The New Sudoku Players' Forum

[ixsetf]

I am have modified my method for making puzzles since my last post. I think the changes will produce more elegant puzzles with more consistent difficulty. You can see the first result of these changes below.

Code: Select all

 *-----------*
 |.25|..3|...|
 |..3|41.|...|
 |.1.|.2.|9.3|
 |---+---+---|
 |2..|.3.|16.|
 |.3.|1..|.58|
 |1.4|..8|.3.|
 |---+---+---|
 |...|397|6..|
 |39.|..1|.8.|
 |..1|...|39.|
 *-----------*


Play/Print this puzzle.

[champagne]

I had a look to these 2 puzzles.

A small remark, they are not minimal, but no doubt, they are valid.

A classical rating (here skfr) rates the second one higher than the first (ED 8.3 against 7.2), but we are still far from the so called "hard puzzles".

[JC Van Hay]

r5c7=4or7->contradiction :=> r5c7=2; "basics" to end.

OR

Code: Select all

+---------------------+-----------------------+--------------------+
| 678(49)  2    5     | 67(89)  67(8)  3      | (48)    147  146   |
| 6789     678  3     | 4       1      6(9)   | 258     27   256   |
| 7-8(46)  1    78(6) | 7(568)  2      (56)   | 9       47   3     |
+---------------------+-----------------------+--------------------+
| 2        578  789   | 579     3      5(49)  | 1       6    79(4) |
| 67       3    679   | 1       467    46(29) | 7-4(2)  5    8     |
| 1        567  4     | 25679   567    8      | 27      3    279   |
+---------------------+-----------------------+--------------------+
| 58       48   28    | 3       9      7      | 6       124  1245  |
| 3        9    27(6) | 25(6)   45(6)  1      | 2457    8    2457  |
| 567      467  1     | 2568    4568   (2456) | 3       9    2457  |
+---------------------+-----------------------+--------------------+

#1. AAHS(56)r3c1346 + 9C6 + (2456)r9c6 :=> [4r1c7==2r5c7==4r4c9]-4r5c7

HP(56-8)r3c46=8r1c45-(8=4)r1c7
||
6r3c1-4r3c1=(4-9)r1c1=9r1c4-9r2c6=*Wing[2r5c7=(2-9)r5c6=*(9-4)r4c6=4r4c9]
||
6r3c3-[6r8c3=6r8c45-6r9c6 AND (6=5)r3c6-5r9c6]=*Wing[2r5c7=2r5c6-(2=*4)r9c6-4r4c6=4r4c9]

Bonus : Wing[4r3c1=4r1c1-(4=8)r1c7-8r1c45=8r3c4]-8r3c1
r46c9=49; HP(24-569)r59c6=[9r5c3 AND LC(6r23c6)-6r13c45]

Code: Select all

+--------------------+------------------+------------------+
| 478-6(9)  2    5   | 789   78    3    | 48    147  1(6)  |
| 678(9)    678  3   | 4     1     (69) | 258   27   25(6) |
| 467       1    678 | 578   2     56   | 9     47   3     |
+--------------------+------------------+------------------+
| 2         578  78  | 579   3     59   | 1     6    4     |
| 67        3    9   | 1     467   24   | 27    5    8     |
| 1         567  4   | 2567  567   8    | 27    3    9     |
+--------------------+------------------+------------------+
| 58        48   28  | 3     9     7    | 6     124  125   |
| 3         9    267 | 256   456   1    | 2457  8    257   |
| 567       467  1   | 2568  4568  24   | 3     9    257   |
+--------------------+------------------+------------------+


#2. Wing[9r1c1=9r2c1-(9=6)r2c6-6r2c9=6r19]-6r1c1=6L1C9
3 Singles; LC(8r12c1)-8r23c23=8r3c4; ste

[ixsetf]

I had a look to these 2 puzzles.

A small remark, they are not minimal, but no doubt, they are valid.

A classical rating (here skfr) rates the second one higher than the first (ED 8.3 against 7.2), but we are still far from the so called "hard puzzles".

