The New Sudoku Players' Forum

by **coloin** » Thu Sep 05, 2024 7:36 pm

Code: Select all: +---+---+---+ |...|.89|...| |..6|5.7|8..| |..9|64.|5..| +---+---+---+ |.65|8..|...| |8.4|.9.|...| |79.|..6|...| +---+---+---+ |647|...|95.| |...|...|.2.| |...|...|..1| +---+---+---+ MagicJim

by **shye** » Fri Sep 06, 2024 12:31 am

Code: Select all: ,---------------,-------------------,---------------------, | 5 7 T123 |T123 8 9 | 12346 1346 2346 | | 4 T123 6 | 5 T123 7 | 8 139 239 | |T123 8 9 | 6 4 T123 | 5 137 237 | :---------------+-------------------+---------------------: |T123 6 5 | 8 B1237 A1234| 12347 13479 23479 | | 8 T123 4 |A1237 9 B1235| 12367 1367 23567 | | 7 9 T123 |B123+4 A123+5 6 | 1234 1348 23458 | :---------------+-------------------+---------------------: | 6 4 7 |#123 #123 1238| 9 5 38 | | 139 135 138 | 3479 3567 3458| 3467 2 34678 | | 239 235 238 | 3479 3567 3458| 3467 34678 1 | '---------------'-------------------'---------------------'

two tridagons to avoid, in cells marked as T+A and T+B
each placement of 7 in b5 results in a naked triple in c4|5 and the placement of 4|5 in b5
each of these orientations nearly completes the tridagon, forcing the other of 4|5 to be placed and disrupt it
the outcome is always the same, +4r6c4 & +5r6c5

XSudo input: Show

some progress can be made, then:

Code: Select all: ,---------------,------------------,--------------------, ,----------,----------,----------, | 5 7 123 | 123 8 9 |F123-46 1346 246 | | 5 7 C | B 8 9 | A . . | | 4 123 6 | 5 123 7 | 8 139 29 | | 4 ab 6 | 5 ac 7 | 8 . . | | 123 8 9 | 6 4 123 | 5 137 27 | | ab 8 9 | 6 4 ac | 5 . . | :---------------+------------------+--------------------: :----------+----------+----------: |R123 6 5 | 8 7-123 R123 | 12347 13479 2479 | | ac 6 5 | 8 . abc| . . . | | 8 123 4 | 1237 9 R123 | 12367 1367 5 | | 8 ac 4 | . 9 abc| . . 5 | | 7 9 F123 | 4 5 6 |F123 138 28 | | 7 9 B | 4 5 6 | C . . | :---------------+------------------+--------------------: :----------+----------+----------: | 6 4 7 | 12 12 8 | 9 5 3 | | 6 4 7 | . . 8 | 9 5 3 | | 139 135 138 | 379 367 45 | 467 2 4678 | | . . . | . . . | . 2 . | | 239 235 238 | 379 367 45 | 467 4678 1 | | . . . | . . . | . . 1 | '---------------'------------------'--------------------' '----------'----------'----------'

firework triple in r6c7b6, F-marked cells must contain 123, -46r1c7
knowing these cells form a triple we can begin to "color" the remaining 123s (the process being to assign each [123] cell a letter/color) the diagram of which is also provided

there are two cases but each reveals a remote triple in R-marked cells, -123r4c5

XSudo input: Show

from here the puzzle is much simpler

8r9c8 = (8-2)r9c3 = [finned x-wing: 2c37 covered by r16 fin r4c7] - (2=8)r6c9
-8r6c8, -8r8c9
finned x-wing: 1c37 covered by r16 fin r4c7
-1r6c8

Hidden Text: Show

solves with BUG+1

brings me a heavy heart to hear about mathimagics passing, this is a lovely tribute <3

by **shye** » Fri Sep 06, 2024 1:10 am

...i only just realised this is an 11.9
amazing find!

Website · by **denis_berthier** » Fri Sep 06, 2024 4:07 am

.
Resolution state after Singles and whips[1]:

Code: Select all: +-------------------+-------------------+-------------------+ ! 5 7 123 ! 123 8 9 ! 12346 1346 2346 ! ! 4 123 6 ! 5 123 7 ! 8 139 239 ! ! 123 8 9 ! 6 4 123 ! 5 137 237 ! +-------------------+-------------------+-------------------+ ! 123 6 5 ! 8 1237 1234 ! 12347 13479 23479 ! ! 8 123 4 ! 1237 9 1235 ! 12367 1367 23567 ! ! 7 9 123 ! 1234 1235 6 ! 1234 1348 23458 ! +-------------------+-------------------+-------------------+ ! 6 4 7 ! 123 123 1238 ! 9 5 38 ! ! 139 135 138 ! 3479 3567 3458 ! 3467 2 34678 ! ! 239 235 238 ! 3479 3567 3458 ! 3467 34678 1 ! +-------------------+-------------------+-------------------+ 190 candidates.

