The New Sudoku Players' Forum

[denis_berthier]

.
For those who prefer harder puzzles.

Code: Select all

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

2...8...4.5..1..3...6.7.5.....1.7...941...726...2.6.....7.5.9...3..2..8.8...6...5 # 96910 FHYK C28/S8.f
SER = 8.4, non-minimal

Code: Select all

Starting point: resolution state after Singles and whips[1]:
   +----------------+----------------+----------------+
   ! 2    179  39   ! 3569 8    359  ! 16   1679 4    !
   ! 47   5    489  ! 469  1    249  ! 268  3    2789 !
   ! 134  189  6    ! 349  7    2349 ! 5    19   1289 !
   +----------------+----------------+----------------+
   ! 356  268  2358 ! 1    49   7    ! 348  459  389  !
   ! 9    4    1    ! 58   3    58   ! 7    2    6    !
   ! 357  78   358  ! 2    49   6    ! 1348 1459 1389 !
   +----------------+----------------+----------------+
   ! 146  126  7    ! 348  5    1348 ! 9    146  123  !
   ! 1456 3    459  ! 479  2    149  ! 146  8    17   !
   ! 8    129  249  ! 3479 6    1349 ! 1234 147  5    !
   +----------------+----------------+----------------+
160 candidates

[DEFISE]

With basics (<=HP) and whips[<=7] :

Single: 3r5c5
Hidden pairs: 23b9p37 => -1r7c9 -1r9c7 -4r9c7
whip[7]: r1n1{c7 c2}- r1n7{c2 c8}- r9c8{n7 n4}- r7c8{n4 n6}- r7c2{n6 n2}- r9c2{n2 n9}- r9c3{n9 .}
=> -1r3c8
Single: 9r3c8
whip[7]: r1n7{c2 c8}- r1n1{c8 c7}- b3n6{r1c7 r2c7}- r8c7{n6 n4}- r9c8{n4 n1}- r9c2{n1 n2}- c7n2{r9 .}
=> -9r1c2
Single: 9r9c2
Hidden pairs: 26c2r47 => -8r4c2 -1r7c2
Box/Line: 1c2b1 => -1r3c1
Naked pairs: 34r3c14 => -3r3c6 -4r3c6
Single: 2r3c6
whip[4]: r8n9{c4 c6}- r2c6{n9 n4}- r2c1{n4 n7}- c9n7{r2 .} => -7r8c4
STTE

[P.O.]

after single and this chain:
r7n2{c2 c9} - r3{c2c8c9}{n1n8n9} - c1n1{r3 r7r8} => r7c2 <> 1

Code: Select all

2      c1+79  39     3569       8     359    d*16  dc*16-79   4             
h(4)7    5     489    469        1     249     268    3       b2+789           
h(34)1  f18-9  6     i(4)39      7    i(24)39  5     e1+9      1289           
 356     268   2358   1          49    7       348    459      389           
 9       4     1      58         3     58      7      2        6             
 357     78    358    2          49    6       1348   1459     1389           
g*146    26    7     j(38)4      5     1348    9      146      123           
g*1456   3     459   a4+79       2     149     146    8       b1-7             
 8      f12+9  249  ja(3)±7×4×9  6     1349    1234   147      5             

c4n7{r9 r8} - c9n7{r8 r2} - r1n7{c8 c2} - r1n1{c2 c7c8} - r3c8{n1 n9} - c2n9{r3 r9} - b7n1{r9c2 r7c1r8c1} - c1{r2r3}{n3n4} - r3{c4c6}{n2n4} - c4{r7r9}{n3n8} => r9c4 <> 4,9


2    c1+79  39    3569  8     359    16   c16-79  4             
47    5     489   469   1     249    268   3     b2+789           
134  e1-89  6     349   7     2349   5     19    e12+89           
356   268   2358  1     49    7      348   459    389           
9     4     1     58    3     58     7     2      6             
357  d7+8   358   2     49    6      1348  1459   1389           
146   26    7     348   5     1348   9     146   f1+23           
1456  3     459  a4+79  2     149    146   8     b1-7             
8     129   249  a×3±7  6     1349  g12+34 147    5             

c4n7{r9 r8} - c9n7{r8 r2} - r1n7{c8 c2} - r6c2{n7 n8} - r3n8{c2 c9} - c9n2{r3 r7} - b9n3{r7c9 r9c7} => r9c4 <> 3


singles.
c2n1{r1 r9} - b9n1{r9c8 r8c7} => r1c7 <> 1
ste.