I did make an attempt to minimize this more recent puzzle, but every subset I produced would end up unraveling after some trivial steps. I am not sure whether it would be better to leave it as is or minimize the puzzle even if it doesn't add much to the difficulty. Hopefully the community here has an opinion on which option to pursue in the future.

As for the difficulty, I know I have a long way to go before I can produce anything near as difficult as Arto Inkala or Escargot. I do wish to make puzzles like them in the future, but there are some things limiting this. Mainly they are my limited experience with constructing puzzles, and a mostly by-hand production. While constructing these I did check a solver to see if removals produced contradictions, but otherwise I used no code.

My current plan is to experiment a bit and find a good method of producing these non-trivial puzzles, and then eventually try to translate that into code where I can more easily brute force a more difficult solution.

[champagne]

As for the difficulty, I know I have a long way to go before I can produce anything near as difficult as Arto Inkala or Escargot. I do wish to make puzzles like them in the future, but there are some things limiting this. Mainly they are my limited experience with constructing puzzles, and a mostly by-hand production. While constructing these I did check a solver to see if removals produced contradictions, but otherwise I used no code.

My remark about the difficulty is not so important.

Many players just stop when the puzzles require long solutions, so, very often, difficult puzzles are of poor value for them.

On top of it, the rating usually evaluates the most difficult step. A skill player can cope with pleasure with puzzles rated very very high if they have a quick solution using special rules but will reject puzzles requiring many steps (as Escargot so far).

Commercial puzzles have normally much smaller ratings.

[ixsetf]

My remark about the difficulty is not so important.

Many players just stop when the puzzles require long solutions, so, very often, difficult puzzles are of poor value for them.

On top of it, the rating usually evaluates the most difficult step. A skill player can cope with pleasure with puzzles rated very very high if they have a quick solution using special rules but will reject puzzles requiring many steps (as Escargot so far).

Commercial puzzles have normally much smaller ratings.

Thanks for the clarification. I do above all wish to create puzzles which are enjoyable to solve, making them challenging is only a secondary goal. I definitely appreciate the feedback, and I will take what you're saying into consideration for future attempts.

[daj95376]

Code: Select all

 after Basics
 +-----------------------------------------------------------------------+
 |  46789  2      5      |  6789   678    3      |  48     147    146    |
 |  6789   678    3      |  4      1      69     |  258    27     256    |
 |  4678   1      678    |  5678   2      56     |  9      47     3      |
 |-----------------------+-----------------------+-----------------------|
 |  2      578    789    |  579    3      459    |  1      6      479    |
 |  67     3      679    |  1      467    2469   |  247    5      8      |
 |  1      567    4      |  25679  567    8      |  27     3      279    |
 |-----------------------+-----------------------+-----------------------|
 |  58     48     28     |  3      9      7      |  6      124    1245   |
 |  3      9      267    |  256    456    1      |  2457   8      2457   |
 |  567    467    1      |  2568   4568   2456   |  3      9      2457   |
 +-----------------------------------------------------------------------+
 # 102 eliminations remain

 -6r2c12 and Kraken Column [c6] for <6>:

 6r2c6
   ||
 6r3c6 - r3c13 =                 ( 6-9)r1 c1 = r1c4 - (9=6)r2c6 - 6r3c6  discontinuous loop
   ||
 6r9c6 - r9c12 = r8c3 - r3c3 = hp(46-9)r13c1 = r1c4 - (9=6)r2c6 - 6r9c6  discontinuous loop
   ||
 6r5c6 - (6=954)r234c6 - r4c9 = (4-2)r5c7 = (2-6)r5c6                    discontinuous loop


 Bottom Line: 6r2c12 = 6r2c6  =>  -6 r2c9


Code: Select all

 after additional Basics
 +-----------------------------------------------------------------------+
 |  489    2      5      |  789    78     3      |  48     1      6      |
 |  89     67     3      |  4      1      69     |  258    27     25     |
 |  48     1      67     |  568    2      56     |  9      47     3      |
 |-----------------------+-----------------------+-----------------------|
 |  2      578    789    |  579    3      459    |  1      6      479    |
 |  67     3      679    |  1      467    2469   |  247    5      8      |
 |  1      567    4      |  25679  567    8      |  27     3      279    |
 |-----------------------+-----------------------+-----------------------|
 |  5      48     28     |  3      9      7      |  6      24     1      |
 |  3      9      267    |  256    456    1      |  2457   8      2457   |
 |  67     467    1      |  2568   4568   2456   |  3      9      2457   |
 +-----------------------------------------------------------------------+
 # 80 eliminations remain

