The New Sudoku Players' Forum

by **mith** » Mon Mar 15, 2021 6:02 pm

Code: Select all: +-------+-------+-------+ | . . . | . . . | . . . | | 3 . . | . . 1 | 5 . . | | . 9 . | . 3 . | . 8 . | +-------+-------+-------+ | . 8 . | . 4 . | . 6 . | | 2 . . | . . 5 | 8 . . | | . . 4 | 8 . . | . 7 9 | +-------+-------+-------+ | . 2 7 | . . . | 6 9 . | | 1 . . | 6 . 2 | . . 4 | | . . . | . 7 . | . . . | +-------+-------+-------+ .........3....15...9..3..8..8..4..6.2....58....48...79.27...69.1..6.2..4....7....

Normally I post pi puzzles on Mondays, but given I did an entire week of them...

This one is non-minimal. If you want an extra challenge (it's not hard as is), removing 6r8c4 doesn't substantially change the easiest-first path but does make finding a one-stepper harder, while removing 2r8c6 bumps it to SER 8.4.

by **SteveG48** » Mon Mar 15, 2021 8:54 pm

Code: Select all: *--------------------------------------------------------------------* | 45678 14567 12568 | 2457 2568 4678 | 9 13 1367 | | 3 467 c68 | 479 689 1 | 5 2 67 | | 567 9 b1256 | 257 3 e67 | 4 8 a167 | *----------------------+----------------------+----------------------| | 79 8 c139 | 12379 4 e379 | 123 6 5 | | 2 1367 c1369 | 1379 f169 5 | 8 4 3-1 | | 56 1356 4 | 8 126 e36 | 123 7 9 | *----------------------+----------------------+----------------------| |d45 2 7 | 1345 15 e34 | 6 9 8 | | 1 35 c89 | 6 89 2 | 7 35 4 | | 45689 3456 c35689 | 459 7 489 | 13 135 2 | *--------------------------------------------------------------------*

1r3c9 = r3c3 - (1=36895)r24589c3 - (5=4)r7c1 - (4=3769)r3467c6 - (6|9=1)r5c5 => -1 r5c9 ; stte

by **pjb** » Mon Mar 15, 2021 11:20 pm

Code: Select all: 4678-5 14567 12568 | 2457 2568 4678 | 9 13 1367 3 467 68 | 479 689 1 | 5 2 67 67-5 9 1256 | 257 3 67 | 4 8 167 ------------------------+----------------------+--------------------- 79 8 139 | 12379 4 79-3 | 123 6 5 2 1367 1369 | 1379 169 5 | 8 4 13 b56 135-6 4 | 8 12-6 a36 | 123 7 9 ------------------------+----------------------+--------------------- c45 2 7 | 135-4 15 d34 | 6 9 8 1 35 89 | 6 89 2 | 7 35 4 4689-5 3456 35689 | 459 7 489 | 13 135 2

(3=6)r6c6 - (6=5)r6c1 - (5=4)r7c1 - (4=3)r7c6 - loop => -6 r6c25; -5 r139c1; -4 r7c4; -3 r4c6; stte

This continuous loop might also be viewed as a 2x2 MSLS: Truths: r67 c16 Links: 6r6 4r7 5c1 3c6 (same eliminations)

Phil

by **SteveG48** » Tue Mar 16, 2021 12:12 am

Removing the 6 at r8c4:

Code: Select all: *----------------------------------------------------------------------* | 45678 14567 12568 | 24567 2568 bi4678 | 9 13 1367 | | 3 aj467 bc8-6 |aj4679 aj689 1 | 5 2 aj67 | |dg567 9 1256 | 2567 3 67 | 4 8 167 | *-----------------------+-----------------------+----------------------| |dg79 8 139 | 12379 4 ch379 | 123 6 5 | | 2 1367 1369 | 13679 169 5 | 8 4 13 | |eg56 1356 4 | 8 126 f36 | 123 7 9 | *-----------------------+-----------------------+----------------------| | g45 2 7 | 1345 15 f34 | 6 9 8 | | 1 356 35689 | 569 5689 2 | 7 35 4 | | 45689 3456 35689 | 4569 7 ci4689 | 13 135 2 | *----------------------------------------------------------------------*

(6=4798)r2c2459 - 8(r1c6)|8(r2c3) = (6r2c3)&((89)r49c6 - (9|6=75)r34c1 - (5=6)r6c1 - (6=34)r67c6 - (4=5679)r2367c1 - 9r4c6 = (98)r19c6 - (8=4796)r2c2459) => -6 r2c3 ; stte

by **SteveG48** » Tue Mar 16, 2021 12:20 am

I love Phil's simple loop, but I get btte, not stte.

