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[AnotherLife]

This creature is very long and also ugly to some people.

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

..4....9.8....95...6......8..28....4.5...1...1...4.2..6....3.1..3..6...9..5..43..


[denis_berthier]

.

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Resolution state after Singles and whips[1]:
   +----------------------+----------------------+----------------------+
   ! 2357   127    4      ! 12357  123578 2578   ! 6      9      123    !
   ! 8      127    137    ! 6      1237   9      ! 5      4      123    !
   ! 2359   6      139    ! 4      1235   25     ! 7      23     8      !
   +----------------------+----------------------+----------------------+
   ! 379    79     2      ! 8      3579   567    ! 1      3567   4      !
   ! 4      5      3678   ! 237    237    1      ! 9      3678   367    !
   ! 1      789    36789  ! 3579   4      567    ! 2      35678  3567   !
   +----------------------+----------------------+----------------------+
   ! 6      4      79     ! 2579   2579   3      ! 8      1      257    !
   ! 27     3      178    ! 1257   6      2578   ! 4      257    9      !
   ! 279    12789  5      ! 1279   12789  4      ! 3      267    267    !
   +----------------------+----------------------+----------------------+
162 candidates.

A long (30 non-W1 steps) but easy resolution path, using only Subsets and reversible chains no longer than 4.

Code: Select all

hidden-pairs-in-a-block: b7{n1 n8}{r8c3 r9c2} ==> r9c2≠9, r9c2≠7, r9c2≠2, r8c3≠7
whip[1]: c2n2{r2 .} ==> r1c1≠2, r3c1≠2
whip[1]: c2n9{r6 .} ==> r4c1≠9, r6c3≠9
finned-x-wing-in-rows: n1{r8 r3}{c3 c4} ==> r1c4≠1
whip[1]: c4n1{r9 .} ==> r9c5≠1
finned-swordfish-in-columns: n2{c1 c8 c6}{r8 r9 r3} ==> r3c5≠2
biv-chain[3]: r6n9{c4 c2} - c2n8{r6 r9} - r9n1{c2 c4} ==> r9c4≠9
biv-chain[3]: c1n2{r8 r9} - r9n9{c1 c5} - b8n8{r9c5 r8c6} ==> r8c6≠2
whip[1]: c6n2{r3 .} ==> r1c4≠2, r1c5≠2, r2c5≠2
biv-chain[4]: r3n9{c3 c1} - r9n9{c1 c5} - b8n8{r9c5 r8c6} - r8c3{n8 n1} ==> r3c3≠1