There are two tridagons, in the same 4 blocks:

Code: Select all: Trid-OR3-relation for digits 1, 2 and 3 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 #): r6c4, r5c6, r4c5 with 3 guardians (in cells marked @): n7r4c5 n5r5c6 n4r6c4 +----------------------+----------------------+----------------------+ ! 5 7 123# ! 123# 8 9 ! 12346 1346 2346 ! ! 4 123# 6 ! 5 123# 7 ! 8 139 239 ! ! 123# 8 9 ! 6 4 123# ! 5 137 237 ! +----------------------+----------------------+----------------------+ ! 123# 6 5 ! 8 1237#@ 1234 ! 12347 13479 23479 ! ! 8 123# 4 ! 1237 9 1235#@ ! 12367 1367 23567 ! ! 7 9 123# ! 1234#@ 1235 6 ! 1234 1348 23458 ! +----------------------+----------------------+----------------------+ ! 6 4 7 ! 123 123 1238 ! 9 5 38 ! ! 139 135 138 ! 3479 3567 3458 ! 3467 2 34678 ! ! 239 235 238 ! 3479 3567 3458 ! 3467 34678 1 ! +----------------------+----------------------+----------------------+ Trid-OR3-relation for digits 1, 2 and 3 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 3 guardians (in cells marked @): n4r4c6 n7r5c4 n5r6c5 +----------------------+----------------------+----------------------+ ! 5 7 123# ! 123# 8 9 ! 12346 1346 2346 ! ! 4 123# 6 ! 5 123# 7 ! 8 139 239 ! ! 123# 8 9 ! 6 4 123# ! 5 137 237 ! +----------------------+----------------------+----------------------+ ! 123# 6 5 ! 8 1237 1234#@ ! 12347 13479 23479 ! ! 8 123# 4 ! 1237#@ 9 1235 ! 12367 1367 23567 ! ! 7 9 123# ! 1234 1235#@ 6 ! 1234 1348 23458 ! +----------------------+----------------------+----------------------+ ! 6 4 7 ! 123 123 1238 ! 9 5 38 ! ! 139 135 138 ! 3479 3567 3458 ! 3467 2 34678 ! ! 239 235 238 ! 3479 3567 3458 ! 3467 34678 1 ! +----------------------+----------------------+----------------------+

whip[4]: c7n1{r6 r1} - c3n1{r1 r8} - c3n8{r8 r9} - c8n8{r9 .} ==> r6c8≠1

Code: Select all: +-------------------+-------------------+-------------------+ ! 5 7 123 ! 123 8 9 ! 12346 1346 2346 ! ! 4 123 6 ! 5 123 7 ! 8 139 239 ! ! 123 8 9 ! 6 4 123 ! 5 137 237 ! +-------------------+-------------------+-------------------+ ! 123 6 5 ! 8 1237 1234 ! 12347 13479 23479 ! ! 8 123 4 ! 1237 9 1235 ! 12367 1367 23567 ! ! 7 9 123 ! 1234 1235 6 ! 1234 348 23458 ! +-------------------+-------------------+-------------------+ ! 6 4 7 ! 123 123 1238 ! 9 5 38 ! ! 139 135 138 ! 3479 3567 3458 ! 3467 2 34678 ! ! 239 235 238 ! 3479 3567 3458 ! 3467 34678 1 ! +-------------------+-------------------+-------------------+

At this point, no ORk-chain rule is available and SudoRules tries eleven's replacement technique based on the tridagon patten

This first try is useless, but I keep it here, in order to recall that replacement is an (educated) variant of T&E:

