The New Sudoku Players' Forum

Website · by **denis_berthier** » Thu Feb 16, 2023 6:57 am

.
Another 3-digit pattern.

Code: Select all: +-------+-------+-------+ ! . . . ! . . . ! 7 8 . ! ! . 5 6 ! . 8 . ! . . . ! ! . 9 8 ! . 1 3 ! . . . ! +-------+-------+-------+ ! 2 . . ! . 3 . ! 8 4 . ! ! . . . ! . . 8 ! 3 . 2 ! ! 8 . . ! . 4 2 ! . 1 7 ! +-------+-------+-------+ ! . . . ! . . . ! . . . ! ! . 4 . ! . 7 1 ! . 3 . ! ! . . 1 ! 3 . 4 ! 2 7 . ! +-------+-------+-------+ ......78..56.8.....98.13...2...3.84......83.28...42.17..........4..71.3...13.427.;221;47805 SER = 11.7

Code: Select all: Resolution state after Singles and whips[1]: +----------------------+----------------------+----------------------+ ! 134 2 34 ! 4569 569 569 ! 7 8 134569 ! ! 1347 5 6 ! 2479 8 79 ! 149 29 1349 ! ! 47 9 8 ! 24567 1 3 ! 456 256 456 ! +----------------------+----------------------+----------------------+ ! 2 167 579 ! 15679 3 5679 ! 8 4 569 ! ! 4569 167 4579 ! 15679 569 8 ! 3 569 2 ! ! 8 36 359 ! 569 4 2 ! 569 1 7 ! +----------------------+----------------------+----------------------+ ! 3569 3678 3579 ! 5689 2 569 ! 14569 569 145689 ! ! 569 4 2 ! 5689 7 1 ! 569 3 5689 ! ! 569 68 1 ! 3 569 4 ! 2 7 5689 ! +----------------------+----------------------+----------------------+ 166 candidates.

Notice that for such a high SER, the number of candidates is unusually low (but that's of no use for solving).

by **Leren** » Thu Feb 16, 2023 8:16 pm

Code: Select all: *---------------------------------------------------* | 134 2 34 | 4569 569 569 | 7 8 134569 | | 1347 5 6 | 2479 8 79 | 149 29 1349 | | 47 9 8 | 24567 1 3 | 456 256 456 | |----------------+----------------+-----------------| | 2 167 579 | 15679 3 5679 | 8 4 569 | | 4569 167 4579 | 15679 569 8 | 3 569 2 | | 8 36 359 | 569 4 2 | 569 1 7 | |----------------+----------------+-----------------| | 3569 3678 3579 | 5689 2 569 | 14 569 14 | | 569 4 2 |a5689 7 1 | 569 3 b5689 | | 569 68 1 | 3 569 4 | 2 7 5689 | *---------------------------------------------------*

I'm no expert in impossible patterns but if r8c4 = 8 there are no solutions. If r8c9 = 8 there is a Trigadon (569) b5689 => r4c6 = 7; stte

Leren

by **Cenoman** » Thu Feb 16, 2023 11:55 pm

Code: Select all: +-----------------------+-----------------------+-----------------------+ | 134 2 c34 | b4569 b569 b569 | 7 8 134569 | | 1347 5 6 | 2479 8 b79 | 149 29 1349 | | 47 9 8 | 24567 1 3 | 456 256 456 | +-----------------------+-----------------------+-----------------------+ | 2 C167 579 | 15679 3 a5679* | 8 4 569* | | D569-4 C167 d4579 | 15679 569* 8 | 3 569* 2 | | 8 C36 359 | 569* 4 2 | 569* 1 7 | +-----------------------+-----------------------+-----------------------+ | 3569 3678 3579 | 5689 2 569* | 14 569* 14 | | 569 4 2 | 5689* 7 1 | 569* 3 5689 | | 569 B68 1 | 3 569* 4 | 2 7 A5689* | +-----------------------+-----------------------+-----------------------+

1. TH(569)b5689 having three guardians, 7r4c6, 8r8c4, 8r9c9
Note that 8r8c4 and 8r9c9 both conjugates of 8r8c9, have the same parity (True or False together) => a chain on anyone is enough.
(7)r4c6 - (7=5694)b2p1236 - r1c3 = (4)r5c3
||
(8)r9c9 - (8=6)r9c2 - r456c2 = (6)r5c1
=> -4 r5c1; lcls, 5 placements

