The New Sudoku Players' Forum

by **coloin** » Fri Mar 28, 2025 5:13 pm

Code: Select all: +---+---+---+ |68.|...|...| |5.7|9.6|..4| |.94|78.|..5| +---+---+---+ |.7.|4..|...| |4..|.97|...| |96.|5.8|...| +---+---+---+ |...|...|.2.| |.56|...|7.9| |...|8..|53.| +---+---+---+

This is minimal and ED 11.7/11.7/3.4 [without uniqueness]. And TE3.
The tridagon can't be used first off either...

by **pjb** » Sat Mar 29, 2025 2:34 am

An interesting workout for Thor's Hammer.
21 Thor's Hammer moves with only simple eliminations on the way:

Code: Select all: 6 8 123* | 123* 45 45 | 1239 179 1237 5 123* 7 | 9 123* 6 | 1238 18 4 123* 9 4 | 7 8 123* | 1236 16 5 ------------------------+----------------------+--------------------- 1238* 7 12358 | 4 1236 123* | 123689 15689 12368 4 123* 12358 | 1236* 9 7 | 12368 1568 12368 9 6 123* | 5 123* 8 | 1234 147 1237 ------------------------+----------------------+--------------------- 1378 134 1389 | 136 134567 13459 | 1468 2 168 1238 5 6 | 123 1234 1234 | 7 148 9 127 124 129 | 8 12467 1249 | 5 3 16 [code][/code]

Hidden Text: Show

Website · by **denis_berthier** » Sat Mar 29, 2025 5:41 am

.
Solution in W6+Trid-OR2W6
Interesting to see the large number of eliminations due to the tridagon.

Code: Select all: Resolution state after Singles (and whips[1]): +----------------------+----------------------+----------------------+ ! 6 8 123 ! 123 12345 12345 ! 1239 179 1237 ! ! 5 123 7 ! 9 123 6 ! 1238 18 4 ! ! 123 9 4 ! 7 8 123 ! 1236 16 5 ! +----------------------+----------------------+----------------------+ ! 1238 7 12358 ! 4 1236 123 ! 123689 15689 12368 ! ! 4 123 12358 ! 1236 9 7 ! 12368 1568 12368 ! ! 9 6 123 ! 5 123 8 ! 1234 147 1237 ! +----------------------+----------------------+----------------------+ ! 1378 134 1389 ! 136 134567 13459 ! 1468 2 168 ! ! 1238 5 6 ! 123 1234 1234 ! 7 148 9 ! ! 127 124 129 ! 8 12467 1249 ! 5 3 16 ! +----------------------+----------------------+----------------------+ 196 candidates.

hidden-pairs-in-a-row: r1{n4 n5}{c5 c6} ==> r1c6≠3, r1c6≠2, r1c6≠1, r1c5≠3, r1c5≠2, r1c5≠1
finned-x-wing-in-rows: n6{r9 r4}{c5 c9} ==> r5c9≠6

Code: Select all: Trid-OR2-relation for digits 2, 3 and 1 in blocks: b1, with cells (marked #): r1c3, r2c2, r3c1 b2, with cells (marked #): r1c4, r2c5, r3c6 b4, with cells (marked #): r6c3, r5c2, r4c1 b5, with cells (marked #): r6c5, r5c4, r4c6 with 2 guardians (in cells marked @): n8r4c1 n6r5c4 +----------------------+----------------------+----------------------+ ! 6 8 123# ! 123# 45 45 ! 1239 179 1237 ! ! 5 123# 7 ! 9 123# 6 ! 1238 18 4 ! ! 123# 9 4 ! 7 8 123# ! 1236 16 5 ! +----------------------+----------------------+----------------------+ ! 1238#@ 7 12358 ! 4 1236 123# ! 123689 15689 12368 ! ! 4 123# 12358 ! 1236#@ 9 7 ! 12368 1568 1238 ! ! 9 6 123# ! 5 123# 8 ! 1234 147 1237 ! +----------------------+----------------------+----------------------+ ! 1378 134 1389 ! 136 134567 13459 ! 1468 2 168 ! ! 1238 5 6 ! 123 1234 1234 ! 7 148 9 ! ! 127 124 129 ! 8 12467 1249 ! 5 3 16 ! +----------------------+----------------------+----------------------+