by **mith** » Tue Mar 16, 2021 12:45 am

Yeah, I think you need at least a naked pair with that one, IIRC. (Still lovely, it kinda looks like it’s surfing the waves; part of why I permuted the digits the way I did was so that it’s on 3456).

by **Leren** » Tue Mar 16, 2021 12:50 am

Code: Select all: *-------------------------------------------------------* | 4678-5 14567 12568 | 2457 2568 4678 | 9 13 1367 | | 3 467 68 | 479 689 1 | 5 2 67 | |*567 9 25-16 | 25-7 3 *67 | 4 8 *167 | 167 |--------------------+------------------+---------------| | 79 8 139 | 12379 4 79-3 | 123 6 5 | | 2 1367 1369 | 1379 169 5 | 8 4 13 | |*56 135-6 4 | 8 12-6 *36 | 123 7 9 | 6 |--------------------+------------------+---------------| |*45 2 7 | 135-4 15 *34 | 6 9 8 | 4 | 1 35 89 | 6 89 2 | 7 35 4 | | 4689-5 3456 35689 | 459 7 489 | 13 135 2 | *-------------------------------------------------------* 5 3

MSLS : 7 Truths r3c169, r67c16 : 7 Links; 167r3 6r6 4r7 ; 5c1 3c6 ; => - 5 r19c1, - 16 r3c3, - 7 r3c4, - 3 r4c6, - 6 r6c25, - 4 r7c4 ; stte

Leren

by **pjb** » Tue Mar 16, 2021 2:40 am

How about a 4x2 MSLS (at least this one is STTE)

Code: Select all: 4678-5 14567 12568 | 2457 2568 4678 | 9 13 1367 3 467 68 | 479 689 1 | 5 2 67 567* 9 125-6 | 25-7 3 67* | 4 8 1-67 ------------------------+----------------------+--------------------- 79* 8 13-9 | 123-79 4 379* | 123 6 5 2 1367 1369 | 1379 169 5 | 8 4 13 56* 135-6 4 | 8 12-6 36* | 123 7 9 ------------------------+----------------------+--------------------- 45* 2 7 | 135-4 15 34* | 6 9 8 1 35 89 | 6 89 2 | 7 35 4 4689-5 3456 35689 | 459 7 489 | 13 135 2

4x2 MSLS at r3467 c16 Links: 67r3 79r4 6r6 4r7 5c1 3c6 Eliminations: -5 r19c1, -6 r6c2, -6 r3c3, -9 r4c3, -7 r34c4, -9 r4c4, -4 r7c4, -6 r6c5, -67 r3c9; stte

(Even simpler, a 3x2 MSLS: r367 c16 Links: 67r3 6r6 4r7 5c1 3c6 Eliminations: -5 r1c1, -6 r6c2, -6 r3c3, -3 r4c6, -7 r3c4, -4 r7c4, -6 r6c5, -5 r9c1, -6 r3c9, -7 r3c9, stte)

Phil

Website · by **denis_berthier** » Tue Mar 16, 2021 7:27 am

mith wrote:If you want an extra challenge (it's not hard as is), removing 6r8c4 doesn't substantially change the easiest-first path but does make finding a one-stepper harder

I tried this.

1) with the n6r8c4 given:

Code: Select all: .........3....15...9..3..8..8..4..6.2....58....48...79.27...69.1..6.2..4....7....

After Singles and whips[1], we have the following RESOLUTION STATE:

Code: Select all: 45678 14567 12568 2457 2568 4678 9 13 1367 3 467 68 479 689 1 5 2 67 567 9 1256 257 3 67 4 8 167 79 8 139 12379 4 379 123 6 5 2 1367 1369 1379 169 5 8 4 13 56 1356 4 8 126 36 123 7 9 45 2 7 1345 15 34 6 9 8 1 35 3589 6 589 2 7 35 4 45689 3456 35689 459 7 489 13 135 2

There are 23 W1-ANTI-BACKDOORS:

Code: Select all: n1r9c7 n8r9c6 n9r9c1 n9r8c5 n8r8c3 n3r7c6 n4r7c1 n6r6c6 n5r6c1 n1r5c9 n7r5c4 n9r5c3 n9r4c6 n7r4c1 n7r3c6 n1r3c3 n8r2c5 n9r2c4 n6r2c3 n4r2c2 n3r1c9 n1r1c8 n8r1c1

One of them gives rise to a single-elimination before stte, with a whip[5]:

Code: Select all: whip[5]: r3n1{c9 c3} - c2n1{r1 r6} - r6n5{c2 c1} - r3n5{c1 c4} - r3n2{c4 .} ==> r5c9 ≠ 1 stte

2) without the n6r8c4:

Code: Select all: .........3....15...9..3..8..8..4..6.2....58....48...79.27...69.1....2..4....7....

