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[mith]

Code: Select all

+-------+-------+-------+
| . . . | . . . | . . . |
| . . 3 | . 1 . | 4 . . |
| 1 . . | 5 . 9 | . . . |
+-------+-------+-------+
| . . . | . 2 . | 6 5 . |
| 3 5 . | . . . | . 8 9 |
| . 7 9 | . 3 . | . . . |
+-------+-------+-------+
| . . . | 2 . 3 | . . 8 |
| . . 4 | . 6 . | 2 . . |
| . . . | . . . | . . . |
+-------+-------+-------+
...........3.1.4..1..5.9.......2.65.35.....89.79.3.......2.3..8..4.6.2...........

That one is on the easy side, so here's a harder pi puzzle:

Code: Select all

+-------+-------+-------+
| . . 3 | . . 1 | 4 . . |
| . . . | . . . | . 1 . |
| 5 . . | . . 9 | . . . |
+-------+-------+-------+
| . . 2 | . 6 . | . . 5 |
| 3 5 . | . . . | . 8 9 |
| 7 . . | . 9 . | 3 . . |
+-------+-------+-------+
| . . . | 2 . . | . . 3 |
| . 8 . | . . . | . . . |
| . . 4 | 6 . . | 2 . . |
+-------+-------+-------+
..3..14.........1.5....9.....2.6...535.....897...9.3.....2....3.8.........46..2..

[denis_berthier]

Code: Select all

+-------+-------+-------+
| . . . | . . . | . . . |
| . . 3 | . 1 . | 4 . . |
| 1 . . | 5 . 9 | . . . |
+-------+-------+-------+
| . . . | . 2 . | 6 5 . |
| 3 5 . | . . . | . 8 9 |
| . 7 9 | . 3 . | . . . |
+-------+-------+-------+
| . . . | 2 . 3 | . . 8 |
| . . 4 | . 6 . | 2 . . |
| . . . | . . . | . . . |
+-------+-------+-------+
...........3.1.4..1..5.9.......2.65.35.....89.79.3.......2.3..8..4.6.2...........

That one is on the easy side, so here's a harder pi puzzle:

Code: Select all

+-------+-------+-------+
| . . 3 | . . 1 | 4 . . |
| . . . | . . . | . 1 . |
| 5 . . | . . 9 | . . . |
+-------+-------+-------+
| . . 2 | . 6 . | . . 5 |
| 3 5 . | . . . | . 8 9 |
| 7 . . | . 9 . | 3 . . |
+-------+-------+-------+
| . . . | 2 . . | . . 3 |
| . 8 . | . . . | . . . |
| . . 4 | 6 . . | 2 . . |
+-------+-------+-------+
..3..14.........1.5....9.....2.6...535.....897...9.3.....2....3.8.........46..2..

Both require more than Subsets.

The first is solved with a typed bivalue-chain[3] in rc-space:

Hidden Text: Show

***********************************************************************************************
*** SudoRules 20.1.s based on CSP-Rules 2.1.s, config = BC+SFin
*** Using CLIPS 6.32-r770
***********************************************************************************************
singles
whip[1]: c6n8{r9 .} ==> r9c5 ≠ 8
whip[1]: r7n7{c3 .} ==> r9c3 ≠ 7, r9c1 ≠ 7
whip[1]: r7n6{c3 .} ==> r9c3 ≠ 6, r9c2 ≠ 6
whip[1]: r7n1{c3 .} ==> r9c3 ≠ 1, r8c2 ≠ 1, r9c2 ≠ 1
whip[1]: r2n8{c2 .} ==> r3c3 ≠ 8, r1c1 ≠ 8, r1c2 ≠ 8, r1c3 ≠ 8
naked-pairs-in-a-row: r7{c5 c7}{n5 n9} ==> r7c3 ≠ 5, r7c2 ≠ 9, r7c1 ≠ 9, r7c1 ≠ 5
naked-single ==> r7c1 = 7
whip[1]: r2n7{c9 .} ==> r1c8 ≠ 7, r1c9 ≠ 7, r3c8 ≠ 7
hidden-pairs-in-a-row: r9{n6 n7}{c8 c9} ==> r9c9 ≠ 5, r9c9 ≠ 1, r9c8 ≠ 9, r9c8 ≠ 3, r9c8 ≠ 1
hidden-single-in-a-row ==> r9c6 = 1
naked-single ==> r8c6 = 8
x-wing-in-rows: n5{r2 r8}{c1 c9} ==> r9c1 ≠ 5, r1c9 ≠ 5, r1c1 ≠ 5
hidden-triplets-in-a-row: r1{n5 n7 n8}{c7 c3 c5} ==> r1c7 ≠ 9, r1c3 ≠ 6
whip[1]: c7n9{r9 .} ==> r8c8 ≠ 9
whip[1]: r8n9{c2 .} ==> r9c1 ≠ 9, r9c2 ≠ 9
biv-chain-rc[3]: r2c2{n8 n9} - r1c1{n9 n2} - r9c1{n2 n8} ==> r2c1 ≠ 8, r9c2 ≠ 8
stte