Code: Select all: ***** STARTING ELEVEN''S REPLACEMENT TECHNIQUE ***** RELEVANT DIGIT REPLACEMENTS WILL BE NECESSARY AT THE END, based on the original givens. Trying in block 4 +-------------------------+-------------------------+-------------------------+ ! 5 7 123 ! 123 8 9 ! 12346 12346 12346 ! ! 4 123 6 ! 5 123 7 ! 8 1239 1239 ! ! 123 8 9 ! 6 4 123 ! 5 1237 1237 ! +-------------------------+-------------------------+-------------------------+ ! 3 6 5 ! 8 1237 1234 ! 12347 123479 123479 ! ! 8 2 4 ! 1237 9 1235 ! 12367 12367 123567 ! ! 7 9 1 ! 1234 1235 6 ! 1234 12348 123458 ! +-------------------------+-------------------------+-------------------------+ ! 6 4 7 ! 123 123 1238 ! 9 5 1238 ! ! 1239 1235 1238 ! 123479 123567 123458 ! 123467 123 1234678 ! ! 1239 1235 1238 ! 123479 123567 123458 ! 123467 1234678 123 ! +-------------------------+-------------------------+-------------------------+

The second try is the good one:

Code: Select all: ***** STARTING ELEVEN''S REPLACEMENT TECHNIQUE ***** RELEVANT DIGIT REPLACEMENTS WILL BE NECESSARY AT THE END, based on the original givens. Trying in block 2 +-------------------------+-------------------------+-------------------------+ ! 5 7 123 ! 3 8 9 ! 12346 12346 12346 ! ! 4 123 6 ! 5 2 7 ! 8 1239 1239 ! ! 123 8 9 ! 6 4 1 ! 5 1237 1237 ! +-------------------------+-------------------------+-------------------------+ ! 123 6 5 ! 8 1237 1234 ! 12347 123479 123479 ! ! 8 123 4 ! 1237 9 1235 ! 12367 12367 123567 ! ! 7 9 123 ! 1234 1235 6 ! 1234 12348 123458 ! +-------------------------+-------------------------+-------------------------+ ! 6 4 7 ! 123 123 1238 ! 9 5 1238 ! ! 1239 1235 1238 ! 123479 123567 123458 ! 123467 123 1234678 ! ! 1239 1235 1238 ! 123479 123567 123458 ! 123467 1234678 123 ! +-------------------------+-------------------------+-------------------------+

Short ORk-chains can now be applied:
Trid-OR3-whip[5]: r7c5{n1 n3} - r4c5{n3 n7} - OR3{{n7r5c4 n5r6c5 | n4r4c6}} - c6n3{r4 r5} - b5n5{r5c6 .} ==> r6c5≠1
whip[3]: r7c4{n2 n1} - c5n1{r9 r4} - b5n7{r4c5 .} ==> r5c4≠2
Trid-OR3-whip[4]: r6c5{n3 n5} - OR3{{n5r5c6 n7r4c5 | n4r6c4}} - b5n1{r6c4 r5c4} - b5n7{r5c4 .} ==> r4c5≠3
naked-pairs-in-a-block: b5{r4c5 r5c4}{n1 n7} ==> r6c4≠1
whip[4]: c9n5{r5 r6} - r6c5{n5 n3} - r7c5{n3 n1} - c4n1{r9 .} ==> r5c9≠1
Trid-OR3-whip[5]: r7c4{n2 n1} - c5n1{r9 r4} - OR3{{n7r4c5 n4r6c4 | n5r5c6}} - r6c5{n5 n3} - r7c5{n3 .} ==> r6c4≠2
naked-single ==> r6c4=4

Code: Select all: +-------------------------+-------------------------+-------------------------+ ! 5 7 12 ! 3 8 9 ! 1246 1246 1246 ! ! 4 13 6 ! 5 2 7 ! 8 139 139 ! ! 23 8 9 ! 6 4 1 ! 5 237 237 ! +-------------------------+-------------------------+-------------------------+ ! 123 6 5 ! 8 17 23 ! 12347 123479 123479 ! ! 8 123 4 ! 17 9 235 ! 12367 12367 23567 ! ! 7 9 123 ! 4 35 6 ! 123 1238 12358 ! +-------------------------+-------------------------+-------------------------+ ! 6 4 7 ! 12 13 238 ! 9 5 1238 ! ! 1239 1235 1238 ! 1279 13567 23458 ! 123467 123 1234678 ! ! 1239 1235 1238 ! 1279 13567 23458 ! 123467 1234678 123 ! +-------------------------+-------------------------+-------------------------+ At least one candidate of a previous Trid-OR3-relation between candidates n4r4c6 n7r5c4 n5r6c5 has just been eliminated. There remains a Trid-OR2-relation between candidates: n7r5c4 n5r6c5

whip[1]: c4n2{r9 .} ==> r8c6≠2, r7c6≠2, r9c6≠2
Trid-OR2-whip[2]: OR2{{n7r5c4 | n5r6c5}} - c9n5{r6 .} ==> r5c9≠7
Trid-OR2-whip[3]: OR2{{n5r6c5 | n7r5c4}} - b5n1{r5c4 r4c5} - r7c5{n1 .} ==> r6c5≠3