Trid-OR2-whip[4]: OR2{{n6r5c4 | n8r4c1}} - r8n8{c1 c8} - r2c8{n8 n1} - r3c8{n1 .} ==> r5c8≠6
t-whip[5]: r9n6{c9 c5} - c5n7{r9 r7} - c5n5{r7 r1} - c5n4{r1 r8} - b9n4{r8c8 .} ==> r7c7≠6
whip[1]: b9n6{r9c9 .} ==> r4c9≠6
Trid-OR2-whip[3]: OR2{{n8r4c1 | n6r5c4}} - b6n6{r5c7 r4c7} - r4n9{c7 .} ==> r4c8≠8
Trid-OR2-whip[3]: OR2{{n8r4c1 | n6r5c4}} - b6n6{r5c7 r4c8} - r4n9{c8 .} ==> r4c7≠8
whip[5]: c3n5{r4 r5} - b4n8{r5c3 r4c1} - r8n8{c1 c8} - r2c8{n8 n1} - r5c8{n1 .} ==> r4c3≠1
whip[5]: c3n5{r4 r5} - b4n8{r5c3 r4c1} - r8n8{c1 c8} - r2c8{n8 n1} - r5c8{n1 .} ==> r4c3≠2
whip[5]: c3n5{r4 r5} - b4n8{r5c3 r4c1} - r8n8{c1 c8} - r2c8{n8 n1} - r5c8{n1 .} ==> r4c3≠3
Trid-OR2-whip[4]: r4n9{c8 c7} - b6n6{r4c7 r5c7} - OR2{{n6r5c4 | n8r4c1}} - r4c3{n8 .} ==> r4c8≠5
singles ==> r5c8=5, r4c3=5
finned-x-wing-in-columns: n8{c3 c9}{r7 r5} ==> r5c7≠8
whip[1]: b6n8{r5c9 .} ==> r7c9≠8
naked-pairs-in-a-block: b9{r7c9 r9c9}{n1 n6} ==> r8c8≠1, r7c7≠1
whip[1]: b9n1{r9c9 .} ==> r1c9≠1, r4c9≠1, r5c9≠1, r6c9≠1
biv-chain[3]: r7c9{n1 n6} - r9n6{c9 c5} - b8n7{r9c5 r7c5} ==> r7c5≠1
biv-chain[4]: b9n1{r7c9 r9c9} - r9n6{c9 c5} - c5n7{r9 r7} - b8n5{r7c5 r7c6} ==> r7c6≠1
t-whip[4]: r8n1{c6 c1} - r8n8{c1 c8} - r2c8{n8 n1} - r3n1{c8 .} ==> r9c6≠1
biv-chain[5]: r7c9{n1 n6} - r9n6{c9 c5} - b8n7{r9c5 r7c5} - r7n5{c5 c6} - r7n9{c6 c3} ==> r7c3≠1
whip[5]: r7n5{c5 c6} - r7n9{c6 c3} - b7n3{r7c3 r8c1} - b7n8{r8c1 r7c1} - r7n7{c1 .} ==> r7c5≠3
whip[5]: r7n5{c6 c5} - r7n7{c5 c1} - b7n3{r7c1 r8c1} - b7n8{r8c1 r7c3} - r7n9{c3 .} ==> r7c6≠3
Trid-OR2-whip[5]: r7c7{n4 n8} - b7n8{r7c1 r8c1} - OR2{{n8r4c1 | n6r5c4}} - b8n6{r7c4 r9c5} - c5n7{r9 .} ==> r7c5≠4
Trid-OR2-whip[5]: r4n9{c8 c7} - r4n6{c7 c5} - OR2{{n6r5c4 | n8r4c1}} - r8n8{c1 c8} - r2c8{n8 .} ==> r4c8≠1
biv-chain[3]: r3c8{n1 n6} - r4c8{n6 n9} - b3n9{r1c8 r1c7} ==> r1c7≠1
Trid-OR2-whip[5]: OR2{{n6r5c4 | n8r4c1}} - b4n1{r4c1 r6c3} - r1n1{c3 c8} - r2c8{n1 n8} - r8n8{c8 .} ==> r5c4≠1
t-whip[5]: r8n1{c6 c1} - r8n8{c1 c8} - r2c8{n8 n1} - b1n1{r2c2 r1c3} - c4n1{r1 .} ==> r9c5≠1
Trid-OR2-whip[5]: c5n7{r9 r7} - b8n6{r7c5 r7c4} - OR2{{n6r5c4 | n8r4c1}} - r8n8{c1 c8} - r8n4{c8 .} ==> r9c5≠4
whip[6]: r7c9{n6 n1} - r7c4{n1 n3} - r7c2{n3 n4} - r9n4{c2 c6} - c6n9{r9 r7} - r7n5{c6 .} ==> r7c5≠6
Trid-OR2-whip[5]: r9c9{n1 n6} - r7n6{c9 c4} - OR2{{n6r5c4 | n8r4c1}} - b7n8{r7c1 r7c3} - c3n9{r7 .} ==> r9c3≠1
biv-chain[4]: r9c3{n2 n9} - b8n9{r9c6 r7c6} - r7n5{c6 c5} - b8n7{r7c5 r9c5} ==> r9c5≠2
whip[6]: r7c9{n1 n6} - r7c4{n6 n3} - b7n3{r7c1 r8c1} - r7c2{n3 n4} - b9n4{r7c7 r8c8} - r8n8{c8 .} ==> r7c1≠1
Trid-OR2-ctr-whip[6]: r2c8{n1 n8} - r8n8{c8 c1} - b7n1{r8c1 r9c1} - r9n7{c1 c5} - b8n6{r9c5 r7c4} - OR2{{n6r5c4 n8r4c1 | .}} ==> r2c2≠1
whip[6]: b1n1{r3c1 r1c3} - b2n1{r1c4 r2c5} - r6n1{c5 c7} - r6n4{c7 c8} - r8c8{n4 n8} - r2c8{n8 .} ==> r3c8≠1
singles ==> r3c8=6, r4c8=9, r1c7=9
Trid-OR2-whip[6]: OR2{{n8r4c1 | n6r5c4}} - r7n6{c4 c9} - r9c9{n6 n1} - b7n1{r9c1 r7c2} - r7c4{n1 n3} - b7n3{r7c1 .} ==> r8c1≠8