 (7=6)r2c2 - (6=9)r2c6 - (9=8)r2c1 - (8=4)r3c1 - (4=7)r3c8  =>  -7 r2c8,r3c3


 Singles


[Edit: replaced logic for =6r5c6]

[Addendum: the discontinuous loop for 6r5c6 is independent of the constraint -6r2c12 ... and should be considered a separate step.]

[JC Van Hay]

Code: Select all

 after Basics
 +-----------------------------------------------------------------------+
 |  46789  2      5      |  6789   678    3      |  48     147    146    |
 |  6789   678    3      |  4      1      69     |  258    27     256    |
 |  4678   1      678    |  5678   2      56     |  9      47     3      |
 |-----------------------+-----------------------+-----------------------|
 |  2      578    789    |  579    3      459    |  1      6      479    |
 |  67     3      679    |  1      467    2469   |  247    5      8      |
 |  1      567    4      |  25679  567    8      |  27     3      279    |
 |-----------------------+-----------------------+-----------------------|
 |  58     48     28     |  3      9      7      |  6      124    1245   |
 |  3      9      267    |  256    456    1      |  2457   8      2457   |
 |  567    467    1      |  2568   4568   2456   |  3      9      2457   |
 +-----------------------------------------------------------------------+
 # 102 eliminations remain

 -6r2c12 and Kraken Column [c6] for <6>:

 6r2c6
   ||
 6r3c6 - r3c13 =                 ( 6-9)r1 c1 = r1c4 - (9=6)r2c6 - 6r3c6  discontinuous loop
   ||
 6r9c6 - r9c12 = r8c3 - r3c3 = hp(46-9)r13c1 = r1c4 - (9=6)r2c6 - 6r9c6  discontinuous loop
   ||
   ||     (6=9)r2c6
   ||   /          \
 6r5c6 -            - (59=4)r4c6 - r4c9 = (4-2)r5c7 = (2-6)r5c6          discontinuous loop
        \          /
          (6=5)r3c6


 Bottom Line: 6r2c12 = 6r2c6  =>  -6 r2c9


An equivalent presentation :

Code: Select all

+-----------------------+------------------------+-------------------+
| 78(469)  2      5     | 678(9)  678   3        | 48     147  146   |
| 789(6)   78(6)  3     | 4       1     (69)     | 258    27   25-6  |
| 78(46)   1      78(6) | 5678    2     (56)     | 9      47   3     |
+-----------------------+------------------------+-------------------+
| 2        578    789   | 579     3     (459)    | 1      6    79(4) |
| 67       3      679   | 1       467   4(2)-69  | 7(24)  5    8     |
| 1        567    4     | 25679   567   8        | 27     3    279   |
+-----------------------+------------------------+-------------------+
| 58       48     28    | 3       9     7        | 6      124  1245  |
| 3        9      27(6) | 256     456   1        | 2457   8    2457  |
| 57(6)    47(6)  1     | 2568    4568  245(6)   | 3      9    2457  |
+-----------------------+------------------------+-------------------+


#1a. [2r5c6=(2-4)r5c7=4r4c9-(4=569)r432c6]-69r5c6
#1b. Kraken 6B1 :=> [6r2c12==6r2c6]-6r2c9

6r2c12
||
HP(46-9)r13c1=9r1c4-(9=6)r2c6
||
6r3c3-ER(6)[r8c3=r9c12-r9c6=*r3c6]=*6r2c6

[999_Springs]

solved this entirely by hand, so solution path may be a little messy, but here goes.

