5 => r4c5=9
Full House: r5c4=7
Hidden Single: 7 in b6 => r6c9=7
Hidden Single: 9 in b6 => r5c9=9
Full House: r5c7=8
Hidden Single: 9 in b4 => r6c3=9
Full House: r6c2=2
Hidden Single: 7 in b2 => r1c5=7
Full House: r3c5=2
Hidden Single: 9 in b1 => r2c1=9
Hidden Single: 9 in b2 => r3c4=9
Full House: r2c4=8
Hidden Single: 8 in b3 => r1c9=8
Hidden Single: 2 in b3 => r2c9=2
Hidden Single: 6 in b3 => r3c9=6
Full House: r8c9=3
Hidden Single: 3 in b3 => r1c8=3
Full House: r8c8=1
Full House: r3c7=1
Hidden Single: 3 in b2 => r2c6=3
Full House: r1c6=1
Hidden Single: 2 in b1 => r1c1=2
Full House: r1c2=6
Hidden Single: 2 in b7 => r7c3=2
Hidden Single: 2 in b9 => r9c7=2
Full House: r7c7=7
Full House: r7c1=8
Hidden Single: 6 in b7 => r9c1=6
Hidden Single: 8 in b4 => r4c2=8
Full House: r4c1=7
Full House: r3c1=3
Full House: r3c3=8
Hidden Single: 7 in b1 => r2c2=7
Full House: r2c3=1
Full House: r9c3=7
Hidden Single: 7 in b8 => r8c6=7
Full House: r8c2=9
Full House: r9c2=1
Full House: r9c6=9


Code: Select all

264571938971863452358924176783692541146735829529418367832146795495287613617359284

[creint]

Leren, a 10th column could be still valid.
And this one is valid:

Code: Select all

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

Missing only implementations to solve if fully with logic

[Leren]

Hi creint,

Your solution is the correct unique solution using 9 x 9 Str8ts rules. The solution is easy because you can deduce that r6c3 must be 7 at the start. Can you see why ?

Do I have to say this ? Str8ts puzzles, as in Sudoku, are supposed to have only one solution.

Leren

[creint]

I can't see why. Is it still easy if I can't see it?

[Leren]

Hi creint.

As I said the solution is unique (I still think I didn't need to say this).

So suppose there was a solution with r6c3 equal to, say, 1. I don't know how much you know about Str8ts solving, but there would have to be another solution with every number replaced by it's tens complement with r6c3 = 9. So the solution would not be unique, so you can eliminate 1 and 9 from r6c3. By the same argument you can eliminate 24568 from r6c3. In the case of 3 and 7 I have told you that r6c3 can't be 3, so it must be 7, since that's the only way that the solution can be unique.

Essentially this shows that the puzzle is one giant UR, and the one hint puzzle is really a 1 clue puzzle (8 hints in the same cell). In fact the puzzle would actually be harder to solve if I removed, say 3 and 4, and much harder if I removed 123 & 4.

Leren

[creint]

If 3 is placed back then you have indeed 2 solutions.

Code: Select all

28 37 5  46 19 37 28 46
19    46 37 28 5     37 46
37 46 28    5  28 46 19 37
   46 37 19 46 28 37 28 5
28 37    46 37 19 5  28 46
46 5  37 28    37 46 19 28
5     19 37 28 46    46 37
37 19 28    46 46 37 5
   28 46 5  37    28 37 19

5 is fully locked but I can't see the logic for both. No symmetry visible.

Even with the 7 placed it is not easy.

What is the first tactic from this point?

Code: Select all

123456    1236789   12345     12345     123456789 123456789 123456789 123456789
12356               12345     12345     1234567   1234567             12356789  12356789
1234      234       1234                456789    456789    45678     456789    456789
          23456     12345     5679      123456789 123456789 12345678  123456789 123456789
238       237                 5679      123456789 123456789 12345678  123456789 123456789
569       56        7         8                   12345     12345     12345     12345
234579              5689      5679      346789    3456789             12345789  12345789
45679     36789     5689                26789     13456789  13456789  13456789
          2678      568       3459      34678               23456789  123456789 123789

[Leren]

Hi creint,

Your two solutions for the totally un-clued and un-hinted puzzle are correct. In Str8ts parlance you say that the black cell pattern admits of just one structural solution.

What this means is that the two solutions are essentially the same, with the only difference being that in each cell, the sum of the two solutions is 10 (you could include the 5's twice in their cells to make this clearer).

The Sudoku-like way of saying this is that the re-labelling factor in Str8ts is not 9 ! it's just 2.

I'm surmising that you have a general purpose guessing solver, and you only need to add the constraints that if you guess a value in a cell, you can remove it from the rest of its row and column, and you can remove other digits that are out of range in it's horizontal and vertical compartments. This will enable you to find every solution for any Str8ts puzzle, which you have done here, but I gather that you don't know all of the humanistic solving methods that have been thought of.

Now to your partial solution. It looks OK at this stage, and I don't want to bore others with a blow-by blow full solution, but here is one next step.

In Column 1 there is an interaction between the two compartments. If r5678c1 contains 2 it must contain 2345, or if it contains no 2 but 3 it must contain 3456. In Case 1 r123c1 would left with 1.6 and Case 2 12. Both bad.

So you can remove 23 from r5678c1, which gives you r5c1 = 8.

Hopefully we have not gone too far off topic here. If we are boring others and you want to go further we might have to start a new thread.

Leren