easy end in W3:
singles ==> r8c8=8, r2c8=1, r1c8=7, r6c8=4, r7c7=4, r9c2=4, r6c9=7, r2c7=8
naked-pairs-in-a-row: r9{c3 c6}{n2 n9} ==> r9c1≠2
naked-triplets-in-a-row: r7{c2 c4 c9}{n1 n3 n6} ==> r7c3≠3, r7c1≠3
finned-x-wing-in-rows: n3{r7 r2}{c2 c4} ==> r1c4≠3
finned-x-wing-in-rows: n3{r2 r7}{c2 c5} ==> r8c5≠3
finned-swordfish-in-columns: n3{c1 c6 c7}{r3 r8 r4} ==> r4c9≠3
finned-x-wing-in-columns: n3{c9 c3}{r1 r5} ==> r5c2≠3
biv-chain[3]: r2c2{n2 n3} - b7n3{r7c2 r8c1} - b7n2{r8c1 r9c3} ==> r1c3≠2
biv-chain[3]: b2n1{r3c6 r1c4} - r1n2{c4 c9} - b3n3{r1c9 r3c7} ==> r3c6≠3
singles ==> r2c5=3, r2c2=2, r5c2=1, r7c2=3, r1c3=1, r1c4=2, r1c9=3, r3c7=2, r3c6=1, r3c1=3
whip[1]: b5n1{r6c5 .} ==> r8c5≠1
naked-pairs-in-a-row: r4{c1 c9}{n2 n8} ==> r4c6≠2, r4c5≠2
stte