[denis_berthier]

.
With the same "radiations" pattern than puzzles radiations-7.2-BC4 and radiations-7.2-W4, this puzzle has a higher SER and a higher W rating (W5).

Simplest-first solution in W5: Show

hidden-pairs-in-a-block: b9{n2 n3}{r7c9 r9c7} ==> r9c7≠4, r9c7≠1, r7c9≠1
biv-chain[3]: r8c9{n1 n7} - b3n7{r2c9 r1c8} - c8n6{r1 r7} ==> r7c8≠1
z-chain[3]: r1n7{c8 c2} - r1n1{c2 c7} - r3c8{n1 .} ==> r1c8≠9
biv-chain[4]: r2c1{n4 n7} - b3n7{r2c9 r1c8} - c8n6{r1 r7} - r8n6{c7 c1} ==> r8c1≠4
biv-chain[4]: r6c2{n8 n7} - r1n7{c2 c8} - c8n6{r1 r7} - c2n6{r7 r4} ==> r4c2≠8
biv-chain[4]: r8c9{n1 n7} - b3n7{r2c9 r1c8} - c8n6{r1 r7} - r8n6{c7 c1} ==> r8c1≠1
z-chain[4]: r4n8{c9 c3} - c3n2{r4 r9} - c7n2{r9 r2} - c7n8{r2 .} ==> r6c9≠8
z-chain[4]: c2n8{r3 r6} - c2n7{r6 r1} - b1n1{r1c2 r3c1} - r3c8{n1 .} ==> r3c2≠9
biv-chain[3]: c2n9{r9 r1} - r1n7{c2 c8} - r9n7{c8 c4} ==> r9c4≠9
biv-chain[5]: r6c2{n8 n7} - r1n7{c2 c8} - c8n6{r1 r7} - c2n6{r7 r4} - b4n2{r4c2 r4c3} ==> r4c3≠8
whip[1]: r4n8{c9 .} ==> r6c7≠8
biv-chain[5]: r8n5{c3 c1} - r8n6{c1 c7} - c8n6{r7 r1} - r1n7{c8 c2} - c2n9{r1 r9} ==> r8c3≠9
whip[1]: r8n9{c6 .} ==> r9c6≠9
biv-chain[5]: c1n1{r7 r3} - r3c2{n1 n8} - r6c2{n8 n7} - r1n7{c2 c8} - c8n6{r1 r7} ==> r7c1≠6
t-whip[5]: c2n9{r9 r1} - r1n7{c2 c8} - r1n1{c8 c7} - b3n6{r1c7 r2c7} - c7n2{r2 .} ==> r9c2≠2
hidden-pairs-in-a-column: c2{n2 n6}{r4 r7} ==> r7c2≠1
whip[5]: r3c8{n9 n1} - r3c2{n1 n8} - r2c3{n8 n4} - c1n4{r3 r7} - c1n1{r7 .} ==> r2c9≠9
whip[1]: b3n9{r3c9 .} ==> r3c4≠9, r3c6≠9
whip[5]: c2n9{r9 r1} - r1n7{c2 c8} - r1n1{c8 c7} - b9n1{r8c7 r8c9} - c9n7{r8 .} ==> r9c2≠1
singles ==> r9c2=9, r7c1=1
whip[1]: b7n4{r9c3 .} ==> r2c3≠4
naked-pairs-in-a-row: r3{c1 c4}{n3 n4} ==> r3c6≠4, r3c6≠3
naked-single ==> r3c6=2
naked-triplets-in-a-row: r1{c2 c7 c8}{n7 n1 n6} ==> r1c4≠6
hidden-single-in-a-block ==> r2c4=6
biv-chain[3]: r9c3{n4 n2} - r7c2{n2 n6} - r7c8{n6 n4} ==> r9c8≠4
naked-pairs-in-a-block: b9{r8c9 r9c8}{n1 n7} ==> r8c7≠1
naked-triplets-in-a-row: r8{c1 c3 c7}{n6 n5 n4} ==> r8c6≠4, r8c4≠4
biv-chain[3]: r9c8{n1 n7} - r1n7{c8 c2} - c2n1{r1 r3} ==> r3c8≠1
naked-single ==> r3c8=9
biv-chain[3]: r4c8{n5 n4} - b9n4{r7c8 r8c7} - r8c3{n4 n5} ==> r4c3≠5
biv-chain[3]: r4c3{n3 n2} - c2n2{r4 r7} - r7c9{n2 n3} ==> r4c9≠3
z-chain[3]: b6n3{r6c9 r4c7} - c7n8{r4 r2} - c3n8{r2 .} ==> r6c3≠3
biv-chain[4]: r9c7{n3 n2} - c3n2{r9 r4} - c3n3{r4 r1} - r3n3{c1 c4} ==> r9c4≠3
biv-chain[4]: r2c1{n7 n4} - b2n4{r2c6 r3c4} - r9c4{n4 n7} - b9n7{r9c8 r8c9} ==> r2c9≠7
stte