After Singles and whips[1], we have the following RESOLUTION STATE:

Code: Select all: 45678 14567 12568 2457 2568 4678 9 13 1367 3 467 68 479 689 1 5 2 67 567 9 1256 257 3 67 4 8 167 79 8 139 12379 4 379 123 6 5 2 1367 1369 1379 169 5 8 4 13 56 1356 4 8 126 36 123 7 9 45 2 7 1345 15 34 6 9 8 1 35 3589 6 589 2 7 35 4 45689 3456 35689 459 7 489 13 135 2

There are 17 W1-ANTI-BACKDOORS:

Code: Select all: n8r9c6 n9r9c1 n8r8c3 n3r7c6 n4r7c1 n6r6c6 n5r6c1 n7r5c4 n9r5c3 n9r4c6 n7r4c1 n7r3c6 n8r2c5 n9r2c4 n6r2c3 n4r2c2 n8r1c1

13 of the them give rise to a single-elimination before stte. The simplest of them uses a whip[6]:

Code: Select all: whip[6]: c1n8{r9 r1} - r2c3{n8 n6} - c1n6{r3 r6} - r6c6{n6 n3} - r7c6{n3 n4} - c1n4{r7 .} ==> r9c1 ≠ 9 stte

As expected, there are fewer W1-anti-backdoors and the one of them giving rise to the simplest 1-elimination before stte involves a longer whip.

by **Cenoman** » Tue Mar 16, 2021 9:44 am

The first puzzle may be solved (ste finish) by a sequence of 5 X-Wings

Code: Select all: +--------------------------+------------------------+---------------------+ | 45678 1567-4 1256-8 | 257-4 256-8 4678 | 9 13 1367 | | 3 467# 68* | 479# 689* 1 | 5 2 67 | | 567 9 1256 | 257 3 67 | 4 8 167 | +--------------------------+------------------------+---------------------+ | 79^ 8 13-9 | 1237-9 4 379^ | 123 6 5 | | 2 1367 1369 | 1379 169 5 | 8 4 13 | | 56 1356 4 | 8 126 36 | 123 7 9 | +--------------------------+------------------------+---------------------+ | 45 2 7 | 135-4 15 34 | 6 9 8 | | 1 35 89* | 6 89* 2 | 7 35 4 | | (456)89^ 3456# 356-89 | 45-9# 7 (4)89^ | 13 135 2 | +--------------------------+------------------------+---------------------+

XW(8)r28\c35 => -8 r19c3, r1c5
XW(9)c16\r49 => -9 r49c34; HP(89)r9c16
XW(4)r29\c24 => -4r1c2, r17c4; HP(48)r1c16, HT(489)b2p345; NP(89)r28c5

Code: Select all: +----------------------+---------------------+---------------------+ | 48 1567 1256 | 257 256 48 | 9 13 1367 | | 3 467 68 | 49 89 1 | 5 2 67 | | 567*^ 9 125-6 | 25-7 3 67*^ | 4 8 1-67 | +----------------------+---------------------+---------------------+ | 79^ 8 13 | 123-7 4 379^ | 123 6 5 | | 2 1367 1369 | 1379 16 5 | 8 4 13 | | 56* 135-6 4 | 8 12-6 36* | 123 7 9 | +----------------------+---------------------+---------------------+ | 45 2 7 | 135 15 34 | 6 9 8 | | 1 35 89 | 6 89 2 | 7 35 4 | | 89 3456 356 | 45 7 89 | 13 135 2 | +----------------------+---------------------+---------------------+

XW(6)c16\r36 => -6 r3c39, r6c25
XW(7)c16\r34 => -7 r3c49, r4c4; ste

Phil's one-step loop has a pattern name: XY-Ring

The second puzzle (w/o 6r8c4 as a given) may be solved (ste finish) by the same sequence of 5 X-Wings, with slightly different eliminations and subsets:

