## Diamond in the Rough

Post puzzles for others to solve here.

### Diamond in the Rough

Code: Select all
`+-------+-------+-------+| . . . | 8 . . | . . 1 || . . 9 | . 7 . | . 2 . || . 1 . | . . 5 | . . 4 |+-------+-------+-------+| . . 2 | . 4 . | . 5 . || 9 . . | 3 . . | 6 . . || . 8 . | . . . | . 7 . |+-------+-------+-------+| 7 . . | . . . | . . 8 || . 6 . | 4 . 1 | . 9 . || . . 5 | . 2 . | . . . |+-------+-------+-------+...8....1..9.7..2..1...5..4..2.4..5.9..3..6...8.....7.7.......8.6.4.1.9...5.2....`
mith

Posts: 301
Joined: 14 July 2020

### Re: Diamond in the Rough

Quick and dirty.

Code: Select all
`.----------------------.---------------------.---------------.|   23456  23457  3467 | 8     h369    23469 |  79   36   1  || fg3468   34     9    | 1      7     h346   | e38   2    5  ||   2368   1      3678 | 269   h369    5     |  79   368  4  |:----------------------+---------------------+---------------:|   136    37     2    | 679    4     c6789  | d18   5    39 ||   9      457    147  | 3     b158    7-8   |  6    148  2  ||   13456  8      1346 | 2569   1569   269   |  14   7    39 |:----------------------+---------------------+---------------:|   7      2349   134  | 569    3569   369   |  25   134  8  ||   238    6      38   | 4     a58-3   1     |  25   9    7  ||  g1348   349    5    | 79     2     h3789  |  134  134  6  |'----------------------'---------------------'---------------'`

(8)r8c5 = r5c5 - @(8)r4c6 = r4c7 - r2c7 = r2c1 - 6r2c1|8r9c1 = (6,93)b2p628,(8)r9c6 => -3 r8c5, -8 r5c6; 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: Diamond in the Rough

There's a solution with Subsets and nothing more complex than Typed bivalue-chains[3], but I also found one with an oddagon[7]:

(solve "...8....1..9.7..2..1...5..4..2.4..5.9..3..6...8.....7.7.......8.6.4.1.9...5.2....")
***********************************************************************************************
*** SudoRules 20.1.s based on CSP-Rules 2.1.s, config = O+S
*** Using CLIPS 6.32-r770
***********************************************************************************************
singles ==> r5c9 = 2, r2c4 = 1
whip[1]: c9n7{r9 .} ==> r9c7 ≠ 7, r8c7 ≠ 7
singles ==> r8c9 = 7, r2c9 = 5, r9c9 = 6
whip[1]: c9n3{r6 .} ==> r4c7 ≠ 3, r6c7 ≠ 3
whip[1]: c9n9{r6 .} ==> r6c7 ≠ 9, r4c7 ≠ 9
hidden-pairs-in-a-column: c7{n2 n5}{r7 r8} ==> r8c7 ≠ 3, r7c7 ≠ 4, r7c7 ≠ 3, r7c7 ≠ 1
hidden-pairs-in-a-column: c7{n7 n9}{r1 r3} ==> r3c7 ≠ 8, r3c7 ≠ 3, r1c7 ≠ 3
swordfish-in-columns: n8{c3 c5 c8}{r3 r8 r5} ==> r8c1 ≠ 8, r5c6 ≠ 8, r3c1 ≠ 8
singles ==> r5c6 = 7, r9c4 = 7, r4c2 = 7
oddagon[7]: r4n1{c1 c7},r4c7{n1 n8},r4n8{c7 c6},c6n8{r4 r9},r9n8{c6 c1},r9c1{n8 n1},c1n1{r9 r4} ==> r9c1 ≠ 1
singles ==> r7c3 = 1, r5c3 = 4, r5c2 = 5, r1c1 = 5, r6c7 = 4
hidden-pairs-in-a-row: r1{n2 n4}{c2 c6} ==> r1c6 ≠ 9, r1c6 ≠ 6, r1c6 ≠ 3, r1c2 ≠ 3
hidden-pairs-in-a-column: c1{n4 n8}{r2 r9} ==> r9c1 ≠ 3, r2c1 ≠ 6, r2c1 ≠ 3
singles and whips[1] to the end
denis_berthier
2010 Supporter

Posts: 1672
Joined: 19 June 2007
Location: Paris

### Re: Diamond in the Rough

Nice. I found something very different, there are lots of ways to go in this one.

The swordfish here is similar to the 3x3 patterns found in some of my other puzzles. Here r249c358 nearly forms a complete 3x3, with no given in r9c8. However, the 8 in box 9 covers this cell, so the three given 8s again force a swordfish (in either r249 or c358).
mith

Posts: 301
Joined: 14 July 2020

### Re: Diamond in the Rough

1) Swordfish of 8s (r249\c167) => -8 r3c1, r5c6, r8c1 (same eliminations as continuous loop on 8 as in SpAce's chain), =>

Code: Select all
` 45-236  2345    3467   | 8      369    23469  | 79     36     1       48-36   34      9      | 1      7      346    | 38     2      5      a236     1       3678   | 269    369    5      | 79     368    4      ------------------------+----------------------+---------------------b136     7       2      | 69     4      689    | 18     5      39      9      b45     b14     | 3      158    7      | 6      148    2      b13456   8       36-14  | 2569   1569   269    | 14     7      39     ------------------------+----------------------+--------------------- 7       2349    134    | 569    3569   369    | 25     134    8      a23      6       38     | 4      358    1      | 25     9      7       148-3   349     5      | 7      2      389    | 134    134    6      `

2) double ALS:
Double ALS at r38c1 and r4c1, r5c23, r6c1, with X-Z values 6 and 3 => -236 r1c1, -36 r2c1, -3 r9c1, -14 r6c3 => btte

Phil
pjb
2014 Supporter

Posts: 2230
Joined: 11 September 2011
Location: Sydney, Australia

### Re: Diamond in the Rough

pjb wrote:1) Swordfish of 8s (r249\c167) => -8 r3c1, r5c6, r8c1 (same eliminations as continuous loop on 8 as in SpAce's chain)

Good point that my subchain actually contains a loop with the 8s. Technically it could have eliminated 8r38c1 as well, but it might have been a bit confusing in an already complex subchain + split-node environment.

2) double ALS

Nice! Btw, it's also a (non-basic) Sue-de-Coq.

SpAce

Posts: 2568
Joined: 22 May 2017