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Website · by **denis_berthier** » Mon Nov 11, 2024 3:52 pm

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#20 from the collection of 3362 puzzles with BxB ≥7 assembled by coloin:

Code: Select all: +-------+-------+-------+ ! . . 3 ! . . . ! 7 8 . ! ! 4 . 7 ! . 8 . ! 2 . 6 ! ! . . . ! . . . ! . . 4 ! +-------+-------+-------+ ! . . . ! 6 . 5 ! . . . ! ! . . 6 ! . 1 . ! . . . ! ! . . . ! 2 . 8 ! . 4 7 ! +-------+-------+-------+ ! 6 . . ! . . . ! 3 . . ! ! 7 . 8 ! . . . ! 4 . 2 ! ! . 3 2 ! 7 . . ! . 6 8 ! +-------+-------+-------+ ..3...78.4.7.8.2.6........4...6.5.....6.1.......2.8.476.....3..7.8...4.2.327...68 #10# 97856 FNBP C28.m/M2.4.11480 B10B

Code: Select all: Resolution state after Singles and whips[1]: +----------------------+----------------------+----------------------+ ! 1259 12569 3 ! 1459 24569 12469 ! 7 8 159 ! ! 4 159 7 ! 1359 8 139 ! 2 1359 6 ! ! 12589 125689 159 ! 1359 235679 123679 ! 159 1359 4 ! +----------------------+----------------------+----------------------+ ! 2389 24789 49 ! 6 3479 5 ! 189 129 139 ! ! 2389 24789 6 ! 349 1 3479 ! 589 259 359 ! ! 1359 159 159 ! 2 39 8 ! 6 4 7 ! +----------------------+----------------------+----------------------+ ! 6 1459 1459 ! 8 259 129 ! 3 7 159 ! ! 7 159 8 ! 1359 3569 1369 ! 4 159 2 ! ! 159 3 2 ! 7 459 149 ! 159 6 8 ! +----------------------+----------------------+----------------------+ 185 candidates.

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by **totuan** » Tue Nov 12, 2024 11:14 am

This one is solvable by “normal” impossible patterns.
After r2c8=3 by tridagon then r1c4=4 by impossible pattern and the puzzle is ER-6.6

Thanks for the puzzle!
totuan

by **eleven** » Tue Nov 12, 2024 2:29 pm

Brilliant as usual

To add the impossible pattern:

Code: Select all: *--------------------------------------------------------------------* | 159 . . | 159 . . | . . 159 | | . 159 . | 159 . . | . . . | | . . 159 | . . . | 159 159 . | |---------------------+-------------------------+--------------------| | . . 159 | . . . | . . 159 | | . 159 . | 159 . . | . 159 . | | 159 . . | . . . | 159 . . | *--------------------------------------------------------------------

*

Hidden Text: Show

After the skyscraper 1r17 (-1r1c1) you can finish with this impossible patten:

Code: Select all: +----------------+----------------+----------------+ | 1 2 3 | 4 59 6 | 7 8 59 | | 4 59 7 | 15 8 19 | 2 3 6 | | 8 6 59 | 3 2 7 | 159 159 4 | +----------------+----------------+----------------+ | 23 8 4 | 6 7 5 |b19 b129 39-1 | | 23 7 6 | 9 1 4 | 8 a25 35 | | 59 159 159 | 2 3 8 | 6 4 7 | +----------------+----------------+----------------+ | 6 4 159 | 8 *59 2 | 3 7 *59+1 | | 7 159 8 |*15 6 3 | 4 *19+5 2 | | 59 3 2 | 7 4 *19 |*15+9 6 8 | +----------------+----------------+----------------+

1r7c9
9r9c7 - (9=1)r4c7
5r8c8 - (5=2)r5c8 - (2=19)r4c78
=> -1r4c9, stte

by **shye** » Tue Nov 12, 2024 5:46 pm

a solution not too different to the ones already posted

Code: Select all: ,----------------,--------------------,----------------, |#159 26 3 | 1459 24569 12469 | 7 8 #159 | | 4 #159 7 | 1359 8 139 | 2 #159+3 6 | | 28 268 #159 | 1359 267 267 |#159 1359 4 | :----------------+--------------------+----------------: | 2389 278 4 | 6 379 5 | 189 129 139 | | 2389 278 6 | 349 1 3479 | 589 259 359 | | 1359 159 159 | 2 39 8 | 6 4 7 | :----------------+--------------------+----------------: | 6 4 #159 | 8 259 129 | 3 7 #159 | | 7 #159 8 | 1359 3569 1369 | 4 #159 2 | |#159 3 2 | 7 459 149 |#159 6 8 | '----------------'--------------------'----------------'

