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Website · by **denis_berthier** » Wed Nov 13, 2024 3:56 am

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#2373 from the same collection of 3362 puzzles with BxB ≥7 assembled by coloin

Code: Select all: +-------+-------+-------+ ! 1 . . ! . 5 . ! . 8 9 ! ! 4 5 . ! . . . ! 1 3 . ! ! . 8 9 ! . 3 . ! . . 4 ! +-------+-------+-------+ ! . . 4 ! . . . ! . 9 3 ! ! 8 . . ! . . . ! 4 . 1 ! ! . 3 . ! . . . ! 8 5 . ! +-------+-------+-------+ ! . 1 . ! 6 . 7 ! . . . ! ! . . . ! . . . ! . . . ! ! . . . ! 3 . 5 ! 9 . . ! +-------+-------+-------+ 1...5..8945....13..89.3...4..4....938.....4.1.3....85..1.6.7...............3.59.. # 8# 97016 FNBP C27.m/M2.8.4920

Code: Select all: Resolution state after Singles and whips[1]: +----------------------+----------------------+----------------------+ ! 1 267 3 ! 247 5 246 ! 267 8 9 ! ! 4 5 267 ! 2789 26789 2689 ! 1 3 267 ! ! 267 8 9 ! 127 3 126 ! 5 267 4 ! +----------------------+----------------------+----------------------+ ! 2567 267 4 ! 12578 12678 1268 ! 267 9 3 ! ! 8 2679 2567 ! 2579 2679 3 ! 4 267 1 ! ! 2679 3 1 ! 2479 24679 2469 ! 8 5 267 ! +----------------------+----------------------+----------------------+ ! 2359 1 258 ! 6 2489 7 ! 23 24 258 ! ! 235679 24679 25678 ! 12489 12489 12489 ! 2367 12467 25678 ! ! 267 2467 2678 ! 3 1248 5 ! 9 12467 2678 ! +----------------------+----------------------+----------------------+ 193 candidates.

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by **shye** » Wed Nov 13, 2024 5:11 am

Code: Select all: ,----------------------,---------------------,--------------------, | 1 #267 3 | 247 5 246 |#267 8 9 | | 4 5 #267 | 2789 26789 2689 | 1 3 #267 | |#267 8 9 | 127 3 126 | 5 #267 4 | :----------------------+---------------------+--------------------: |*2567 #267 4 | 12578 12678 1268 |#267 9 3 | | 8 2679 #2567 | 2579 2679 3 | 4 #267 1 | |#267+9 3 1 | 2479 24679 2469 | 8 5 #267 | :----------------------+---------------------+--------------------: | 2359 1 258 | 6 2489 7 | 23 24 258 | | 235679 24679 25678 | 12489 12489 12489 | 2367 12467 25678 | |*267 2467 2678 | 3 1248 5 | 9 12467 2678 | '----------------------'---------------------'--------------------'

tridagon with two guardians
9r6c1 = 5r5c3 - (5=2679)r3496c1
+9r6c1

Code: Select all: ,----------------,------------------,-------------------, | 1 #267 3 | 247 5 246 |#267 8 9 | | 4 5 A267 |c278 267+8 9 | 1 3 B267 | |#267 8 9 | 127 3 126 | 5 #267 4 | :----------------+------------------+-------------------: |#267 267 4 | 5 18 18 |#267 9 3 | | 8 #267 5 | 9 c267 3 | 4 #267 1 | | 9 3 #1 | 247 2467 246 | 8 5 C267 | :----------------+------------------+-------------------: | 35 1 28 | 6 9 7 | 23 4 258 | | 35 9 2678 | 1248 1248 1248 | 2367 1267 25678 | | 267 4 2678 | 3 128 5 | 9 1267 2678 | '----------------'------------------'-------------------'

then a different tridagon (already prevented)
label RT as ABC
C in b5 is in p5
another RT sees r2c5 and determines the cell
+8r2c5

C in r2 is in c4
after singles C can be determined as 7
solves with a locked candidate (or fw single)

by **eleven** » Wed Nov 13, 2024 11:17 am

Very nice. So i can save my time to find a longer solution

by **Cenoman** » Wed Nov 13, 2024 9:59 pm

All is said. Nothing to add to shye's post nor to eleven's.

