## More Pi 3

Post puzzles for others to solve here.

### More Pi 3

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 | 6 . . | 4 3 . |
| . . . | . . 3 | 8 . . |
+-------+-------+-------+
..31......41..59..2....6.535......89....7....93......238.4....6..26..43......38..
mith

Posts: 301
Joined: 14 July 2020

### Re: More Pi 3

Code: Select all
(solve-sudoku-grid
+-------+-------+-------+
! . . 3 ! 1 . . ! . . . !
! . 4 1 ! . . 5 ! 9 . . !
! 2 . . ! . . 6 ! . 5 3 !
+-------+-------+-------+
! 5 . . ! . . . ! . 8 9 !
! . . . ! . 7 . ! . . . !
! 9 3 . ! . . . ! . . 2 !
+-------+-------+-------+
! 3 8 . ! 4 . . ! . . 6 !
! . . 2 ! 6 . . ! 4 3 . !
! . . . ! . . 3 ! 8 . . !
+-------+-------+-------+
)

Subsets, bivalue-chains and z-chains are not enough. But add one t-whip and it's OK:

Code: Select all
***********************************************************************************************
***  SudoRules 20.1.s based on CSP-Rules 2.1.s, config = tW+SFin
***  Using CLIPS 6.32-r770
***********************************************************************************************
hidden-single-in-a-row ==> r3c7 = 1
hidden-single-in-a-row ==> r3c5 = 4
hidden-single-in-a-row ==> r1c2 = 5
whip[1]: r1n9{c6 .} ==> r3c4 ≠ 9
whip[1]: b1n6{r2c1 .} ==> r9c1 ≠ 6, r5c1 ≠ 6
finned-x-wing-in-rows: n8{r3 r6}{c3 c4} ==> r5c4 ≠ 8
z-chain[3]: r3c2{n7 n9} - r8c2{n9 n1} - r8c1{n1 .} ==> r9c2 ≠ 7
z-chain[4]: c3n5{r7 r9} - c3n9{r9 r3} - r3c2{n9 n7} - b4n7{r4c2 .} ==> r7c3 ≠ 7
z-chain[4]: c3n5{r9 r7} - c3n9{r7 r3} - r3c2{n9 n7} - b4n7{r4c2 .} ==> r9c3 ≠ 7
z-chain[4]: c4n9{r9 r5} - r5n3{c4 c7} - r5n5{c7 c9} - r8n5{c9 .} ==> r9c4 ≠ 5
whip[1]: b8n5{r9c5 .} ==> r6c5 ≠ 5
z-chain[4]: r1n9{c5 c6} - r5n9{c6 c4} - b5n5{r5c4 r6c4} - c4n8{r6 .} ==> r1c5 ≠ 8
t-whip[4]: r8n5{c9 c5} - r8n8{c5 c6} - r8n9{c6 c2} - r7c3{n9 .} ==> r7c7 ≠ 5
whip[1]: b9n5{r9c9 .} ==> r5c9 ≠ 5
hidden-pairs-in-a-row: r5{n3 n5}{c4 c7} ==> r5c7 ≠ 6, r5c4 ≠ 9, r5c4 ≠ 2
stte

One can even require all the chain patterns to be 2D, although it implies slightly longer chains:

Code: Select all
***********************************************************************************************
***  SudoRules 20.1.s based on CSP-Rules 2.1.s, config = TyZ+TytW+SFin
***  Using CLIPS 6.32-r770
***********************************************************************************************
hidden-single-in-a-row ==> r3c7 = 1
hidden-single-in-a-row ==> r3c5 = 4
hidden-single-in-a-row ==> r1c2 = 5
whip[1]: r1n9{c6 .} ==> r3c4 ≠ 9
whip[1]: b1n6{r2c1 .} ==> r9c1 ≠ 6, r5c1 ≠ 6
finned-x-wing-in-rows: n8{r3 r6}{c3 c4} ==> r5c4 ≠ 8
z-chain-rc[3]: r3c2{n7 n9} - r8c2{n9 n1} - r8c1{n1 .} ==> r9c2 ≠ 7
t-whip-rn[5]: r1n9{c5 c6} - r5n9{c6 c4} - r5n3{c4 c7} - r5n5{c7 c9} - r8n5{c9 .} ==> r8c5 ≠ 9
biv-chain-rn[4]: r3n8{c4 c3} - r3n9{c3 c2} - r8n9{c2 c6} - r8n8{c6 c5} ==> r1c5 ≠ 8, r2c5 ≠ 8
t-whip-rn[5]: r5n9{c6 c4} - r5n3{c4 c7} - r5n5{c7 c9} - r8n5{c9 c5} - r8n8{c5 .} ==> r5c6 ≠ 8, r8c6 ≠ 9
stte
denis_berthier
2010 Supporter

Posts: 1672
Joined: 19 June 2007
Location: Paris

### Re: More Pi 3

After basic SSTS:
Code: Select all
*--------------------------------------------------------------------*
| 678    5      3      | 1      289    2789   | 267    2467   478    |
| 678    4      1      | 2378   238    5      | 9      267    78     |
| 2      79     789    | 78     4      6      | 1      5      3      |
|----------------------+----------------------+----------------------|
| 5      1267   467    | 23     1236   124    | 367    8      9      |
| 148    126    468    | 23589  7      12489  | 356    146    145    |
| 9      3      4678   | 58     1568   148    | 567    1467   2      |
|----------------------+----------------------+----------------------|
| 3      8      579    | 4      1259   1279   | 257    1279   6      |
| 17     179    2      | 6      1589   1789   | 4      3      157    |
| 147    1679   45679  | 2579   1259   3      | 8      1279   157    |
*--------------------------------------------------------------------*

My path for this one.