tridagon
+3r2c8

Code: Select all: ,----------------,----------------------,---------------, | 159 26 3 | 4-159 24569 12469 | 7 8 159 | | 4 A159 7 |bc159 8 bc19 | 2 3 6 | | 28 268 159 | 3 267 267 | 159 159 4 | :----------------+----------------------+---------------: | 2389 278 4 | 6 379 5 | 189 129 139 | | 2389 278 6 | 49 1 3479 | 589 259 359 | | 1359 159 159 | 2 39 8 | 6 4 7 | :----------------+----------------------+---------------: | 6 4 159 | 8 259 129 | 3 7 159 | | 7 B159 8 | a159 36 36 | 4 C159 2 | | 159 3 2 | 7 459 149 | 159 6 8 | '----------------'----------------------'---------------'

label tridagon RT as ABC
A in r8 is in c4
along with BC pair in r2 forms another RT
-159r1c4
later in the solve after basics, A can be determined as 5 (only shared candidate in r2c2 and r8c4)

Code: Select all: ,--------------,---------,---------------, |#19 2 3 | 4 5 6 | 7 8 #19 | | 4 5 7 | 1 8 9 | 2 3 6 | | 8 6 19 | 3 2 7 | 19-5#159 4 | :--------------+---------+---------------: | 23 8 4 | 6 7 5 | 19 129 139 | | 23 7 6 | 9 1 4 | 8 25 35 | |#159 #19 159 | 2 3 8 | 6 4 7 | :--------------+---------+---------------: | 6 4 15 | 8 9 2 | 3 7 15 | | 7 #19 8 | 5 6 3 | 4 #19 2 | |*59 3 2 | 7 4 1 |*59 6 8 | '--------------'---------'---------------'

bivalue oddagon
5r3c8 = 5r6c1 - 5r9c1 = 5r9c7
-5r3c7 stte

by **yzfwsf** » Tue Nov 12, 2024 6:25 pm

eleven wrote:After the skyscraper 1r17 (-1r1c1) you can finish with this impossible patten:
Code: Select all
+----------------+----------------+----------------+ | 1 2 3 | 4 59 6 | 7 8 59 | | 4 59 7 | 15 8 19 | 2 3 6 | | 8 6 59 | 3 2 7 | 159 159 4 | +----------------+----------------+----------------+ | 23 8 4 | 6 7 5 |b19 b129 39-1 | | 23 7 6 | 9 1 4 | 8 a25 35 | | 59 159 159 | 2 3 8 | 6 4 7 | +----------------+----------------+----------------+ | 6 4 159 | 8 *59 2 | 3 7 *59+1 | | 7 159 8 |*15 6 3 | 4 *19+5 2 | | 59 3 2 | 7 4 *19 |*15+9 6 8 | +----------------+----------------+----------------+

1r7c9
9r9c7 - (9=1)r4c7
5r8c8 - (5=2)r5c8 - (2=19)r4c78
=> -1r4c9, stte

Only use Trivalue Oddagon:
AIC Type 2 with Triplet Oddagon(r28c28,r1c19,r3c37,r7c39,r9c17): 5r9c7 = (5-1)r3c7 = r3c8 - r8c8 = r8c2 - r7c3 = 1r7c9 => r9c7<>1,r7c9<>5

by **eleven** » Tue Nov 12, 2024 8:07 pm

1r8c8 = r8c2
Are you using the remote triple here ?

by **yzfwsf** » Tue Nov 12, 2024 10:13 pm

eleven wrote:1r8c8 = r8c2
Are you using the remote triple here ?

Yes.

by **Cenoman** » Tue Nov 12, 2024 10:34 pm

Using only Tridagon pattern and its Remote Triple sub-pattern:
After lcls:

Code: Select all: +---------------------+-------------------------+---------------------+ | 159* 26 3 | 1459 24569 12469 | 7 8 159* | | 4 a159*# 7 | 1359 8 39-1 | 2 159+3 6 | | 28 268 159* | 1359 267 267 | 159* 1359 4 | +---------------------+-------------------------+---------------------+ | 2389 278 4 | 6 379 5 | 189 129 139 | | 2389 278 6 | 349 1 3479 | 589 259 359 | | 1359 159 159 | 2 39 8 | 6 4 7 | +---------------------+-------------------------+---------------------+ | 6 4 159* | 8 259 d129 | 3 7 159* | | 7 b159*# 8 | c1359 3569 c1369 | 4 b159*# 2 | | 159* 3 2 | 7 459 d149 | 159* 6 8 | +---------------------+-------------------------+---------------------+