The end is easy (for this kind of puzzle):

Code: Select all: singles ==> r6c5=5, r5c9=5 whip[1]: c5n3{r9 .} ==> r8c6≠3, r7c6≠3, r9c6≠3 naked-single ==> r7c6=8 naked-triplets-in-a-block: b9{r7c9 r8c8 r9c9}{n3 n2 n1} ==> r9c8≠3, r9c8≠2, r9c8≠1, r9c7≠3, r9c7≠2, r9c7≠1, r8c9≠3, r8c9≠2, r8c9≠1, r8c7≠3, r8c7≠2, r8c7≠1 whip[1]: c7n3{r4 .} ==> r4c8≠3, r4c9≠3, r5c8≠3, r6c8≠3, r6c9≠3 whip[5]: r6n2{c9 c3} - r1c3{n2 n1} - r2c2{n1 n3} - b4n3{r5c2 r4c1} - r4c6{n3 .} ==> r4c9≠2 whip[5]: r6n2{c9 c3} - r1c3{n2 n1} - r2c2{n1 n3} - b4n3{r5c2 r4c1} - r4c6{n3 .} ==> r4c8≠2 whip[5]: r6n2{c9 c3} - r1c3{n2 n1} - r2c2{n1 n3} - b4n3{r5c2 r4c1} - r4c6{n3 .} ==> r4c7≠2 whip[4]: r6n1{c9 c3} - r6n3{c3 c7} - c7n2{r6 r1} - r1c3{n2 .} ==> r5c7≠1 whip[5]: r6n2{c9 c3} - r6n3{c3 c7} - c7n2{r6 r1} - c7n1{r1 r4} - r6n1{c7 .} ==> r5c8≠2 whip[5]: c7n2{r6 r1} - c8n2{r1 r8} - c3n2{r8 r9} - r9n8{c3 c8} - r6n8{c8 .} ==> r6c9≠2 whip[3]: r8n8{c3 c9} - r6c9{n8 n1} - b9n1{r7c9 .} ==> r8c3≠1 whip[4]: r6n3{c3 c7} - r6n2{c7 c8} - c7n2{r5 r1} - r1c3{n2 .} ==> r6c3≠1 whip[1]: r6n1{c9 .} ==> r5c8≠1, r4c9≠1, r4c8≠1, r4c7≠1 whip[3]: b1n3{r2c2 r3c1} - b1n2{r3c1 r1c3} - r6c3{n2 .} ==> r5c2≠3 whip[3]: b1n2{r3c1 r1c3} - b1n1{r1c3 r2c2} - r5c2{n1 .} ==> r4c1≠2 singles ==> r4c6=2, r5c6=3 whip[3]: c3n1{r9 r1} - c7n1{r1 r6} - r6n3{c7 .} ==> r9c3≠3 whip[3]: r6c3{n3 n2} - r1c3{n2 n1} - c7n1{r1 .} ==> r6c7≠3 singles ==> r4c7=3, r4c1=1, r4c5=7, r5c4=1, r7c4=2, r5c2=2, r6c3=3 hidden-pairs-in-a-column: c7{n1 n2}{r1 r6} ==> r1c7≠6, r1c7≠4 whip[1]: c7n4{r9 .} ==> r8c9≠4, r9c8≠4 naked-pairs-in-a-row: r1{c3 c7}{n1 n2} ==> r1c9≠2, r1c9≠1, r1c8≠2, r1c8≠1 finned-x-wing-in-columns: n2{c9 c1}{r3 r9} ==> r9c3≠2 whip[3]: r6c9{n1 n8} - r8n8{c9 c3} - r9c3{n8 .} ==> r9c9≠1 whip[4]: r9n8{c8 c3} - c3n1{r9 r1} - r1n2{c3 c7} - r6n2{c7 .} ==> r6c8≠8 singles ==> r6c9=8, r9c8=8, r9c3=1, r1c3=2, r1c7=1, r6c7=2, r6c8=1, r3c1=3, r2c2=1, r8c3=8, r7c9=1, r7c5=3, r9c5=6, r8c5=1 whip[4]: r9n9{c1 c4} - r9n7{c4 c7} - c9n7{r8 r3} - c9n2{r3 .} ==> r9c1≠2 stte