by **Cenoman** » Sat Mar 29, 2025 8:32 am

Code: Select all: +-----------------------+--------------------------+---------------------------+ | 6 8 123* | 123* 45 45 | 1239 179 1237 | | 5 123* 7 | 9 123* 6 | 1238 18 4 | | 123* 9 4 | 7 8 123* | 1236 16 5 | +-----------------------+--------------------------+---------------------------+ | c1238* 7 12358 | 4 1236 123* | 123689 15689 12368 | | 4 123* 12358 | d1236* 9 7 | 12368 1568 12368 | | 9 6 123* | 5 123* 8 | 1234 147 1237 | +-----------------------+--------------------------+---------------------------+ | 1378 134 1389 | e136 134567 13459 | 1468 2 168 | | b1238 5 6 | e123 e1234 e1234 | 7 a18-4 9 | | 127 124 129 | 8 12467 1249 | 5 3 16 | +-----------------------+--------------------------+---------------------------+

1. Tridagon (123)b1245 (*), having two guardians => 8r4c1 = 6r5c4
(8)r8c8 = r8c1 - (8)r4c1 == (6)r5c4 - (6=1234)b8p1456 => -4 r8c8; 10 placements

Code: Select all: +----------------------+------------------------+-----------------------+ | 6 8 123 | 123 45 45 | 9 7 123 | | 5 123 7 | 9 123 6 | 1238 18 4 | | 123 9 4 | 7 8 123 | 123 6 5 | +----------------------+------------------------+-----------------------+ | a1238 7 5 | 4 1236 123 | d1236-8 9 *12368 | | 4 123 *1238 | b1236 9 7 | c1236-8 5 *12368 | | 9 6 123 | 5 123 8 | 123 4 7 | +----------------------+------------------------+-----------------------+ | 1378 13 *1389 | 136 13567 1359 | 4 2 *168 | | 1238 5 6 | 123 1234 1234 | 7 18 9 | | 127 4 129 | 8 1267 129 | 5 3 16 | +----------------------+------------------------+-----------------------+

Re-using the tridagon derived strong link:
2. (8)r4c1 == (6)r5c4 - r5c7 = (6)r4c7 => -8 r4c7
3. X-Chain: (8)r5c3 = r7c3 - r7c9 = r45c9 => -8 r5c7; lcls, 3 placements

End with single digit patterns:

Code: Select all: +----------------------+-----------------------+--------------------+ | 6 8 1-23 | 123 45 45 | 9 7 ^23 | | 5 ^*23 7 | 9 ^*23 6 | 8 1 4 | | 123 9 4 | 7 8 123 | 23 6 5 | +----------------------+-----------------------+--------------------+ | 1238 7 5 | 4 1236 123 | 1236 9 ^238 | | 4 123 1238 | 1236 9 7 | 1236 5 ^238 | | 9 6 ^123 | 5 ^123 8 | ^123 4 7 | +----------------------+-----------------------+--------------------+ | 78 *13 89 | *136 57 59 | 4 2 16 | | 123 5 6 | 123 1234 1234 | 7 8 9 | | 127 4 129 | 8 1267 129 | 5 3 16 | +----------------------+-----------------------+--------------------+

4. (3)r2c5 = r2c2 - r7c2 = r7c4 => -3 r1c4

5. Kraken row (3)r6c357
(3)r6c3
(3)r6c5 - r2c5 = (3)r2c2
(3)r6c7 - r45c9 = (3)r1c9
=> -3 r1c3

6. Kraken row (2)r6c357
(2)r6c3
(2)r6c5 - r2c5 = (2)r2c2
(2)r6c7 - r45c9 = (2)r1c9
=> -2 r1c3; lclste

by **m_b_metcalf** » Sat Mar 29, 2025 9:39 am

coloin wrote:This is minimal and ED 11.7/11.7/3.4 [without uniqueness].