The second requires several type-unrestricted bivalue-chains[3 and 4] (in addition to Subsets). Notice that allowing whips doesn't change the resolution path.

Hidden Text: Show

***********************************************************************************************
*** SudoRules 20.1.s based on CSP-Rules 2.1.s, config = BC+SFin
*** Using CLIPS 6.32-r770
***********************************************************************************************
singles
whip[1]: r5n4{c6 .} ==> r6c6 ≠ 4, r4c4 ≠ 4, r4c6 ≠ 4, r6c4 ≠ 4
whip[1]: r5n2{c6 .} ==> r6c6 ≠ 2
hidden-single-in-a-column ==> r5c6 = 2
whip[1]: c6n4{r8 .} ==> r7c5 ≠ 4, r8c5 ≠ 4
whip[1]: c4n1{r6 .} ==> r5c5 ≠ 1
hidden-pairs-in-a-block: b3{r1c8 r2c7}{n5 n9} ==> r2c7 ≠ 8, r2c7 ≠ 7, r1c8 ≠ 7, r1c8 ≠ 6, r1c8 ≠ 2
hidden-single-in-a-column ==> r6c8 = 2
whip[1]: c8n6{r8 .} ==> r7c7 ≠ 6, r8c7 ≠ 6, r8c9 ≠ 6
x-wing-in-columns: n9{c3 c7}{r2 r7} ==> r7c8 ≠ 9, r7c2 ≠ 9, r7c1 ≠ 9, r2c2 ≠ 9, r2c1 ≠ 9
biv-chain[3]: r5c3{n1 n6} - b6n6{r5c7 r6c9} - r6n4{c9 c2} ==> r6c2 ≠ 1
biv-chain[3]: r6c2{n4 n6} - r5c3{n6 n1} - b1n1{r3c3 r3c2} ==> r3c2 ≠ 4
whip[1]: r3n4{c5 .} ==> r2c4 ≠ 4, r2c5 ≠ 4
biv-chain[3]: r9c1{n1 n9} - b9n9{r9c8 r7c7} - b9n8{r7c7 r9c9} ==> r9c9 ≠ 1
hidden-pairs-in-a-column: c9{n1 n4}{r6 r8} ==> r8c9 ≠ 7, r6c9 ≠ 6
hidden-single-in-a-block ==> r5c7 = 6
naked-single ==> r5c3 = 1
hidden-single-in-a-block ==> r3c2 = 1
whip[1]: r5n7{c5 .} ==> r4c4 ≠ 7, r4c6 ≠ 7
whip[1]: c6n7{r9 .} ==> r7c5 ≠ 7, r8c5 ≠ 7, r9c5 ≠ 7
biv-chain[3]: c3n5{r8 r7} - r7n9{c3 c7} - r2c7{n9 n5} ==> r8c7 ≠ 5
naked-pairs-in-a-column: c7{r4 r8}{n1 n7} ==> r7c7 ≠ 7, r7c7 ≠ 1, r3c7 ≠ 7
naked-single ==> r3c7 = 8
hidden-single-in-a-column ==> r9c9 = 8
whip[1]: b9n1{r8c9 .} ==> r8c5 ≠ 1
naked-pairs-in-a-column: c4{r3 r5}{n4 n7} ==> r2c4 ≠ 7, r1c4 ≠ 7
biv-chain[3]: r9n7{c6 c8} - r4c8{n7 n4} - r7n4{c8 c6} ==> r7c6 ≠ 7
biv-chain[3]: r3c3{n7 n6} - c1n6{r1 r7} - r7c2{n6 n7} ==> r1c2 ≠ 7, r2c2 ≠ 7, r7c3 ≠ 7, r8c3 ≠ 7
hidden-single-in-a-block ==> r7c2 = 7
biv-chain[3]: r8c3{n5 n6} - r6c3{n6 n8} - r6c6{n8 n5} ==> r8c6 ≠ 5
biv-chain[3]: r2c9{n2 n7} - c3n7{r2 r3} - r3n6{c3 c9} ==> r3c9 ≠ 2
hidden-single-in-a-row ==> r3c5 = 2
hidden-single-in-a-block ==> r3c4 = 4
naked-single ==> r5c4 = 7
naked-single ==> r5c5 = 4
biv-chain[4]: r6n5{c6 c4} - r6n1{c4 c9} - b6n4{r6c9 r4c8} - r7n4{c8 c6} ==> r7c6 ≠ 5
biv-chain[4]: r8n6{c8 c3} - b4n6{r6c3 r6c2} - r6n4{c2 c9} - r4c8{n4 n7} ==> r8c8 ≠ 7
biv-chain[4]: c7n5{r2 r7} - c3n5{r7 r8} - r8c5{n5 n3} - b2n3{r2c5 r2c4} ==> r2c4 ≠ 5
biv-chain[4]: r9c1{n9 n1} - r9c5{n1 n5} - r2n5{c5 c7} - r2n9{c7 c3} ==> r7c3 ≠ 9, r1c1 ≠ 9
stte