Note that, for this puzzle, the key to the solution is eleven's replacement (also present in shye's solution in the form of "colouring" the tridagon digits).
.

by **marek stefanik** » Fri Sep 06, 2024 9:58 am

Same start as shye (45r6c45). Then:

Code: Select all: ,---------------,-----------------,--------------------, | 5 7 123 | 123 8 9 |#12346 1346 246 | | 4 123 6 | 5 123 7 | 8 139 29 | | 123 8 9 | 6 4 123 | 5 137 27 | :---------------+-----------------+--------------------: | 123 6 5 | 8 1237 123 | 12347 13479 2479 | | 8 123 4 | 1237 9 123 | 12367 1367 5 | | 7 9 123 | 4 5 6 | 123 #138 #28 | :---------------+-----------------+--------------------: | 6 4 7 | 12 12 8 | 9 5 3 | | 139 135 #138 | 379 367 45 | 467 2 *4678 | | 239 235 #238 | 379 367 45 | 467 *4678 1 | '---------------'-----------------'--------------------'

The non-8 in r6c89 is in c7 forced into r1c7, in c3 forced into r89c3. If it were 1 or 2, the 8s in b67 would break b9, so it's 3.

Code: Select all: ,--------------,----------------,----------------, | 5 7 #12 |#12 8 9 | 3 46 46 | | 4 #123 6 | 5 #123 7 | 8 19 29 | |#123 8 9 | 6 4 #123 | 5 17 27 | :--------------+----------------+----------------: |#123 6 5 | 8 *1237 *123 | 1247 479 479 | | 8 #123 4 |*37 9 *123 | 1267 67 5 | | 7 9 #12 | 4 5 6 | 12 3 8 | :--------------+----------------+----------------: | 6 4 7 | 12 12 8 | 9 5 3 | | 19 15 8 | 379 367 45 | 467 2 467 | | 29 25 3 | 79 67 45 | 467 8 1 | '--------------'----------------'----------------'

Look at 123b124. r1c4 and r6c3 contain the same digit, so the digit in r3c6 must take r4c1 (parity transfer via b1) and is then forced into r5c4 in b5, so it's 3.
Solves with a BUG+1.

Marek

by **DEFISE** » Fri Sep 06, 2024 11:45 am

I don't have time to go into detail but this puzzle is in (OR3-gB11 + B6) or in (OR3-S2B7 + B6).
In both cases, using tridagon1 and tridagon2 successively.

by **Cenoman** » Fri Sep 06, 2024 1:23 pm

Code: Select all: +--------------------+-----------------------+--------------------------+ | 5 7 123*^ | 123*^ 8 9 | 12346 1346 2346 | | 4 123*^ 6 | 5 123*^ 7 | 8 139 239 | | 123*^ 8 9 | 6 4 123*^ | 5 137 237 | +--------------------+-----------------------+--------------------------+ | 123*^ 6 5 | 8 a1237* 1234^ | 12347 13479 23479 | | 8 123*^ 4 | 1237^ 9 1235* | 12367 1367 23567 | | 7 9 123*^ | 1234* 1235^ 6 | 1234 1348 23458 | +--------------------+-----------------------+--------------------------+ | 6 4 7 | 123 123 1238 | 9 5 38 | | 139 135 138 | 379-4 367-5 3458 | 3467 2 34678 | | 239 235 238 | 379-4 367-5 3458 | 3467 34678 1 | +--------------------+-----------------------+--------------------------+

1. Tridagon 1: (123)b124, b5p267 (*), having three guardians:
(7)r4c5 - r5c4 = (79)r89c4
(5)r5c6 - r6c5 = (5679)r89c45
(4)r6c4
=> -4 r89c4

2. Tridagon 2: (123)b124, b5p348 (^), having three guardians:
(4)r4c6 - r6c4 = (4679)r89c45
(7)r5c4 - r4c5 = (76)r89c5
(5)r6c5
=> -5 r89c5; lcls, 5 placements