Code: Select all: +--------------------+-----------------------+----------------------+ | 14 2 3 | 4569 569 569 | 7 8 14569 | | 147 5 6 | 2479 8 79 | 149 29 3 | | 47 9 8 | 24567 1 3 | 456 256 456 | +--------------------+-----------------------+----------------------+ | 2 167 b579 | 15679 3 A5679 | 8 4 569 | | 569 17 4 | 17 569 8 | 3 569 2 | | 8 3 59 | 569 4 2 | 569 1 7 | +--------------------+-----------------------+----------------------+ | 3 C68-7 c579 | 5689 2 569 | 14 569 14 | | 569 4 2 | 5689 7 1 | 569 3 5689 | | 569 B68 1 | 3 569 4 | 2 7 A5689 | +--------------------+-----------------------+----------------------+

2. Same TH(569)b5689, same guardians
(7)r4c6 - r4c3 = (7)r7c3
||
(8)r9c9 - r9c2 = (8)r7c2
=> - 7 r7c2; lcls, 2 placements

Code: Select all: +------------------+-----------------------+----------------------+ | 14 2 3 | 4569 569 569 | 7 8 14569 | | 147 5 6 | 2479 8 79 | 149 29 3 | | 47 9 8 | 24567 1 3 | 456 256 456 | +------------------+-----------------------+----------------------+ | 2 17* 59 | 15679* 3 569+7 | 8 4 569 | | 6 17* 4 | 17* 59 8 | 3 59 2 | | 8 3 59 | 569 4 2 | 569 1 7 | +------------------+-----------------------+----------------------+ | 3 68 7 | 5689 2 569 | 14 569 14 | | 59 4 2 | 5689 7 1 | 569 3 5689 | | 59 68 1 | 3 569 4 | 2 7 5689 | +------------------+-----------------------+----------------------+

3. UR(17)r45c24 using single external => +7 r4c6, lcls, 19 placements

Code: Select all: +-----------------+-------------------+------------------+ | 1 2 3 | 4 56 56 | 7 8 9 | | 4 5 6 | 7 8 9 | 1 2 3 | | 7 9 8 | 2 1 3 | 5 6 4 | +-----------------+-------------------+------------------+ | 2 1 59 | 56-9 3 7 | 8 4 56 | | 6 7 4 | 1 59* 8 | 3 59* 2 | | 8 3 59 | 56-9 4 2 | 69 1 7 | +-----------------+-------------------+------------------+ | 3 68 7 | 589* 2 56 | 4 59* 1 | | 59 4 2 | 589 7 1 | 69 3 568 | | 59 68 1 | 3 56-9 4 | 2 7 58 | +-----------------+-------------------+------------------+

4. Skyscraper (9)r5c5 = r5c8 - r7c8 = r7c4 => -9 r9c5, r46c4; ste

by **totuan** » Fri Feb 17, 2023 8:30 am

Code: Select all: *-----------------------------------------------------------------------------* | 134 2 34 | 4569 569 569 | 7 8 134569 | | 1347 5 6 | 2479 8 79 | 149 29 1349 | | 47 9 8 | 24567 1 3 | 456 256 456 | |-------------------------+-------------------------+-------------------------| | 2 167 579 | 15679 3 *5679 | 8 4 *569 | | 4569 167 4579 | 15679 *569 8 | 3 *569 2 | | 8 36 359 |*569 4 2 |*569 1 7 | |-------------------------+-------------------------+-------------------------| | 3569 3678 3579 | 5689 2 *569 | 14 *569 14 | | 569 4 2 |*5689 7 1 |*569 3 5689 | | 569 68 1 | 3 *569 4 | 2 7 *5689 | *-----------------------------------------------------------------------------*

Tridagon (569) * marked cells => (7)r4c6=(8)r8c4=(8)r9c9

Code: Select all: *-----------------------------------------------------------------------------* | 134 2 34 | 4569 569 569 | 7 8 134569 | | 1347 5 6 | 2479 8 79 | 149 29 1349 | | 47 9 8 | 24567 1 3 | 456 256 456 | |-------------------------+-------------------------+-------------------------| | 2 167 579 | 15679 3 5679 | 8 4 569 | |*4569 167 4579 | 15679 *569 8 | 3 *569 2 | | 8 36 359 |*569 4 2 |*569 1 7 | |-------------------------+-------------------------+-------------------------| | 3569 3678 3579 |*5689 2 *569 | 14 *569 14 | |*569 4 2 | 5689 7 1 |*569 3 *5689 | | 569 68 1 | 3 *569 4 | 2 7 569-8 | *-----------------------------------------------------------------------------*

My path for this one:
Impossible pattern (569) * marked cell => (4)r5c1=(8)r7c4=(8)r8c9
Note: (8)r7c4 lead to eliminate (8)r9c9 by 8's R8 or C1
Impossible pattern:

Hidden Text: Show

01: (8=6)r9c2-r789c1=(6)r5c1-(4)r5c1==(8)r7c4/r8c9 => r9c9<>8, some singles
02: Tridagon (569) => r4c6=7, stte

Thanks for the puzzle!
totuan

Website · by **denis_berthier** » Fri Feb 17, 2023 8:48 am

Leren wrote: If r8c9 = 8 there is a Trigadon (569) b5689 => r4c6 = 7; stte

Hi Leren,
"If r8c9 = 8": this is guessing.

by **totuan** » Fri Feb 17, 2023 8:54 am

Maybe need 10 cells for impossible pattern only

Code: Select all: *-----------------------------------------------------------* | . . . | . . . | . . . | | . . . | . . . | . . . | | . . . | . . . | . . . | |-------------------+-------------------+-------------------| | . . . | . . . | . . . | | 569 . . | . 569 . | . 569 . | | . . . | . . . | . . . | |-------------------+-------------------+-------------------| | . . . | 569 . 569 | . 569 . | |A569 . . | . . . | 569 . 569 | | . . . | . 569 . | . . . | *-----------------------------------------------------------*

totuan

Website · by **denis_berthier** » Fri Feb 17, 2023 8:59 am

.
Thanks for your solutions.

There's indeed a solution that doesn't use any other impossible pattern than tridagon. It requires no chain longer than 7: W7+OR2W7 (with length 8, Cenoman's 1st forcing chain is not far).
Here's a solution that uses one impossible pattern (EL10c4) besides Tridagon and that requires only chains of length ≤ 4.

The first OR3-tridagon relation immediately splits into two OR2 relations:

Code: Select all: hidden-pairs-in-a-row: r7{n1 n4}{c7 c9} ==> r7c9≠9, r7c9≠8, r7c9≠6, r7c9≠5, r7c7≠9, r7c7≠6, r7c7≠5 +----------------------+----------------------+----------------------+ ! 134 2 34 ! 4569 569 569 ! 7 8 134569 ! ! 1347 5 6 ! 2479 8 79 ! 149 29 1349 ! ! 47 9 8 ! 24567 1 3 ! 456 256 456 ! +----------------------+----------------------+----------------------+ ! 2 167 579 ! 15679 3 5679 ! 8 4 569 ! ! 4569 167 4579 ! 15679 569 8 ! 3 569 2 ! ! 8 36 359 ! 569 4 2 ! 569 1 7 ! +----------------------+----------------------+----------------------+ ! 3569 3678 3579 ! 5689 2 569 ! 14 569 14 ! ! 569 4 2 ! 5689 7 1 ! 569 3 5689 ! ! 569 68 1 ! 3 569 4 ! 2 7 5689 ! +----------------------+----------------------+----------------------+ OR3-anti-tridagon[12] for digits 5, 6 and 9 in blocks: b5, with cells: r4c6, r5c5, r6c4 b6, with cells: r4c9, r5c8, r6c7 b8, with cells: r7c6, r9c5, r8c4 b9, with cells: r7c8, r9c9, r8c7 with 3 guardians: n7r4c6 n8r8c4 n8r9c9 Trid-OR3-relation between candidates n7r4c6, n8r8c4 and n8r9c9 + same valence for candidates n8r9c9 and n8r8c4 via c-chain[2]: n8r9c9,n8r8c9,n8r8c4 ==> Trid-OR3-relation can be split into two Trid-OR2-relations with respective lists of guardians: n7r4c6 n8r8c4 and n7r4c6 n8r9c9

Here is now the new pattern I wanted to illustrate with this puzzle (see http://forum.enjoysudoku.com/how-to-deal-with-large-numbers-of-patterns-t40889.html for details about this pattern):

OR3-EL10c4 relation for digits: 5, 6 and 9
in cells (marked #): (r5c1 r5c8 r5c5 r9c5 r7c8 r7c6 r7c4 r8c1 r8c9 r8c7)
with 3 guardians (in cells marked @) : n4r5c1 n8r7c4 n8r8c9

Code: Select all: +----------------------+----------------------+----------------------+ ! 134 2 34 ! 4569 569 569 ! 7 8 134569 ! ! 1347 5 6 ! 2479 8 79 ! 149 29 1349 ! ! 47 9 8 ! 24567 1 3 ! 456 256 456 ! +----------------------+----------------------+----------------------+ ! 2 167 579 ! 15679 3 5679 ! 8 4 569 ! ! 4569#@ 167 4579 ! 15679 569# 8 ! 3 569# 2 ! ! 8 36 359 ! 569 4 2 ! 569 1 7 ! +----------------------+----------------------+----------------------+ ! 3569 3678 3579 ! 5689#@ 2 569# ! 14 569# 14 ! ! 569# 4 2 ! 5689 7 1 ! 569# 3 5689#@ ! ! 569 68 1 ! 3 569# 4 ! 2 7 5689 ! +----------------------+----------------------+----------------------+