Website · by **denis_berthier** » Thu Nov 14, 2024 4:46 am

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This puzzle has many more impossible patterns than tridagon.
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Website · by **denis_berthier** » Fri Nov 15, 2024 4:16 am

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This T&E(2) puzzle is a rare example of having several impossible patterns with only one or only few guardians, which can moreover be effectively used within very short chains.
As these chains are no longer than 2, the impossible patterns are not all detected at the start. (It's a matter of priorities in SudoRules: Tridagons and impossible patterns are detected only after whips[2] and Subsets[3].)
Note that not all of these patterns are necessary to find a solution with so short chains.

finned-x-wing-in-rows: n9{r7 r6}{c1 c5} ==> r5c5≠9

Code: Select all: Trid-OR2-relation for digits 6, 7 and 2 in blocks: b1, with cells (marked #): r1c2, r2c3, r3c1 b3, with cells (marked #): r1c7, r2c9, r3c8 b4, with cells (marked #): r4c2, r5c3, r6c1 b6, with cells (marked #): r4c7, r5c8, r6c9 with 2 guardians (in cells marked @): n5r5c3 n9r6c1 +----------------------+----------------------+----------------------+ ! 1 267# 3 ! 247 5 246 ! 267# 8 9 ! ! 4 5 267# ! 2789 26789 2689 ! 1 3 267# ! ! 267# 8 9 ! 127 3 126 ! 5 267# 4 ! +----------------------+----------------------+----------------------+ ! 2567 267# 4 ! 12578 12678 1268 ! 267# 9 3 ! ! 8 2679 2567#@ ! 2579 267 3 ! 4 267# 1 ! ! 2679#@ 3 1 ! 2479 24679 2469 ! 8 5 267# ! +----------------------+----------------------+----------------------+ ! 2359 1 258 ! 6 2489 7 ! 23 24 258 ! ! 235679 24679 25678 ! 12489 12489 12489 ! 2367 12467 25678 ! ! 267 2467 2678 ! 3 1248 5 ! 9 12467 2678 ! +----------------------+----------------------+----------------------+

Trid-OR2-whip[2]: OR2{{n5r5c3 | n9r6c1}} - b5n9{r6c4 .} ==> r5c4≠5
singles ==> r4c4=5, r5c3=5
hidden-pairs-in-a-block: b7{n3 n5}{r7c1 r8c1} ==> r8c1≠9, r8c1≠7, r8c1≠6, r8c1≠2, r7c1≠9, r7c1≠2
singles ==> r8c2=9, r6c1=9, r5c4=9, r2c6=9, r7c5=9, r7c8=4, r9c2=4
hidden-pairs-in-a-block: b5{n1 n8}{r4c5 r4c6} ==> r4c6≠6, r4c6≠2, r4c5≠7, r4c5≠6, r4c5≠2

Code: Select all: EL13c290s-OR3-relation for digits: 2, 6 and 7 in cells (marked #): (r8c8 r8c7 r8c3 r4c7 r4c1 r5c8 r5c2 r1c7 r1c2 r3c8 r3c1 r2c9 r2c3) with 3 guardians (in cells marked @) : n1r8c8 n3r8c7 n8r8c3 +----------------------+----------------------+----------------------+ ! 1 267# 3 ! 247 5 246 ! 267# 8 9 ! ! 4 5 267# ! 278 2678 9 ! 1 3 267# ! ! 267# 8 9 ! 127 3 126 ! 5 267# 4 ! +----------------------+----------------------+----------------------+ ! 267# 267 4 ! 5 18 18 ! 267# 9 3 ! ! 8 267# 5 ! 9 267 3 ! 4 267# 1 ! ! 9 3 1 ! 247 2467 246 ! 8 5 267 ! +----------------------+----------------------+----------------------+ ! 35 1 28 ! 6 9 7 ! 23 4 258 ! ! 35 9 2678#@ ! 1248 1248 1248 ! 2367#@ 1267#@ 25678 ! ! 267 4 2678 ! 3 128 5 ! 9 1267 2678 ! +----------------------+----------------------+----------------------+

Code: Select all: EL14c159s-OR2-relation for digits: 2, 6 and 7 in cells (marked #): (r9c9 r9c3 r9c1 r6c9 r5c8 r4c7 r4c2 r4c1 r2c9 r2c3 r3c8 r3c1 r1c7 r1c2) with 2 guardians (in cells marked @) : n8r9c9 n8r9c3 +----------------------+----------------------+----------------------+ ! 1 267# 3 ! 247 5 246 ! 267# 8 9 ! ! 4 5 267# ! 278 2678 9 ! 1 3 267# ! ! 267# 8 9 ! 127 3 126 ! 5 267# 4 ! +----------------------+----------------------+----------------------+ ! 267# 267# 4 ! 5 18 18 ! 267# 9 3 ! ! 8 267 5 ! 9 267 3 ! 4 267# 1 ! ! 9 3 1 ! 247 2467 246 ! 8 5 267# ! +----------------------+----------------------+----------------------+ ! 35 1 28 ! 6 9 7 ! 23 4 258 ! ! 35 9 2678 ! 1248 1248 1248 ! 2367 1267 25678 ! ! 267# 4 2678#@ ! 3 128 5 ! 9 1267 2678#@ ! +----------------------+----------------------+----------------------+

EL14c159s-OR2-whip[1]: OR2{{n8r9c3 n8r9c9 | .}} ==> r9c5≠8
whip[1]: b8n8{r8c6 .} ==> r8c3≠8, r8c9≠8