(9)r8c2=[X-wing 9’s: r18c56]-r5c6=(9-35)r5c47=(5)r5c9-r8c9=(5-89)r8c56=(9)r8c2 => r8c2=9, stte

totuan
totuan

Posts: 52
Joined: 25 May 2010
Location: vietnam

### Re: More Pi 3

Code: Select all
+----------------+------------------+--------------+
| 678 5    3     | 1     289  2789  | 267 2467 478 |
| 678 4    1     | 2378  238  5     | 9   267  78  |
| 2   79   789   | 78    4    6     | 1   5    3   |s
+----------------+------------------+--------------+
| 5   1267 467   | 23    1236 124   | 367 8    9   |
| 148 126  468   | 23589 7    12489 | 356 146  145 |
| 9   3    4678  | 58    1568 148   | 567 1467 2   |
+----------------+------------------+--------------+
| 3   8    579   | 4     1259 1279  | 257 1279 6   |
| 17  179  2     | 6     1589 1789  | 4   3    157 |
| 147 1679 45679 | 2579  1259 3     | 8   1279 157 |
+----------------+------------------+--------------+

5r8c5=r8c9-r5c9=(1468)r5c1389-(1468=29)r5c26=>singles =>5r8c5=>btte

Paolo
Ajò Dimonios

Posts: 201
Joined: 07 November 2019

### Re: More Pi 3

Just a boring variant of totuan's solution.

Code: Select all
.------------------.-----------------------.------------------.
| 678  5     3     |  1      289     2789  |  267  2467   478 |
| 678  4     1     |  2378   238     5     |  9    267    78  |
| 2    79    789   |  78     4       6     |  1    5      3   |
:------------------+-----------------------+------------------:
| 5    1267  467   |  23     1236    124   |  367  8      9   |
| 148  126   468   | b23589  7       12489 | b356  146   b145 |
| 9    3     4678  |  58     1568    148   |  567  1467   2   |
:------------------+-----------------------+------------------:
| 3    8     579   |  4      1259    1279  |  257  1279   6   |
| 17   179   2     |  6     d158-9  d178-9 |  4    3     c157 |
| 147  1679  45679 | a2579   1259    3     |  8    1279   157 |
'------------------'-----------------------'------------------'

(9)r9c4 = (935)r5c479 - r8c9 = (58)r8c56 => -9 r8c56; btte
-SpAce-: Show
Code: Select all
*             |    |               |    |    *
*        |=()=|    /  _  \    |=()=|               *
*    |    |   |-=( )=-|   |    |      *
*                     \  ¯  /                   *

"If one is to understand the great mystery, one must study all its aspects, not just the dogmatic narrow view of the Jedi."

SpAce

Posts: 2568
Joined: 22 May 2017

### Re: More Pi 3

Code: Select all
*--------------------------------------------------------------------*
| 678    5      3      | 1      289    2789   | 267    2467   478    |
| 678    4      1      | 2378   238    5      | 9      267    78     |
| 2      79     789    | 78     4      6      | 1      5      3      |
*----------------------+----------------------+----------------------|
| 5      1267   467    | 23     1236   124    | 367    8      9      |
| 148    126    468    |d23589  7      12489  |d356    146   d145    |
| 9      3      4678   | 58     1568   148    | 567    1467   2      |
*----------------------+----------------------+----------------------|
| 3      8      579    | 4      1259   1279   | 257    1279   6      |
|e17    a9-17   2      | 6     b1589  b1789   | 4      3     e157    |
| 147    1679   45679  |c2579   1259   3      | 8      1279   157    |
*--------------------------------------------------------------------*

Another variant:

9r8c2 = (89)r8c56 - 9r9c4 = (935)r5c479 - (5=17)r8c19 => -17 r8c2 ; btte

And here's a variant that gives a singles solution:

Code: Select all
*--------------------------------------------------------------------*
| 678    5      3      | 1      289    2789   | 267    2467   478    |
| 678    4      1      | 2378   238    5      | 9      267    78     |
| 2    ef79     789    | 78     4      6      | 1      5      3      |
*----------------------+----------------------+----------------------|
| 5     g1267  g467    | 23     1236   124    | 367    8      9      |
| 148    126    468    |b23589  7     a9-1248 |b356    146   b145    |
| 9      3     g4678   | 58     1568   148    | 567    1467   2      |
*----------------------+----------------------+----------------------|
| 3      8    ef579    | 4      1259   1279   |d257    1279   6      |
|d17    d179    2      | 6      1589   1789   | 4      3    cd157    |
| 147    1679   45679  | 2579   1259   3      | 8      1279  c157    |
*--------------------------------------------------------------------*

9r5c6 = (935)r5c479 - 5r89c9 = ((179)r8c129)&(5r7c7) - (5|9)r3c2,r7c3 = 7r3c2&7r7c3 - 7b4p239 => contradiction => r5c6 = 9 ; stte

SpAce, I'll bet you can write this better.
Steve

SteveG48
2019 Supporter

Posts: 3052
Joined: 08 November 2013
Location: Orlando, Florida