hidden-single-in-a-row ==> r3c5=1
z-chain[3]: r3n3{c3 c8} - r4n3{c8 c5} - b2n3{r2c5 .} ==> r1c1≠3
biv-chain[3]: r1c1{n7 n5} - r3n5{c1 c6} - c6n2{r3 r1} ==> r1c6≠7
z-chain[3]: r1c1{n7 n5} - r1c4{n5 n3} - r2c5{n3 .} ==> r1c5≠7
biv-chain[4]: r3n2{c8 c6} - r3n5{c6 c1} - r1c1{n5 n7} - r8c1{n7 n2} ==> r8c8≠2
biv-chain[4]: r1c1{n7 n5} - r3n5{c1 c6} - r3n2{c6 c8} - r2n2{c9 c2} ==> r2c2≠7
biv-chain[3]: r2n7{c5 c3} - r7c3{n7 n9} - r9n9{c1 c5} ==> r9c5≠7
z-chain[4]: r2n7{c5 c3} - c3n1{r2 r8} - r8n8{c3 c6} - c6n7{r8 .} ==> r4c5≠7, r5c5≠7
z-chain[4]: r4n5{c6 c8} - r8c8{n5 n7} - c6n7{r8 r4} - c6n6{r4 .} ==> r6c6≠5
z-chain[4]: c1n3{r4 r3} - r3n5{c1 c6} - b5n5{r4c6 r6c4} - b5n9{r6c4 .} ==> r4c5≠3
biv-chain[4]: r4c5{n5 n9} - c2n9{r4 r6} - c2n8{r6 r9} - c5n8{r9 r1} ==> r1c5≠5
finned-x-wing-in-columns: n5{c5 c9}{r7 r4} ==> r4c8≠5
whip[1]: b6n5{r6c9 .} ==> r6c4≠5
z-chain[4]: b5n3{r5c5 r6c4} - r6n9{c4 c2} - r4c2{n9 n7} - r4c1{n7 .} ==> r5c3≠3
z-chain[4]: c6n7{r6 r8} - b8n8{r8c6 r9c5} - c2n8{r9 r6} - r6n9{c2 .} ==> r6c4≠7
biv-chain[5]: c8n2{r9 r3} - c6n2{r3 r1} - r1n8{c6 c5} - r9n8{c5 c2} - r9n1{c2 c4} ==> r9c4≠2
biv-chain[3]: r9c4{n7 n1} - r8n1{c4 c3} - r8n8{c3 c6} ==> r8c6≠7
whip[1]: c6n7{r6 .} ==> r5c4≠7
naked-pairs-in-a-block: b5{r5c4 r5c5}{n2 n3} ==> r6c4≠3
singles ==> r6c4=9, r4c5=5, r4c2=9
whip[1]: b5n3{r5c5 .} ==> r5c8≠3, r5c9≠3
biv-chain[3]: b5n7{r6c6 r4c6} - r4n6{c6 c8} - r5c9{n6 n7} ==> r6c8≠7, r6c9≠7
biv-chain[3]: r6c2{n8 n7} - r6c6{n7 n6} - b4n6{r6c3 r5c3} ==> r5c3≠8
hidden-single-in-a-row ==> r5c8=8
biv-chain[4]: c1n3{r4 r3} - r3n5{c1 c6} - r8c6{n5 n8} - c3n8{r8 r6} ==> r6c3≠3
hidden-single-in-a-block ==> r4c1=3
naked-pairs-in-a-block: b6{r4c8 r5c9}{n6 n7} ==> r6c9≠6, r6c8≠6
biv-chain[4]: c8n2{r9 r3} - r3c6{n2 n5} - r3c1{n5 n9} - r9n9{c1 c5} ==> r9c5≠2
biv-chain[4]: r3n5{c6 c1} - c1n9{r3 r9} - r9c5{n9 n8} - b2n8{r1c5 r1c6} ==> r1c6≠5
biv-chain[4]: c3n1{r2 r8} - r8n8{c3 c6} - r1c6{n8 n2} - c2n2{r1 r2} ==> r2c2≠1
naked-single ==> r2c2=2
biv-chain[4]: r9n8{c2 c5} - b2n8{r1c5 r1c6} - r1n2{c6 c9} - r1n1{c9 c2} ==> r9c2≠1
stte