9r4c9(-9-r4c6)=4=r5c7(-4-r1c7-8-r1c45=3=r3c4-8-r3c3)=2=r5c6(-6)=9=r2c6(-6)-9-r2c1=9=r1c1=4=r3c1-4-r3c8-7-r3c3-6-(r3c6)r8c3=6=r8c34-6-r9c6 => r4c9=/=9 (edit: it turns out that this chain and the single after it are totally unnecessary, and after following the rest of these steps, all i needed was a naked pair 56 in r6 followed by a three strong links in 6 in b1 c9 r8 => r1c4=/=6)

single r6c9=9

467r13c1=9=r2c1-9-r2c6-6-r2c9=6=r1c9=1=r7c9=5=r7c1-5-als:567r59c1-67-r13c1 => r13c1=/=67

w-wing 8r2 + 48r3c1r1c7 => r1c1r3c8=/=4

singles r3c1=4, r2c8=2, r3c8=7

4r8c5=4=r8c79-4-r7c8-1-r1c8-4-r1c7(-8-r1c1-9-r2c1=9=r2c6-9-r4c6)-8-r1c45=8=r3c4(=5=r3c6-5-r4c6-4-r5c5)-8-r9c4=8=r9c5=4=r8c5 => r8c5=4

naked pair 67 in r5 => r5c3=9

turbot fish 7 in c3 and c7 => r4c9r6c2=/=7, singles to end


with regards to difficulty and puzzle creation: it's true what champagne said that puzzles that have a short and neat solution are much more enjoyable to solve than puzzles that require tons of aic-nets (like top1465 #77, or escargot; not so much arto inkala, since that has a multi fish at the start that you can do stuff with). however puzzles like those are hard to find, and your "typical" puzzle at around se 8.x will not be a neat one-stepper. personally i don't mind slogging out a solution to a decently (but not overly) hard puzzle like this one, i find it part of the challenge, and they only start to get annoying for me at se high-8 or 9.0. this thing is certainly much harder compared to most of the stuff that gets posted in this subforum anyway. enjoying this, keep up the good work.

[JC Van Hay]

solved this entirely by hand, so solution path may be a little messy, but here goes.

9r4c9(-9-r4c6)=4=r5c7(-4-r1c7-8-r1c45=3=r3c4-8-r3c3)=2=r5c6(-6)=9=r2c6(-6)-9-r2c1=9=r1c1=4=r3c1-4-r3c8-7-r3c3-6-(r3c6)r8c3=6=r8c34-6-r9c6 => r4c9=/=9 (edit: it turns out that this chain and the single after it are totally unnecessary, and after following the rest of these steps, all i needed was a naked pair 56 in r6 followed by a three strong links in 6 in b1 c9 r8 => r1c4=/=6)

....

One can write 999_Springs chain as the following "exclusion matrix" :

Code: Select all

9r4c9
4r4c9=4r5c7
      4r1c7=8r1c7
            8r1c45=8r3c4
      2r5c7==============2r5c6
9r4c6====================9r5c6=9r2c6
                               9r1c4=9r1c1
                                     4r1c1=4r3c1
                                           4r3c7=7r3c8
                   8r3c3=========================7r3c3=6r3c3
                                                       6r3c6=5r3c6
                                                       6r8c3=======6r8c34
                         6r5c6=6r2c6=========================6r3c6=6r9c6

Such a matrix not only shows the exclusion of 9r4c9, but also the exclusion of 4r4c6 because of the derived SIS 4r4c9==9r4c6.
IOW, whatever the solution of the 12 constraints in the 12 last rows, either r4c9=4 or r4c6=9.

Furthermore, all the solutions of these constraints also exclude 8r3c1 and 7r3c4 because of the weak coupling between the 3rd and the 8th rows/constraints [4r1c7-4r1c1].
This allows one to write : 8r3c4=8r1c45-8r1c7=4r1c7-4r1c1=4r3c1*-4r3c7=7r3c8 :=> -8r3c1*,-7r3c4.

Conclusion : r46c9=49,-8r3c1 and then, as in my previous post.