Hidden Text: Show

XW(8)r28\c35 => -8 r19c3, r1c5
XW(9)c16\r49 => -9 r49c34; HP(89)r9c16, HP(89)b7p67

Hidden Text: Show

XW(4)r29\c24 => -4r1c2, r17c4; HP(48)r1c16, HT(489)b2p345

Hidden Text: Show

XW(6)c16\r36 => -6 r3c39, r6c25
XW(7)c16\r34 => -7 r3c49, r4c4; ste

The XY-Ring still exists, but needs an additional AIC:

Code: Select all: +----------------------+------------------------+-----------------+ | b4678 15 125 | 24567 2568 4678 | 9 3 67 | | 3 c467 68 | 4679 689 1 | 5 2 67 | | 67 9 25 | 25 3 67 | 4 8 1 | +----------------------+------------------------+-----------------+ | e79 8 13 | 123 4 79 | 12 6 5 | | 2 d167 169 | 1679 169 5 | 8 4 3 | | 56 35 4 | 8 12 36 | 12 7 9 | +----------------------+------------------------+-----------------+ | 45 2 7 | 135 15 34 | 6 9 8 | | 1 36 3689 | 69 689 2 | 7 5 4 | | a468-9 456 5689 | 4569 7 4689 | 3 1 2 | +----------------------+------------------------+-----------------+

2. (8)r9c1 = r1c1 - (8=6)r2c3 - (6=7)r3c1 - (7=9)r4c1 => -9 r9c1; ste

One-step with a kraken cell, using the same cells:

Code: Select all: +--------------------------+------------------------+---------------------+ | 45678 14567 12568 | 24567 2568 4678 | 9 13 1367 | | 3 467 68 | 4679 689 1 | 5 2 67 | | 567 9 1256 | 2567 3 67 | 4 8 167 | +--------------------------+------------------------+---------------------+ | 79 8 139 | 12379 4 379 | 123 6 5 | | 2 1367 1369 | 13679 169 5 | 8 4 13 | | 56 1356 4 | 8 126 36 | 123 7 9 | +--------------------------+------------------------+---------------------+ | 45 2 7 | 1345 15 34 | 6 9 8 | | 1 356 35689 | 569 5689 2 | 7 35 4 | | 45689 3456 35689 | 4569 7 4689 | 13 135 2 | +--------------------------+------------------------+---------------------+

Kraken cell (567)r3c1
(5)r3c1-(5=6)r6c1-(6=3)r6c6-(3=4)r7c6-r7c1=(48)r19c1
(6)r3c1-(6=8)r2c3-r1c1=(8)r9c1
(7)r3c1-(7=9)r4c1
=> -9 r9c1; ste

The third puzzle (w/o 2r8c6 as a given) is solved by a sequence of four simple AICs:

Code: Select all: +--------------------------+-------------------------+---------------------+ | 45678 14567 12568 | 2457 2568 24678 | 9 13 1367 | | 3 467 68 | 479 689 1 | 5 2 67 | | 567 9 1256 | 257 3 267 | 4 8 167 | +--------------------------+-------------------------+---------------------+ | 79 8 139 | 12379 4 2379 | 123 6 5 | | 2 1367 1369 | 1379 169 5 | 8 4 13 | | 56 1356 4 | 8 126 236 | 123 7 9 | +--------------------------+-------------------------+---------------------+ | 45 2 7 | 1345 15 34 | 6 9 8 | | 1 35 89 | 6 289 289 | 7 35 4 | | 45689 3456 35689 | 459 7 489 | 13 135 2 | +--------------------------+-------------------------+---------------------+

1. (5)r9c3 = (5-21)r13c3 = r1c2 - r1c8 = (1)r9c8 => -5 r9c8

Code: Select all: +--------------------------+-------------------------+--------------------+ | 45678 14567 12568 | 2457 2568 24678 | 9 13 1367 | | 3 467 68 | 479 689 1 | 5 2 67 | | 567 9 1256 | 257 3 267 | 4 8 167 | +--------------------------+-------------------------+--------------------+ | 79 8 139 | 12379 4 2379 | 123 6 5 | | 2 167 1369 | 1379 169 5 | 8 4 13 | | 56 156 4 | 8 126 236 | 123 7 9 | +--------------------------+-------------------------+--------------------+ | 45 2 7 | 1345 15 34 | 6 9 8 | | 1 3 89 | 6 289 289 | 7 5 4 | | 45689 456 5689 | 459 7 489 | 13 13 2 | +--------------------------+-------------------------+--------------------+