1. Tridagon (159)b1379 having a single guardian => +3 r2c8 AND Remote Triple (159)r2c2, r8c28
(1)r2c2 =RT= r8c28 - r8c46 = r79c6 => -1 r2c6; lcls, 3 placements

Code: Select all: +---------------------+----------------------+--------------------+ | 159 26 3 | 145 2456 1246 | 7 8 159 | | 4 15# 7 | 15 8 9 | 2 3 6 | | 28 268 159 | 3 267 267 | 159 159 4 | +---------------------+----------------------+--------------------+ | 2389 278 4 | 6 379 5 | 189 129 139 | | 2389 278 6 | 49 1 347 | 589 259 359 | | 1359 159 159 | 2 39 8 | 6 4 7 | +---------------------+----------------------+--------------------+ | 6 4 159 | 8 259 12 | 3 7 159 | | 7 159# 8 | 15-9 36 36 | 4 159# 2 | | 159 3 2 | 7 459 14 | 159 6 8 | +---------------------+----------------------+--------------------+

2. (9)r8c2 =RT= r8c8 => -9 r8c4; lcls, 24 placements

Code: Select all: +-------------------+-----------------+--------------------+ | 19* 2 3 | 4 5 6 | 7 8 19* | | 4 5 7 | 1 8 9 | 2 3 6 | | 8 6 9-1 | 3 2 7 | 159 159 4 | +-------------------+-----------------+--------------------+ | 23 8 4 | 6 7 5 | 19 129 139 | | 23 7 6 | 9 1 4 | 8 25 35 | | 159 19 159 | 2 3 8 | 6 4 7 | +-------------------+-----------------+--------------------+ | 6 4 15* | 8 9 2 | 3 7 15* | | 7 19 8 | 5 6 3 | 4 19 2 | | 59 3 2 | 7 4 1 | 59 6 8 | +-------------------+-----------------+--------------------+

3. Skyscraper (1)r1c1 = r1c9 - r7c9 = r7c3 => -1r3c3; 3 placements

Code: Select all: +-----------------+-----------------+------------------+ | 1 2 3 | 4 5 6 | 7 8 9 | | 4 5 7 | 1 8 9 | 2 3 6 | | 8 6 9 | 3 2 7 | 15 15 4 | +-----------------+-----------------+------------------+ | 23 8 4 | 6 7 5 | 19 29+1 13 | | 23 7 6 | 9 1 4 | 8 25 35 | | 59 19 15 | 2 3 8 | 6 4 7 | +-----------------+-----------------+------------------+ | 6 4 15 | 8 9 2 | 3 7 15 | | 7 19 8 | 5 6 3 | 4 19 2 | | 59 3 2 | 7 4 1 | 59 6 8 | +-----------------+-----------------+------------------+

4. BUG+1 =>+1 r4c8; ste

by **Leren** » Tue Nov 12, 2024 11:49 pm

Same as Cenoman except replace the Skyscraper reasoning by :

Code: Select all: *------------------------------------* | 19 2 3 | 4 5 6 | 7 8 19 | | 4 5 7 | 1 8 9 | 2 3 6 | | 8 6 *9-1 | 3 2 7 | 159 159 4 | |-------------+-------+--------------| | 239 8 4 | 6 7 5 | 19 129 139 | | 23 7 6 | 9 1 4 | 8 25 35 | | 159 19 159 | 2 3 8 | 6 4 7 | |-------------+-------+--------------| | 6 4 *15 | 8 9 2 | 3 7 *15 | | 7 19 8 | 5 6 3 | 4 19 2 | | 59 3 2 | 7 4 1 | 59 6 8 | *------------------------------------*

Trigadon Remote Triple Naked Pair. Remove NP digits from 3rd RT Cell.