Code: Select all: +--------------------+----------------------+-------------------------+ | 5 7 123 | 123 8 9 | 123-46 1346 246 | | 4 123 6 | 5 123 7 | 8 139 29 | | 123 8 9 | 6 4 123 | 5 137 27 | +--------------------+----------------------+-------------------------+ | 123 6 5 | 8 1237 123 | 12347* 49-137 49-27 | | 8 123 4 | 1237 9 123 | 12367* 67-13 5 | | 7 9 123 | 4 5 6 | 123* 138* 28* | +--------------------+----------------------+-------------------------+ | 6 4 7 | 12 12 8 | 9 5 3 | | 139 135 138 | 379 367 45 | 467* 2 4678 | | 239 235 238 | 379 367 45 | 467* 4678 1 | +--------------------+----------------------+-------------------------+

3. MSLS b6p14789, r89c7: 7 cells (Truths), 7 links: 1238b6, 467c7
=> 7 eliminations: -46r1c7, -13r45c8, -2r4c9; lcls

Code: Select all: +--------------------+----------------------+------------------------+ | 5 7 Aa123*^ | 123 8 9 | 3-12 46 46 | | 4 123 6 | 5 123 7 | 8 EA139^ ea29* | | 123 8 9 | 6 4 123 | 5 EA137V ea27* | +--------------------+----------------------+------------------------+ | 123 6 5 | 8 y1237 123 | y12347 49-7 49-7 | | 8 123 4 | 1237 9 123 | z12367 z67 5 | | 7 9 Aa123*^ | 4 5 6 | 123 DAc138^ da28* | +--------------------+----------------------+------------------------+ | 6 4 7 | 12 12 8 | 9 5 3 | | 139 135 B138 | 379 367# 45 | 467# 2 B4678 | | 239 235 b238 | 379 367# 45 | 467# Cb4678 1 | +--------------------+----------------------+------------------------+

Two almost skyscrapers, then one UR
4. (2)[r23c9 = r6c9 - r6c3 = r1c3] = (28)r9c38 - r6c8 = (8-2)r6c9 = (2)r23c9 => -2 r1c7
5. (1)[r23c8 = r6c8 - r6c3 = r1c3] = (18)r8c39 - r6c9 = (8-1)r6c8 = (1)r23c8 => -1 r1c7; lcls, 6 placements
6. UR(67)r89c57 (#), using externals: (7)r4c57 == (67)r5c78 => -7 r4c89; lcls

Code: Select all: +-------------------+---------------------+-------------------+ | 5 7 12 | 12 8 9 | 3 46 46 | | 4 123 6 | 5 123 7 | 8 19 29 | | 123 8 9 | 6 4 123 | 5 17 27 | +-------------------+---------------------+-------------------+ | 123 6 5 | 8 1237 123 | 127 49 49 | | 8 123 4 | 37 9 123 | 1267 67 5 | | 7 9 12 | 4 5 6 | 12 3 8 | +-------------------+---------------------+-------------------+ | 6 4 7 | 12 12 8 | 9 5 3 | | 19 15 8 | 379 367 45 | 467 2 67 | | 29 25 3 | 79 67 45 | 467 8 1 | +-------------------+---------------------+-------------------+

7. (7)r4c5 = r5c4 - r5c8 = r3c8 - (7=2)r3c9 - r3c6 = (2)r45c6 => -2 r4c5
8. Kraken cell (123)r4c1
(1)r4c1
(2)r4c1 - (2=1)r6c3 - r1c3 = r1c4 - r7c4 = (1)r7c5
(3)r4c1 - r3c1 = (3-1)r3c6 = (1)r45c6
=> -1 r4c5; lcls, 7 placements

Hidden Text: Show

9. BUG+1 => +7 r8c7; ste

by **DEFISE** » Sat Sep 07, 2024 7:30 am

After basics :

Code: Select all: |-----------------------------------------------------------| | 5 7 123 | 123 8 9 | 12346 1346 2346 | | 4 123 6 | 5 123 7 | 8 139 239 | | 123 8 9 | 6 4 123 | 5 137 237 | |-----------------------------------------------------------| | 123 6 5 | 8 1237 1234 | 12347 13479 23479 | | 8 123 4 | 1237 9 1235 | 12367 1367 23567 | | 7 9 123 | 1234 1235 6 | 1234 1348 23458 | |-----------------------------------------------------------| | 6 4 7 | 123 123 1238 | 9 5 38 | | 139 135 138 | 3479 3567 3458 | 3467 2 34678 | | 239 235 238 | 3479 3567 3458 | 3467 34678 1 | |-----------------------------------------------------------|