[pjb]

First puzzle:

Code: Select all

 259     269     567    | 3      78     4      | 589    169    156   
 589     89      3      | 6      1      2      | 4      79     57     
 1       4       67     | 5      78     9      | 38     36     2     
------------------------+----------------------+---------------------
 4       18      18     | 9      2      7      | 6      5      3     
 3       5       2      | 1      4      6      | 7      8      9     
 6       7       9      | 8      3      5      | 1      2      4     
------------------------+----------------------+---------------------
 7       16      16     | 2     *59     3      |*59     4      8     
 59      39      4      | 7      6      8      | 2      139    15     
 2589    2389    58     | 4     *59     1      |*3-59   67     67     


Type 1 unique rectangle of 59 at r79c57 => -59 r9c7; stte

Phil

[pjb]

Second puzzle: much harder! I'll leave it to the group for one stepper,
Two chains, with 43 basic eliminations after first
(5=9)r2c7 - (9)r2c3 = (9-5)r7c3 = (5)r8c3 => -5 r8c7
(9=5)r1c8 - (5=8)r1c4 - r1c5 = (8-1)r7c5 = r7c1 - (1=9)r9c1, -9r1c1 => -9 r9c8; stte

Phil

[Cenoman]

Phil calls for solving the second puzzle in one step, but his solution is one of the most reasonable.
Here is a one step solution, that I hardly dare to post:

Code: Select all

 +-------------------------+--------------------------+-------------------------+
 |  689    2679    3       |  578     2578     1      |  4       59      2678   |
 |  489    2479    789     |  34578   234578   6      |  59      1       278    |
 |  5      12467   1678    |  478     2478     9      |  678     3       2678   |
 +-------------------------+--------------------------+-------------------------+
 |  1489   149     2       |  1378    6        378    |  17      47      5      |
 |  3      5       16      |  147     47       2      |  167     8       9      |
 |  7      146     168     |  158     9        58     |  3       2       146    |
 +-------------------------+--------------------------+-------------------------+
 |  169    1679    15679   |  2       1578     4578   |  15789   45679   3      |
 |  2      8       1567    |  9       1357     3457   |  157     4567    147    |
 |  19     3       4       |  6       1578     578    |  2       579     178    |
 +-------------------------+--------------------------+-------------------------+

Multi Kraken: rows (4)r8c689 & (5)r2c457, column (7)r4789c8, as a net:

Code: Select all

       (3)r8c6 = = = = = = = r8c5 - - - - - - - r2c5 = = = = = = = (3-5)r2c4
       /                                                              ||
(4)r8c6                                                              (5)r2c7 *
 ||    \                                                              ||
 ||    (4)r7c6 = r7c8 - (4=1378)r4c4678 - (8=5)r6c6 - r6c4 = r12c4 - (5)r2c5
 ||
(4-6)r8c8 = (6-5)r8c3 = (5-9)r7c3 = (9)r2c3
 ||
 ||                       (7)r7c8 - - r7c2  =  (75)r78c3
 ||                        ||                         \
(4)r8c9 - r6c9 = (4-7)r4c8 = (7-9)r9c8  =  (9)r9c1 - (9)r7c3 = (9)r2c3 *
                           ||                         /
                          (7-6)r8c8 = (6-5)r8c3 = (5)r7c3
---------------
=> -9 r2c7; ste