By allowing longer but still reversible chains, one can reduce the number of non-W1 steps to 10 (and maybe fewer; I made only one try):

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1) hidden-pairs-in-a-block: b7{n1 n8}{r8c3 r9c2} ==> r9c2≠9, r9c2≠7, r9c2≠2, r8c3≠7
whip[1]: c2n2{r2 .} ==> r1c1≠2, r3c1≠2
whip[1]: c2n9{r6 .} ==> r4c1≠9, r6c3≠9
2) finned-x-wing-in-rows: n1{r3 r8}{c3 c5} ==> r9c5≠1
whip[1]: c5n1{r3 .} ==> r1c4≠1
3) z-chain[8]: c1n5{r1 r3} - r3c6{n5 n2} - r3c8{n2 n3} - r4n3{c8 c5} - c4n3{r5 r6} - b5n9{r6c4 r4c5} - r4c2{n9 n7} - r4c1{n7 .} ==> r1c1≠3
     with z-candidates = n3r4c1 n3r1c4
4) biv-chain[3]: r6n9{c4 c2} - c2n8{r6 r9} - r9n1{c2 c4} ==> r9c4≠9
5) biv-chain[4]: r8c3{n1 n8} - b8n8{r8c6 r9c5} - r9n9{c5 c1} - b1n9{r3c1 r3c3} ==> r3c3≠1
hidden-single-in-a-row ==> r3c5=1
6) biv-chain[3]: c1n2{r8 r9} - r9n9{c1 c5} - b8n8{r9c5 r8c6} ==> r8c6≠2
whip[1]: c6n2{r3 .} ==> r1c4≠2, r1c5≠2, r2c5≠2
7) z-chain[7]: c1n3{r4 r3} - r3n5{c1 c6} - c6n2{r3 r1} - c6n8{r1 r8} - r9n8{c5 c2} - r6c2{n8 n9} - r4c2{n9 .} ==> r4c1≠7
     with z-candidates = n7r6c2 n7r4c2
naked-single ==> r4c1=3
8) biv-chain[5]: r9n8{c2 c5} - r9n9{c5 c1} - b1n9{r3c1 r3c3} - b1n3{r3c3 r2c3} - c3n1{r2 r8} ==> r9c2≠1, r8c3≠8
singles ==> r8c3=1, r9c2=8, r8c6=8, r1c5=8, r9c4=1
9) z-chain[7]: c9n5{r7 r6} - c4n5{r6 r1} - r1n3{c4 c9} - r3c8{n3 n2} - r3c6{n2 n5} - r4n5{c6 c8} - r8n5{c8 .} ==> r7c5≠5
     with z-candidates = n5r8c4 n5r7c4 n5r4c5
singles ==> r4c5=5, r6c4=9, r6c2=7, r4c2=9, r6c6=6, r4c6=7, r4c8=6, r6c3=8, r5c3=6, r5c8=8, r5c9=7, r9c9=6
whip[1]: c6n5{r3 .} ==> r1c4≠5
10) z-chain[8]: b9n5{r8c8 r7c9} - r6c9{n5 n3} - r1n3{c9 c4} - c4n7{r1 r7} - c3n7{r7 r2} - c3n3{r2 r3} - c8n3{r3 r6} - c8n5{r6 .} ==> r8c8≠7, r8c4≠5
     with z-candidates = n7r8c4 n5r8c8
stte

[Cenoman]

In five steps:

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 +----------------------+--------------------------+----------------------+
 |  e57-3  127   4      | a12357   123578  B2578   |  6    9       123    |
 |   8     127   137    |  6       1237     9      |  5    4       123    |
 |  d59-3  6     139    |  4       1235   Ac25     |  7  Ac23      8      |
 +----------------------+--------------------------+----------------------+
 |FAa37 zwF79    2      |  8     wa3579     567    |  1   b3567    4      |
 |   4     5     368-7  | a237     237      1      |  9    3678    367    |
 |   1   zF789   368-7  | a3579    4        567    |  2    35678   3567   |
 +----------------------+--------------------------+----------------------+
 |   6     4    w79     |  2579   w2579     3      |  8    1       257    |
 |  A27    3    D18     |  1257    6      CA2578   |  4    257     9      |
 |   279 yE18    5      |  1279   x12789    4      |  3    267     267    |
 +----------------------+--------------------------+----------------------+

1. Almost kite:
[(3)r1c4 = r56c4 - r4c5 = r4c1] = (3)r4c8 - (3=25)r3c68 - r3c1 = (5)r1c1 => -3 r1c1
2. Almost ALS W-Wing:
[(3=2)r3c8 - r3c6 = r8c6 - (2=73)r48c1] = (2-8)r1c6 = r8c6 - r8c2 = r9c2 - (8=793)b4p128 => -3 r3c1; 1 placement
3. Almost W-Wing
[(7=9)r4c2 - r4c5 = r7c5 - (9=7)r7c5] = (9-8)r9c5 = r9c2 - (8=97)r46c2 => -7 r56c3; 6 placements & ls

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 +------------------+----------------------+----------------------+
 |  57    12   4    |  357    8      257   |  6    9       123    |
 |  8     12  d37   |  6     e37     9     |  5    4       12     |
 | C59    6    39   |  4      1     C25    |  7   D23      8      |
 +------------------+----------------------+----------------------+
 |  3     79   2    |  8      579    567   |  1    567     4      |
 |  4     5    68   |  237    237    1     |  9    3678    367    |
 |  1     79   68   |  3579   4      567   |  2    35678   3567   |
 +------------------+----------------------+----------------------+
 |  6     4   c79   | G2579  G2579   3     |  8    1      F257    |
 |  27    3    1    |  257    6      8     |  4   E257     9      |
 |Bb279   8    5    |  1    Aa9-27   4     |  3   E267     267    |
 +------------------+----------------------+----------------------+

