The New Sudoku Players' Forum

[urhegyi]

Code: Select all

1...8..7...326.9...2...3.5.7..4..1....83.6....9..5..2.6..1..7...5...2..9....3..8.
1...8..7...32..9...2...3.5.7..4..1....83.6....9..5..2.6..1..7...5...2.19....3..8.

[P.O.]

are not these 2 puzzles from this one which has 2 solutions with an UA of 10 bivalue cells giving 20 unique solution puzzles?
1...8..7...32..9...2...3.5.7..4..1....83.6....9..5..2.6..1..7...5...2..9....3..8.
its resolution with templates:

Hidden Text: Show

Code: Select all

#VT: (4 4 4 281 4 40 8 5 13)
Cells: nil nil nil nil (10 30) nil nil nil nil
SetVC: ( n5r2c1   n5r4c3   n2r5c1   n2r4c5 )

#VT: (4 3 4 281 4 40 8 5 13)
Cells: nil nil nil nil nil nil nil nil nil
Candidates:nil nil (63) nil nil nil nil nil (23)
2
#VT: (4 3 3 143 4 23 6 2 8)
Cells: nil nil nil nil nil nil nil nil nil
Candidates:nil nil (36 71) nil nil nil (14) (27 51 54) nil
2
#VT: (4 3 2 127 4 22 6 2 7)
Cells: nil nil nil nil nil nil nil nil nil
Candidates:nil nil (52) nil nil nil nil nil nil
2
#VT: (4 3 2 116 4 21 6 2 7)
Cells: nil nil nil nil nil nil nil nil nil
Candidates:nil nil nil nil nil nil nil nil nil
2 3
#VT: (4 3 2 9 2 7 5 2 4)
Cells: nil nil nil nil (43 63) nil nil nil nil
SetVC: ( n5r5c7   n5r7c9   n2r7c3 )

#VT: (4 2 2 9 2 7 5 2 4)
Cells: nil nil nil nil nil nil nil nil nil
Candidates:nil nil nil (7 9 45 54 56 60 64 71 79) nil (7 9 11 18 67) nil nil (6 76 78)
EraseCC: ( n7r5c9 )

#VT: (4 2 2 9 2 7 6 2 4)
Cells: nil nil nil nil nil nil nil nil nil
Candidates:nil nil nil nil nil nil nil nil nil
2
#VT: (4 2 2 4 2 7 4 2 4)
Cells: nil nil nil nil nil nil nil nil nil
Candidates:nil nil nil (2 14 17 21 23 48 73 78) nil nil (67) nil nil
EraseCC: ( n6r1c2   n3r4c2   n4r6c1   n8r7c2   n9r7c6   n3r8c1
           n8r8c4   n9r9c1   n8r3c1   n8r4c6   n6r4c9   n1r5c2
           n9r5c5   n4r5c8   n6r6c3   n7r6c4   n1r6c6   n8r6c7
           n3r6c9   n4r7c5   n3r7c8   n2r1c9   n9r4c8   n3r1c7
           n2r9c7   n6r9c4   n8r2c9   n9r3c4   n7r8c5   n5r9c6
           n5r1c4   n4r1c6   n7r2c6   n7r3c3   n9r1c3   n4r2c2
           n7r9c2 )

#VT: (2 1 1 2 1 2 1 1 1)
Cells: nil nil nil nil nil nil nil nil nil
Candidates:nil nil nil nil nil nil nil nil nil
2 3 4 5 6 7 8 9

Left in pool: (2)
#VT: (2 1 1 2 1 2 1 1 1)

1   6   9   5   8   4   3   7   2           
5   4   3   2   16  7   9   16  8           
8   2   7   9   16  3   46  5   14           
7   3   5   4   2   8   1   9   6           
2   1   8   3   9   6   5   4   7           
4   9   6   7   5   1   8   2   3           
6   8   2   1   4   9   7   3   5           
3   5   14  8   7   2   46  16  9           
9   7   14  6   3   5   2   8   14           

169584372543267918827913654735428196218396547496751823682149735351872469974635281
169584372543217968827963451735428196218396547496751823682149735354872619971635284


[jco]

A quick comparison for the (small) difference in rating

Code: Select all

.--------------------------------------------------------------------.
| 1     A46     4569   | 59     8      459    | 23     7      23     |
| 58-4  e478    3      | 2      6     f1457   | 9      14     148    |
| 89-4   2      479    | 9-7    1479   3      | 468    5      1468   | <= weakness at BVC r3c4
|----------------------+----------------------+----------------------| Y-wing (weaker) not needed
| 7     B36     25     | 4      29     89     | 1      369    3568   |
| 25     1-4    8      | 3      1279   6      | 45     49     457    |
|C34     9      146    |a78     5      18-7   | 3468   2      34678  |
|----------------------+----------------------+----------------------|
| 6     d38     249    | 1      49     4589   | 7      34     2345   |
|c38     5      147    |b678    47     2      | 346    1346   9      |
| 249    147    12479  | 5679   3      4579   | 2456   8      12456  | #1
'--------------------------------------------------------------------'