With uniqueness: 1r8c1; stte.

by **totuan** » Sun Mar 30, 2025 10:30 am

Code: Select all: *-----------------------------------------------------------------------------* | 6 8 #123 |#123 *45 *45 | 1239 179 1237 | | 5 #123 7 | 9 #123 6 | 1238 18 4 | |#123 9 4 | 7 8 #123 | 1236 16 5 | |-------------------------+-------------------------+-------------------------| | 123-8 7 #1235+8 | 4 %1236 #123 | 123689 15689 12368 | | 4 #123 #1235+8 |#123+6 9 7 | 12368 1568 12368 | | 9 6 #123 | 5 #123 8 | 1234 147 1237 | |-------------------------+-------------------------+-------------------------| | 1378 134 *1389 | 136 134567 *13459 | 1468 2 168 | |#123+8 5 6 |#123 #123+4 1234 | 7 148 9 | | 127 124 129 | 8 12467 1249 | 5 3 16 | *-----------------------------------------------------------------------------*

My path for this one:
Tridagon(123) with two guardians (6)r5c4 & (8)r4c1
Impossible pathern(123) #-marked cell – like twin => (8)r45c3,r8c1=(4)r8c5=(6)r5c4

Present as diagram: => r4c1<>8, Tridagon(123) => r5c4=6 then ER-6.6 and not hard to finish.

Code: Select all: (8)r45c3,r8c1* || (4)r8c5------------------(4=5)r1c5-r1c6=(5-9)r7c6=(9-8)r7c3=(8)r45c3* || | (6)r5c4-(1236=4)r2468c5-

Prove for impossible pattern(123):

Hidden Text: Show

Code: Select all: A=(1|2|3) *-----------------------------------------------------------* | . . 123 | 123 . . | . . . | | . 123 . | . 123 . | . . . | | 123 . . | . . 123 | . . . | |-------------------+-------------------+-------------------| | . . 1235 | . . 123 | . . . | | . A123 1235 | 123 . . | . . . | | . . 123 | . 123 . | . . . | |-------------------+-------------------+-------------------| | . . . | . . . | . . . | | 123 . . | 123 123 . | . . . | | . . . | . . . | . . . | *-----------------------------------------------------------* Let A=1 => r1c3=1 => r8c4=1 *-----------------------------------------------------------* | . . 1 |h23 . . | . . . | | . b23 . | . a23+1 . | . . . | |c23 . . | . . i23-1 | . . . | |-------------------+-------------------+-------------------| | . . 235 | . . 123 | . . . | | . 1 235 |g23 . . | . . . | | . . 23 | . f23-1 . | . . . | |-------------------+-------------------+-------------------| | . . . | . . . | . . . | |d23 . . | 1 e23 . | . . . | | . . . | . . . | . . . | *-----------------------------------------------------------* Oddagon(23) abcde => r2c5=1 => r3c6,r6c5<>1 => Oddagon(23) cdefghi => impossible The same for A=(2|3)

Thanks for the puzzle!
totuan

by **champagne** » Sun Mar 30, 2025 1:24 pm

m_b_metcalf wrote:
coloin wrote:This is minimal and ED 11.7/11.7/3.4 [without uniqueness].

With uniqueness: 1r8c1; stte.

can you tell more,

by **m_b_metcalf** » Sun Mar 30, 2025 3:13 pm

champagne wrote:
m_b_metcalf wrote:
coloin wrote:This is minimal and ED 11.7/11.7/3.4 [without uniqueness].

With uniqueness: 1r8c1; stte.

can you tell more,

It's a backdoor, for which uniqueness must be assumed.

by **champagne** » Sun Mar 30, 2025 3:21 pm

Ok Mike, I thought that you had something close to what totuan wrote.
I had already seen a backdoor in other puzzles of the loki family;

The New Sudoku Players' Forum

Double Jeopardy

Double Jeopardy

Re: Double Jeopardy

Re: Double Jeopardy

Re: Double Jeopardy

Re: Double Jeopardy

Re: Double Jeopardy

Re: Double Jeopardy

Re: Double Jeopardy

Re: Double Jeopardy