At least one candidate of a previous EL13c290s-OR3-relation between candidates n1r8c8 n3r8c7 n8r8c3 has just been eliminated.
There remains an EL13c290s-OR2-relation between candidates: n1r8c8 n3r8c7

EL13c290s-OR2-whip[2]: OR2{{n1r8c8 | n3r8c7}} - r7c7{n3 .} ==> r8c8≠2

Code: Select all: EL14c159-OR2-relation for digits: 2, 6 and 7 in cells (marked #): (r1c2 r1c7 r3c1 r3c8 r2c5 r2c3 r2c9 r4c2 r4c7 r6c5 r6c9 r5c5 r5c2 r5c8) with 2 guardians (in cells marked @) : n8r2c5 n4r6c5 +----------------------+----------------------+----------------------+ ! 1 267# 3 ! 247 5 246 ! 267# 8 9 ! ! 4 5 267# ! 278 2678#@ 9 ! 1 3 267# ! ! 267# 8 9 ! 127 3 126 ! 5 267# 4 ! +----------------------+----------------------+----------------------+ ! 267 267# 4 ! 5 18 18 ! 267# 9 3 ! ! 8 267# 5 ! 9 267# 3 ! 4 267# 1 ! ! 9 3 1 ! 247 2467#@ 246 ! 8 5 267# ! +----------------------+----------------------+----------------------+ ! 35 1 28 ! 6 9 7 ! 23 4 258 ! ! 35 9 267 ! 1248 1248 1248 ! 2367 167 2567 ! ! 267 4 2678 ! 3 12 5 ! 9 1267 2678 ! +----------------------+----------------------+----------------------+

Code: Select all: EL14c13s-OR1-relation for digits: 2, 6 and 7 in cells (marked #): (r9c1 r9c9 r6c9 r5c2 r5c8 r4c2 r4c1 r4c7 r3c1 r3c8 r1c2 r1c7 r2c3 r2c9) with 1 guardians (in cells marked @) : n8r9c9 +----------------------+----------------------+----------------------+ ! 1 267# 3 ! 247 5 246 ! 267# 8 9 ! ! 4 5 267# ! 278 2678 9 ! 1 3 267# ! ! 267# 8 9 ! 127 3 126 ! 5 267# 4 ! +----------------------+----------------------+----------------------+ ! 267# 267# 4 ! 5 18 18 ! 267# 9 3 ! ! 8 267# 5 ! 9 267 3 ! 4 267# 1 ! ! 9 3 1 ! 247 2467 246 ! 8 5 267# ! +----------------------+----------------------+----------------------+ ! 35 1 28 ! 6 9 7 ! 23 4 258 ! ! 35 9 267 ! 1248 1248 1248 ! 2367 167 2567 ! ! 267# 4 2678 ! 3 12 5 ! 9 1267 2678#@ ! +----------------------+----------------------+----------------------+

EL14c13s-ORk-relation with only one candidate => r9c9=8
hidden-single-in-a-row ==> r7c3=8
whip[1]: r7n2{c9 .} ==> r8c7≠2, r8c9≠2, r9c8≠2

Code: Select all: EL14c13-OR1-relation for digits: 2, 6 and 7 in cells (marked #): (r6c9 r4c1 r4c2 r4c7 r5c5 r5c2 r5c8 r1c2 r1c7 r3c1 r3c8 r2c5 r2c3 r2c9) with 1 guardians (in cells marked @) : n8r2c5 +----------------------+----------------------+----------------------+ ! 1 267# 3 ! 247 5 246 ! 267# 8 9 ! ! 4 5 267# ! 278 2678#@ 9 ! 1 3 267# ! ! 267# 8 9 ! 127 3 126 ! 5 267# 4 ! +----------------------+----------------------+----------------------+ ! 267# 267# 4 ! 5 18 18 ! 267# 9 3 ! ! 8 267# 5 ! 9 267# 3 ! 4 267# 1 ! ! 9 3 1 ! 247 2467 246 ! 8 5 267# ! +----------------------+----------------------+----------------------+ ! 35 1 8 ! 6 9 7 ! 23 4 25 ! ! 35 9 267 ! 1248 1248 1248 ! 367 167 567 ! ! 267 4 267 ! 3 12 5 ! 9 167 8 ! +----------------------+----------------------+----------------------+

EL14c13-ORk-relation with only one candidate => r2c5=8
singles ==> r4c5=1, r4c6=8, r9c5=2, r8c5=4, r8c6=1, r8c4=8, r3c4=1, r9c8=1, r8c3=2

At least one candidate of a previous EL13c290s-OR2-relation between candidates n1r8c8 n3r8c7 has just been eliminated.
There remains an EL13c290s-OR1-relation between candidates: n3r8c7

EL13c290s-ORk-relation with only one candidate => r8c7=3

Easy end in SFin[2]
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by **totuan** » Sat Nov 16, 2024 9:40 am

shye wrote:then a different tridagon (already prevented)

Sharp eyes - very nice find!
By labeling or coloring then it's easy to see triples, thanks for sharing it.

totuan

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