(7=8)r6c4 - (8)r8c4 = (8)r8c1 - (8)r7c2 = (8-7)r2c2 = (7)r2c6 => -7 r3c4; ste [4 strong links in two digits]

Code: Select all

.--------------------------------------------------------------------.
| 1     A46     4569   | 569    8      459    | 23     7      23     |
| 58-4   4678   3      | 2      1467   1457   | 9      46     1468   |
| 89-4   2      4679   | 679    14679  3      | 468    5      1468   |<= no weakness here
|----------------------+----------------------+----------------------| perhaps Y-wing is the best
| 7     B36     25     | 4      29     89     | 1      369    3568   |
| 25     1-4    8      | 3      1279   6      | 45     49     457    |
|C34     9      146    | 78     5      178    | 3468   2      34678  |
|----------------------+----------------------+----------------------|
| 6      38     249    | 1      49     4589   | 7      34     2345   |
| 38     5      47     | 678    467    2      | 346    1      9      |
| 249    147    12479  | 5679   3      4579   | 2456   8      2456   | #2
'--------------------------------------------------------------------'

1. Y-wing (346)r14c2, r5c1 => -4 r23c1, r5c2 [14 placements and basics]
2. (5): r4c3 = r1c3 - r1c4 = r9c4 - r9c7 = r5c7 => -5 r4c9, r5c1; ste [4 strong links in one digit]

[denis_berthier]

.

Code: Select all

1...8..7...326.9...2...3.5.7..4..1....83.6....9..5..2.6..1..7...5...2..9....3..8. SER = 7.1
1...8..7...32..9...2...3.5.7..4..1....83.6....9..5..2.6..1..7...5...2.19....3..8. SER = 6.7

Two preliminary remarks:
- in Sudoku, "almost the same puzzle" (say measured in terms of Hamming distance) doesn't imply much in terms of difficulty (whichever way you measure it). As shown by the tridagon examples, eliminating a single candidate can bring a puzzle down from T&E(3) to BC4;
- "difficulty" doesn't mean anything if you don't say how you measure it. In the present case, difficulty is reversed, whether you consider simplest-first solution or number of steps. This is quite common.

The two puzzles are not very different in difficulty in my rating system: both can be solved within S3Fin+BC3.
The first has slightly fewer candidates at the start (which is not meaningful) but it has a slightly longer simplest-first resolution path.

They are quite different if you consider the number of steps (restricted to chains of reasonable length): the first puzzle has two 1-step solutions in BC4, while the second doesn't have any, even in W5. Even for a 2-step solution, it requires W5.

1) Simplest-first solution of first puzzle:

Code: Select all

Resolution state after Singles and whips[1]:
   +-------------------+-------------------+-------------------+
   ! 1     46    4569  ! 59    8     459   ! 2346  7     2346  !
   ! 458   478   3     ! 2     6     1457  ! 9     14    148   !
   ! 489   2     4679  ! 79    1479  3     ! 468   5     1468  !
   +-------------------+-------------------+-------------------+
   ! 7     36    256   ! 4     29    89    ! 1     369   3568  !
   ! 245   14    8     ! 3     1279  6     ! 45    49    457   !
   ! 34    9     146   ! 78    5     178   ! 3468  2     34678 !
   +-------------------+-------------------+-------------------+
   ! 6     348   249   ! 1     49    4589  ! 7     34    2345  !
   ! 348   5     147   ! 678   47    2     ! 346   1346  9     !
   ! 249   147   12479 ! 5679  3     4579  ! 2456  8     12456 !
   +-------------------+-------------------+-------------------+
169 candidates.

hidden-pairs-in-a-block: b7{n3 n8}{r7c2 r8c1} ==> r8c1≠4, r7c2≠4
hidden-pairs-in-a-block: b4{n2 n5}{r4c3 r5c1} ==> r5c1≠4, r4c3≠6
hidden-pairs-in-a-row: r1{n2 n3}{c7 c9} ==> r1c9≠6, r1c9≠4, r1c7≠6, r1c7≠4
whip[1]: b3n6{r3c9 .} ==> r3c3≠6
finned-x-wing-in-columns: n9{c1 c4}{r9 r3} ==> r3c5≠9
finned-x-wing-in-columns: n3{c2 c8}{r4 r7} ==> r7c9≠3
finned-swordfish-in-columns: n5{c7 c1 c4}{r9 r5 r2} ==> r2c6≠5
singles ==> r2c1=5, r5c1=2, r4c3=5, r4c5=2
swordfish-in-columns: n8{c1 c4 c7}{r3 r8 r6} ==> r6c9≠8, r6c6≠8, r3c9≠8
biv-chain[3]: r1c2{n4 n6} - b4n6{r4c2 r6c3} - b4n1{r6c3 r5c2} ==> r5c2≠4
singles ==> r5c2=1, r6c6=1, r3c5=1
whip[1]: c5n4{r8 .} ==> r7c6≠4, r9c6≠4
whip[1]: r5n4{c9 .} ==> r6c7≠4, r6c9≠4
x-wing-in-columns: n7{c2 c6}{r2 r9} ==> r9c4≠7, r9c3≠7
biv-chain[3]: r6n4{c1 c3} - b4n6{r6c3 r4c2} - r1c2{n6 n4} ==> r3c1≠4
biv-chain[3]: r8n8{c4 c1} - r3c1{n8 n9} - r3c4{n9 n7} ==> r8c4≠7
biv-chain[3]: c5n4{r7 r8} - b8n7{r8c5 r9c6} - r9c2{n7 n4} ==> r7c3≠4
biv-chain[3]: c8n6{r4 r8} - r8c4{n6 n8} - r6n8{c4 c7} ==> r6c7≠6
biv-chain[3]: c1n3{r8 r6} - r6c7{n3 n8} - c4n8{r6 r8} ==> r8c1≠8
stte