[denis_berthier]

Hi ixsetf

Here is a 100% non-manual complete solution, with chains of maximal length 4:

Code: Select all

*******************************************************************************************************
***  SudoRules 20.0.s based on CSP-Rules 2.0.s, using CLIPS 6.30-r152, config = gW-S
*******************************************************************************************************
.25..3.....341.....1..2.9.32...3.16..3.1...581.4..8.3....3976..39...1.8...1...39.
33 givens, 162 candidates
whip[1]: b8n8{r9c5 .} ==> r9c2 ≠ 8, r9c1 ≠ 8
whip[1]: c1n5{r9 .} ==> r9c2 ≠ 5
whip[1]: c2n4{r9 .} ==> r9c1 ≠ 4
whip[1]: c1n5{r7 .} ==> r7c2 ≠ 5
whip[1]: c2n4{r7 .} ==> r7c1 ≠ 4
whip[1]: c3n9{r5 .} ==> r5c1 ≠ 9
whip[1]: c8n7{r2 .} ==> r2c9 ≠ 7, r2c7 ≠ 7, r1c9 ≠ 7, r1c7 ≠ 7
whip[1]: b3n5{r2c9 .} ==> r2c6 ≠ 5
biv-chain[3]: b1n9{r1c1 r2c1} - r2c6{n9 n6} - c9n6{r2 r1} ==> r1c1 ≠ 6
whip[3]: b1n4{r3c1 r1c1} - r1c7{n4 n8} - r2n8{c7 .} ==> r3c1 ≠ 8
whip[3]: b1n4{r1c1 r3c1} - r3c8{n4 n7} - r2n7{c8 .} ==> r1c1 ≠ 7
whip[3]: r3c8{n7 n4} - r1c7{n4 n8} - b2n8{r1c4 .} ==> r3c4 ≠ 7
whip[1]: b2n7{r1c5 .} ==> r1c8 ≠ 7
whip[4]: c5n8{r9 r1} - r1c7{n8 n4} - c8n4{r1 r7} - r8n4{c7 .} ==> r9c5 ≠ 4
biv-chain[2]: r4n4{c9 c6} - b8n4{r9c6 r8c5} ==> r8c9 ≠ 4
whip[4]: c6n2{r5 r9} - b8n4{r9c6 r8c5} - r5n4{c5 c7} - r5n2{c7 .} ==> r5c6 ≠ 9
hidden-single-in-a-row ==> r5c3 = 9
biv-chain[4]: c3n6{r3 r8} - c3n2{r8 r7} - c8n2{r7 r2} - b3n7{r2c8 r3c8} ==> r3c3 ≠ 7
hidden-pairs-in-a-row: r3{n4 n7}{c1 c8} ==> r3c1 ≠ 6
whip[2]: b9n7{r9c9 r8c7} - c3n7{r8 .} ==> r4c9 ≠ 7
biv-chain[3]: r5c1{n6 n7} - c3n7{r4 r8} - c3n6{r8 r3} ==> r2c1 ≠ 6
whip[4]: r3c6{n5 n6} - r3c3{n6 n8} - c1n8{r1 r7} - b7n5{r7c1 .} ==> r9c6 ≠ 5
whip[4]: b8n5{r9c4 r8c5} - r8n4{c5 c7} - r1c7{n4 n8} - b2n8{r1c4 .} ==> r3c4 ≠ 5
hidden-single-in-a-block ==> r3c6 = 5
naked-pairs-in-a-row: r4{c6 c9}{n4 n9} ==> r4c4 ≠ 9
whip[2]: b7n6{r9c2 r8c3} - r3n6{c3 .} ==> r9c4 ≠ 6
biv-chain[3]: r2c6{n6 n9} - b5n9{r4c6 r6c4} - b5n2{r6c4 r5c6} ==> r5c6 ≠ 6
biv-chain[3]: r3c4{n8 n6} - c6n6{r2 r9} - r9c5{n6 n8} ==> r9c4 ≠ 8
hidden-single-in-a-block ==> r9c5 = 8
biv-chain[3]: r4c4{n7 n5} - c5n5{r6 r8} - c5n4{r8 r5} ==> r5c5 ≠ 7
biv-chain[2]: r5n7{c7 c1} - c3n7{r4 r8} ==> r8c7 ≠ 7
whip[1]: b9n7{r9c9 .} ==> r6c9 ≠ 7
biv-chain[3]: b8n4{r9c6 r8c5} - r5c5{n4 n6} - c1n6{r5 r9} ==> r9c6 ≠ 6
singles to the end

825973416
973416825
416825973
258739164
739164258
164258739
582397641
397641582
641582397