It doesn't have any 1- or 2- step solution in W8.

It has 4-step solutions in W7, e.g.:
whip[7]: r1n1{c8 c2} - r1n7{c2 c8} - r9c8{n7 n4} - r7c8{n4 n6} - r7c2{n6 n2} - r9c3{n2 n9} - r9c2{n9 .} ==> r3c8≠1
naked-single ==> r3c8=9
whip[7]: r1n7{c2 c8} - r1n1{c8 c7} - b3n6{r1c7 r2c7} - r8c7{n6 n4} - r9c8{n4 n1} - r9c2{n1 n2} - c7n2{r9 .} ==> r1c2≠9
hidden-single-in-a-column ==> r9c2=9
whip[3]: r1c7{n6 n1} - r1c8{n1 n7} - r1c2{n7 .} ==> r2c7≠6
hidden-single-in-a-row ==> r2c4=6
biv-chain[6]: r1n7{c8 c2} - r6c2{n7 n8} - b1n8{r3c2 r2c3} - b1n9{r2c3 r1c3} - c4n9{r1 r8} - r8n7{c4 c9} ==> r2c9≠7, r9c8≠7
stte

François: the Hidden Pair is not necessary before your first two steps. Indeed, for each of these steps, there is only one possibility with the best score. I think this is why we find the same first two steps (disregarding your initial Pair).
I don't know if one can find a real 3-step solution in W7, without any non counted Pairs. Does your program allow to disable Pairs?

[DEFISE]

.
François: the Hidden Pair is not necessary before your first two steps. Indeed, for each of these steps, there is only one possibility with the best score. I think this is why we find the same first two steps (disregarding your initial Pair).
I don't know if one can find a real 3-step solution in W7, without any non counted Pairs. Does your program allow to disable Pairs?

Indeed the first HP does not simplify the rest of my solution.
But if I don’t use the 2nd HP or if I only don't use the NP after, I need 2 whips instead of one to finish.

In my program I can limit the basics to (Singles + W1).
I then get a solution similar to yours:

Hidden Text: Show

Single: 3r5c5
whip[7]: r1n1{c7 c2}- r1n7{c2 c8}- r9c8{n7 n4}- r7c8{n4 n6}- r7c2{n6 n2}- r9c2{n2 n9}- r9c3{n9 .}
=> -1r3c8
Single: 9r3c8
whip[7]: r1n7{c2 c8}- r1n1{c8 c7}- b3n6{r1c7 r2c7}- r8c7{n6 n4}- r9c8{n4 n1}- r9c2{n1 n2}- c7n2{r9 .}
=> -9r1c2
Single: 9r9c2
whip[3]: r1c7{n6 n1}- r1c2{n1 n7}- r1c8{n7 .} => -6r1c4
Single: 6r2c4
whip[5]: r2c7{n8 n2}- r2c9{n2 n7}- r8n7{c9 c4}- r8n9{c4 c6}- r2n9{c6 .} => -8r2c3
STTE

Nevertheless I prefer to minimize the number of chains.

[denis_berthier]

I prefer to minimize the number of chains.

I see. But it makes it look like there were more steps.