2) Simplest-first solution of second puzzle:

Code: Select all

Resolution state after Singles and whips[1]:
   +-------------------+-------------------+-------------------+
   ! 1     46    4569  ! 569   8     459   ! 2346  7     2346  !
   ! 458   4678  3     ! 2     1467  1457  ! 9     46    1468  !
   ! 489   2     4679  ! 679   14679 3     ! 468   5     1468  !
   +-------------------+-------------------+-------------------+
   ! 7     36    256   ! 4     29    89    ! 1     369   3568  !
   ! 245   14    8     ! 3     1279  6     ! 45    49    457   !
   ! 34    9     146   ! 78    5     178   ! 3468  2     34678 !
   +-------------------+-------------------+-------------------+
   ! 6     348   249   ! 1     49    4589  ! 7     34    2345  !
   ! 348   5     47    ! 678   467   2     ! 346   1     9     !
   ! 249   147   12479 ! 5679  3     4579  ! 2456  8     2456  !
   +-------------------+-------------------+-------------------+
173 candidates.

hidden-pairs-in-a-block: b7{n3 n8}{r7c2 r8c1} ==> r8c1≠4, r7c2≠4
hidden-pairs-in-a-block: b4{n2 n5}{r4c3 r5c1} ==> r5c1≠4, r4c3≠6
hidden-pairs-in-a-row: r1{n2 n3}{c7 c9} ==> r1c9≠6, r1c9≠4, r1c7≠6, r1c7≠4
x-wing-in-columns: n3{c2 c8}{r4 r7} ==> r7c9≠3, r4c9≠3
finned-x-wing-in-columns: n9{c1 c4}{r9 r3} ==> r3c5≠9
finned-swordfish-in-columns: n5{c7 c1 c4}{r9 r5 r2} ==> r2c6≠5
singles ==> r2c1=5, r5c1=2, r4c3=5, r4c5=2
swordfish-in-columns: n8{c1 c4 c7}{r3 r8 r6} ==> r6c9≠8, r6c6≠8, r3c9≠8
biv-chain[3]: r1c2{n4 n6} - b4n6{r4c2 r6c3} - b4n1{r6c3 r5c2} ==> r5c2≠4
singles ==> r5c2=1, r6c6=1, r9c3=1, r7c3=2, r9c1=9, r1c6≠9
whip[1]: r5n4{c9 .} ==> r6c7≠4, r6c9≠4
hidden-pairs-in-a-column: c6{n8 n9}{r4 r7} ==> r7c6≠5, r7c6≠4
singles ==> r7c9=5, r5c7=5
x-wing-in-columns: n7{c2 c6}{r2 r9} ==> r9c4≠7, r2c5≠7
t-whip[2]: r7n4{c5 c8} - c7n4{r9 .} ==> r3c5≠4
biv-chain[3]: r6n4{c1 c3} - b4n6{r6c3 r4c2} - r1c2{n6 n4} ==> r3c1≠4
stte

3) The first puzzle has two 1-step solutions in BC4:

Code: Select all

biv-chain[4]: r6c4{n7 n8} - b8n8{r8c4 r7c6} - c2n8{r7 r2} - b1n7{r2c2 r3c3} ==> r3c4≠7
stte

Code: Select all

biv-chain[4]: r8n8{c4 c1} - b7n3{r8c1 r7c2} - r4c2{n3 n6} - c8n6{r4 r8} ==> r8c4≠6
stte

4) The second puzzle doesn't have any 1-step solution in W5, let alone in BC4. Even for 2-step solutions, it requires W5. Here's one:

Code: Select all

finned-swordfish-in-rows: n5{r7 r4 r2}{c6 c9 c3} ==> r1c3≠5
singles ==> r2c1=5, r4c3=5, r5c1=2, r4c5=2
whip[5]: r1c2{n6 n4} - r5c2{n4 n1} - r6c3{n1 n4} - r8c3{n4 n7} - r9c2{n7 .} ==> r4c2≠6
stte