2. (1)r3c3 = r3c9 - (1=3)r1c8 - r1c9 = r5c9 - r5c3 = (3)r4c3 => -1 r4c3
3. (1)r4c4 = (1-2)r4c7 = (2-3)r6c7 = r6c6 - r7c6 = (3)r7c4 => -1 r7c4

Code: Select all: +------------------------+------------------------+--------------------+ | 4678 1467 1268 | 247 5 24678 | 9 13 1367 | | 3 467 68 | 479 689 1 | 5 2 67 | | 567 9 1256 | 27 3 267 | 4 8 167 | +------------------------+------------------------+--------------------+ | 79 8 39 | 12379 4 2379 | 123 6 5 | | 2 167 1369 | 1379 69 5 | 8 4 13 | | 56 156 4 | 8 26 236 | 123 7 9 | +------------------------+------------------------+--------------------+ | 45 2 7 | 345 1 34 | 6 9 8 | | 1 3 89 | 6 289 289 | 7 5 4 | | 45689 456 5689 | 459 7 489 | 13 13 2 | +------------------------+------------------------+--------------------+

4. (1)r1c2 = (1-25)r13c3 = r3c1 - r6c1 = (5)r6c2 => -1 r6c2; ste

ADDED: one step-solution,

Code: Select all: +--------------------------+-------------------------+---------------------+ | 45678 zd14567 12568 | 2457 v2568 24678 | 9 3-1 d1367 | | 3 467 68 | 479 689 1 | 5 2 67 | | a567 9 A1256 | u257 3 267 | 4 8 Bd167 | +--------------------------+-------------------------+---------------------+ | 79 8 z139 | y12379 4 2379 | z123 6 5 | | 2 zd1367 1369 | 1379 169 5 | 8 4 d13 | | b56 zc1356 4 | 8 126 236 | 123 7 9 | +--------------------------+-------------------------+---------------------+ | 45 2 7 | x1345 w15 34 | 6 9 8 | | 1 35 89 | 6 289 289 | 7 35 4 | | 45689 3456 35689 | 459 7 489 | z13 z135 2 | +--------------------------+-------------------------+---------------------+

Kraken row (5)r3c134
(5)r3c1 - r6c1 = (5-1)r6c2 = [r1c2*=*r5c2 - r5c9 = r13c9]
(5-1)r3c3 = (1)r3c9
(5)r3c4 - r1c5 = (5-1)r7c5 = r7c4 - r4c4 = [r1c2 = r56c2 - r4c3*=*r4c7 - r9c7 = r9c8]
=> -1 r1c8; ste

by **Ngisa** » Tue Mar 16, 2021 5:21 pm

Code: Select all: +-----------------------+---------------------+-----------------+ | 45678 14567 12568 | 2457 2568 4678 | 9 13 1367 | | 3 467 68 | 479 689 1 | 5 2 67 | |a567 9 1256 | 257 3 ca67 | 4 8 a167 | +-----------------------+---------------------+-----------------+ | 79 8 139 | 12379 4 c379 | 123 6 5 | | 2 1367 1369 | 1379 c169 5 | 8 4 3-1 | | 56 1356 4 | 8 126 c36 | 123 7 9 | +-----------------------+---------------------+-----------------+ |b45 2 7 | 1345 15 b34 | 6 9 8 | | 1 35 89 | 6 89 2 | 7 35 4 | | 45689 3456 35689 | 3459 7 3489 | 13 135 2 | +-----------------------+---------------------+-----------------+

Almost like Steve
(1=5)r3c961 - (5=3)r7c16 - (3=1)r634c6,r5c5 => -1r5c9; stte

Clement

by **DEFISE** » Wed Mar 17, 2021 1:08 pm

For the third puzzle (removing 2r8c6):

.........3....15...9..3..8..8..4..6.2....58....48...79.27...69.1..6....4....7....

Singles: 4r5c8, 2r2c8, 7r8c7, 9r1c7, 4r3c7, 5r4c9, 2r9c9, 8r7c9
Alignment: 1r7b8 => -1r9c4
Alignment: 3r7b8 => -3r8c6 -3r9c4 -3r9c6
Naked pair: 35r8c28 => -3r8c3 -5r8c3 -5r8c5
whip[6]: r3n1{c9 c3}- c2n1{r1 r6}- r6n5{c2 c1}- r3n5{c1 c4}- c5n5{r1 r7}- c5n1{r7 .} => -1r5c9
STTE

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