4. S-Wing
(9)r9c5 = r9c1 - (9=7)r7c3 - r2c3 = (7)r2c5 => -7 r9c5
5. ALS S-wing with groups and transport
(9)r9c5 = r9c1 - (9=52)r3c16 - r3c8 = r89c8 - r7c9 = (2)r7c45 => -2 r9c5; ste

[AnotherLife]

Hi, Cenoman, thanks for your almost short solution. It is instructive to see how you manage to replace krakens by these ‘almost patterns’. Actually, none of the first three eliminations can be done by a single chain. I solved this puzzle some months ago by simpler methods, but I could not come to a solution of reasonable length.

In my approach, this puzzle is of ALSC-class, that is, its solution needs at least one AIC with ALS’s in addition to AICs with or without groups, but no forcing chains are needed. According to its ER 7.8, its solution should require Nishio Forcing Chains, which is less informative to a manual solver.

Another side of the puzzle’s complexity is how long the solution is, and this is harder to formalize. HoDoKu’s rating is based on the sum of the weights of the methods used in its default solution, and it will be great even if the methods used are rather simple but the solution is long. On the other hand, programs rarely provide good solutions, and in most cases the number of steps can be greatly lessened after optimization made by hand. So for now I think it is useful to add an inexplicit parameter ‘long’ to the formal rating based on the methods used if the solution is long enough.

Now let us consider concrete puzzles. The current puzzle surely requires a long solution, so I rate is as ALSC (long) (ER 7.8 in standard terms). One of my previous puzzles also requires a long solution, but as it is solvable by standard patterns and basic AICs, I rate is as C (long) (ER 6.9 in standard terms). The third puzzle is solvable in two moves by AICs with groups, so I rate it as GC (ER 8.3 in standard terms).

[eleven]

Hi Bogdan,

i appreciate your effort to find more relevant ratings (concerning techniques ER does not have, and especially, how many steps a solution needs), those drawbacks of ER are well known.
However the selection and rating of techniques can never reflect well, what is easier or harder for (different) manual solvers.

In this puzzle i only had a good start in my eyes, easy to find for me (but could not find a nice way to continue). But in all ratings i know of, it would be be classified a hard step (harder than a lot of chains i see in solvers, which i never would spot).

Code: Select all

   +----------------------+----------------------+----------------------+
   ! 2357   12+7   4      ! 12357  123578 2578   ! 6      9      12+3   !
   ! 8      12+7   137    ! 6      1237   9      ! 5      4      12+3   !
   ! 2359   6      139    ! 4      1235  b25     ! 7     a23     8      !
   +----------------------+----------------------+----------------------+
   ! 379   e79     2      ! 8    c#3579  *567    ! 1     #3567   4      !
   ! 4      5      3678   ! 237    237    1      ! 9      3678   367    !
   ! 1      789    36789  !d357+9  4     *567    ! 2      35678  3567   !
   +----------------------+----------------------+----------------------+
   ! 6      4      79     ! 2579   2579   3      ! 8      1      257    !
   ! 27     3      178    !#1257   6     *2578   ! 4     #257    9      !
   ! 279    12789  5      ! 1279   12789  4      ! 3      267    267    !
   +----------------------+----------------------+----------------------+

UR 12 r12c29, 7r12c2 = 3r12c9
7r12c2 - (7=9)r4c2 - r4c5 = 9r6c4
3r12c9 - (3=2)r3c8 - (2=5)r3c6
Now 5r3c6 opens a skyskraper 5 in r48 eliminating 5r6c4 too -> (5-9)r4c5 = 9r6c4
=> 9r6c4

[AnotherLife]

Hi Eleven,

A rating system should provide an average human solver with some information about the conventional methods and the number of steps needed to solve a puzzle, and it cannot take account of non-standard solutions. I have rated the current puzzle as ALSC (long), and I think this is enough for a player with average abilities to solve it if he is very determined and patient.

As to your first move proving r6c4=9, it could be called ‘a UR dynamic forcing chain’, and this placement can be reached by no single chain and even no kraken. This is a really complicated and non-standard solution.