There are many more useless ORk relations (not displayed here).

biv-chain[3]: r2c6{n7 n9} - r2c8{n9 n2} - b2n2{r2c4 r3c4} ==> r3c4≠7
hidden-single-in-a-row ==> r3c1=7
Trid-OR2-whip[3]: OR2{{n7r4c6 | n8r9c9}} - c2n8{r9 r7} - r7n7{c2 .} ==> r4c3≠7
z-chain[3]: c3n7{r7 r5} - r5n4{c3 c1} - c1n9{r5 .} ==> r7c3≠9
whip[1]: b7n9{r9c1 .} ==> r5c1≠9
z-chain[3]: c3n7{r7 r5} - r5n4{c3 c1} - c1n5{r5 .} ==> r7c3≠5
whip[1]: b7n5{r9c1 .} ==> r5c1≠5
Trid-OR2-whip[3]: OR2{{n8r9c9 | n7r4c6}} - r2c6{n7 n9} - b3n9{r2c7 .} ==> r9c9≠9
EL10c4-OR3-whip[4]: r9c2{n8 n6} - c1n6{r9 r5} - OR3{{n4r5c1 n8r7c4 | n8r8c9}} - c4n8{r8 .} ==> r7c2≠8
singles ==> r9c2=8, r8c9=8, r7c4=8

Code: Select all: +----------------------+----------------------+----------------------+ ! 134 2 34 ! 4569 569 569 ! 7 8 134569 ! ! 134 5 6 ! 2479 8 79 ! 149 29 1349 ! ! 7 9 8 ! 2456 1 3 ! 456 256 456 ! +----------------------+----------------------+----------------------+ ! 2 167 59 ! 15679 3 5679 ! 8 4 569 ! ! 46 167 4579 ! 15679 569 8 ! 3 569 2 ! ! 8 36 359 ! 569 4 2 ! 569 1 7 ! +----------------------+----------------------+----------------------+ ! 3569 367 37 ! 8 2 569 ! 14 569 14 ! ! 569 4 2 ! 569 7 1 ! 569 3 8 ! ! 569 8 1 ! 3 569 4 ! 2 7 56 ! +----------------------+----------------------+----------------------+

At least one candidate of a previous Trid-OR2-relation between candidates n7r4c6 n8r8c4 has just been eliminated.
There remains a Trid-OR1-relation between candidates: n7r4c6
Trid-ORk-relation with only one candidate => r4c6=7

stte

Website · by **denis_berthier** » Fri Feb 17, 2023 3:10 pm

totuan wrote:Maybe need 10 cells for impossible pattern only

Yes. We find the same pattern.

by **eleven** » Fri Feb 17, 2023 7:50 pm

totuan wrote:Maybe need 10 cells for impossible pattern only
Code: Select all
*-----------------------------------------------------------* | . . . | . . . | . . . | | . . . | . . . | . . . | | . . . | . . . | . . . | |-------------------+-------------------+-------------------| | . . . | . . . | . . . | | 569 . . | . 569 . | . 569 . | | . . . | . . . | . . . | |-------------------+-------------------+-------------------| | . . . | 569 . 569 | . 569 . | |A569 . . | . . . | 569 . 569 | | . . . | . 569 . | . . . | *-----------------------------------------------------------*

totuan

Easy to see: the digit in A goes to r7c8 and r9c5, killing all in r5.

by **Leren** » Sat Feb 18, 2023 2:01 am

Why not have another go.

Code: Select all: *-------------------------------------------------* | 14 2 3 | 4569 569 569 | 7 8 14569 | | 147 5 6 | 2479 8 79 | 149 29 3 | | 47 9 8 | 24567 1 3 | 456 256 456 | |------------+------------------+-----------------| | 2 167 59 | 15679 3 5679 | 8 4 569 | |*569 167 4 | 15679 *569 8 | 3 *569 2 | | 8 3 59 | 569 4 2 | 569 1 7 | |------------+------------------+-----------------| | 3 8 7 |*569 2 *569 | 14 *569 148 | |*569 4 2 | 8 7 1 |*569 3 *569 | | 569 68 1 | 3 *569 4 | 2 7 5689 | *-------------------------------------------------*

r8c4 = 8 => 10 cell DP (569) => r8c4 <> 8. (Only a few basic moves were required to expose the DP). The rest is as per my first post.

I prefer Cenoman's solution.

Leren

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