1st tridagon 123 in b1p357, b2p159, b4p159, b5p267 (3 guardians : 7r4c5, 5r5c6, 4r6c4)

Trid-OR3-S2-whip[7]: b8{n4r89 HP:n49r89}- c4n7{r8 r5}- OR3{{n7r4c5,n4r6c4 | n5r5c6}}- b8{n5r89 HP:n56r89}- c5n7{r8 .} => -4r4c6
Single(s): 4r6c4

A tridagon guardian has been validated so the OR3 property is no longer exploitable.

Code: Select all: |-----------------------------------------------------------| | 5 7 123 | 123 8 9 | 12346 1346 2346 | | 4 123 6 | 5 123 7 | 8 139 239 | | 123 8 9 | 6 4 123 | 5 137 237 | |-----------------------------------------------------------| | 123 6 5 | 8 1237 123 | 12347 13479 23479 | | 8 123 4 | 1237 9 1235 | 12367 1367 23567 | | 7 9 123 | 4 1235 6 | 123 138 2358 | |-----------------------------------------------------------| | 6 4 7 | 123 123 1238 | 9 5 38 | | 139 135 138 | 379 3567 3458 | 3467 2 34678 | | 239 235 238 | 379 3567 3458 | 3467 34678 1 | |-----------------------------------------------------------|

2 nd tridagon 123 b1p357, b2p159, b4p159, b5p348 (2 guardians : 7r5c4, 5r6c5)

Trid-OR2-S2-whip[4]: OR2{{n5r6c5 | n7r5c4}}- c5{n7r4 HP:56r89}- c5n7{r8 .} => -5r6c9

Single(s): 5r6c5, 5r5c9
Hidden pairs: 45c6r89 => -3r8c6 -8r8c6 -3r9c6 -8r9c6
Single(s): 8r7c6, 3r7c9

A guardian has been validated so the OR2 property is no longer exploitable.
Classic end in W4 :

whip[4]: r8n8{c3 c9}- r6c9{n8 n2}- c3n2{r6 r1}- c7n2{r1 .} => -8r9c3
Single(s): 8r9c8, 8r6c9, 8r8c3
whip[2]: c3n1{r6 r1}- c7n1{r1 .} => -1r6c8
Single(s): 3r6c8, 3r1c7, 3r9c3
Box/Line: 1c7b6 => -1r4c8 -1r5c8
Box/Line: 2c7b6 => -2r4c9
Naked pairs: 12r1c34 => -1r1c8 -2r1c9
Naked pairs: 12c4r17 => -1r5c4 -2r5c4
whip[4]: r9c1{n2 n9}- r9c4{n9 n7}- r5c4{n7 n3}- r4n3{c5 .} => -2r4c1
whip[3]: r4c1{n1 n3}- r3n3{c1 c6}- c6n1{r3 .} => -1r4c5
Box/Line: 1b5c6 => -1r3c6
whip[4]: r4c1{n3 n1}- c3n1{r6 r1}- b2n1{r1c4 r2c5}- r2n3{c5 .} => -3r5c2
Single(s): 3r2c2, 3r3c6, 3r5c4, 3r4c1, 3r8c5, 6r9c5, 7r4c5
Naked pairs: 49r4c89 => -4r4c7
Box/Line: 4c7b9 => -4r8c9
Naked pairs: 12r5c26 => -1r5c7 -2r5c7
whip[4]: r9c4{n7 n9}- r9c1{n9 n2}- r3n2{c1 c9}- c9n7{r3 .} => -7r9c7
STTE

N.B: contrary to what I said yesterday, my solution is in Trid-OR3-S2W7 + W4

Website · by **denis_berthier** » Sat Sep 07, 2024 7:35 am

.
Bonjour François

Very interesting use of ORk-S2-whips - making a very clean solution, with only one tridagon step for each of the two tridagons.
.

The New Sudoku Players' Forum

Puzzle for Mathimagics

Puzzle for Mathimagics

Re: Puzzle for Mathimagics

Re: Puzzle for Mathimagics

Re: Puzzle for Mathimagics

Re: Puzzle for Mathimagics

Re: Puzzle for Mathimagics

Re: Puzzle for Mathimagics

Re: Puzzle for Mathimagics

Re: Puzzle for Mathimagics