Leren

Website · by **denis_berthier** » Wed Nov 13, 2024 3:42 am

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Thanks for your solutions.
I chose this puzzle because it can be solved without any impossible pattern other than tridagon, but using some reduces the rating.
Here's a solution with two impossible patterns, starting from the RS after whips[1]:

naked-triplets-in-a-column: c2{r2 r6 r8}{n9 n5 n1} ==> r7c2≠9, r7c2≠5, r7c2≠1, r5c2≠9, r4c2≠9, r3c2≠9, r3c2≠5, r3c2≠1, r1c2≠9, r1c2≠5, r1c2≠1
singles ==> r7c2=4, r4c3=4

The impossible patterns used:

Code: Select all: Trid-OR2-relation for digits 1, 5 and 9 in blocks: b1, with cells (marked #): r1c1, r2c2, r3c3 b3, with cells (marked #): r1c9, r2c8, r3c7 b7, with cells (marked #): r9c1, r8c2, r7c3 b9, with cells (marked #): r9c7, r8c8, r7c9 with 2 guardians (in cells marked @): n2r1c1 n3r2c8 +----------------------+----------------------+----------------------+ ! 1259#@ 26 3 ! 1459 24569 12469 ! 7 8 159# ! ! 4 159# 7 ! 1359 8 139 ! 2 1359#@ 6 ! ! 12589 268 159# ! 1359 235679 123679 ! 159# 1359 4 ! +----------------------+----------------------+----------------------+ ! 2389 278 4 ! 6 379 5 ! 189 129 139 ! ! 2389 278 6 ! 349 1 3479 ! 589 259 359 ! ! 1359 159 159 ! 2 39 8 ! 6 4 7 ! +----------------------+----------------------+----------------------+ ! 6 4 159# ! 8 259 129 ! 3 7 159# ! ! 7 159# 8 ! 1359 3569 1369 ! 4 159# 2 ! ! 159# 3 2 ! 7 459 149 ! 159# 6 8 ! +----------------------+----------------------+----------------------+ EL14c30-OR4-relation for digits: 1, 5 and 9 in cells (marked #): (r2c2 r3c8 r3c7 r3c3 r1c4 r1c9 r1c1 r9c7 r9c1 r7c9 r7c3 r8c4 r8c8 r8c2) with 4 guardians (in cells marked @) : n3r3c8 n4r1c4 n2r1c1 n3r8c4 +----------------------+----------------------+----------------------+ ! 1259#@ 26 3 ! 1459#@ 24569 12469 ! 7 8 159# ! ! 4 159# 7 ! 1359 8 139 ! 2 1359 6 ! ! 12589 268 159# ! 1359 235679 123679 ! 159# 1359#@ 4 ! +----------------------+----------------------+----------------------+ ! 2389 278 4 ! 6 379 5 ! 189 129 139 ! ! 2389 278 6 ! 349 1 3479 ! 589 259 359 ! ! 1359 159 159 ! 2 39 8 ! 6 4 7 ! +----------------------+----------------------+----------------------+ ! 6 4 159# ! 8 259 129 ! 3 7 159# ! ! 7 159# 8 ! 1359#@ 3569 1369 ! 4 159# 2 ! ! 159# 3 2 ! 7 459 149 ! 159# 6 8 ! +----------------------+----------------------+----------------------+ EL13c179-OR4-relation for digits: 1, 5 and 9 in cells (marked #): (r3c4 r3c7 r3c3 r2c4 r2c8 r2c2 r9c7 r9c1 r7c9 r7c3 r8c4 r8c8 r8c2) with 4 guardians (in cells marked @) : n3r3c4 n3r2c4 n3r2c8 n3r8c4 +----------------------+----------------------+----------------------+ ! 1259 26 3 ! 1459 24569 12469 ! 7 8 159 ! ! 4 159# 7 ! 1359#@ 8 139 ! 2 1359#@ 6 ! ! 12589 268 159# ! 1359#@ 235679 123679 ! 159# 1359 4 ! +----------------------+----------------------+----------------------+ ! 2389 278 4 ! 6 379 5 ! 189 129 139 ! ! 2389 278 6 ! 349 1 3479 ! 589 259 359 ! ! 1359 159 159 ! 2 39 8 ! 6 4 7 ! +----------------------+----------------------+----------------------+ ! 6 4 159# ! 8 259 129 ! 3 7 159# ! ! 7 159# 8 ! 1359#@ 3569 1369 ! 4 159# 2 ! ! 159# 3 2 ! 7 459 149 ! 159# 6 8 ! +----------------------+----------------------+----------------------+

naked-quads-in-a-row: r3{c3 c8 c4 c7}{n9 n5 n3 n1} ==> r3c6≠9, r3c6≠3, r3c6≠1, r3c5≠9, r3c5≠5, r3c5≠3, r3c1≠9, r3c1≠5, r3c1≠1

EL13c179-OR4-relation between candidates n3r3c4, n3r2c4, n3r2c8 and n3r8c4
+ same valence for candidates n3r2c8 and n3r3c4 via c-chain[2]: n3r2c8,n3r3c8,n3r3c4
==> EL13c179-OR4-relation can be split into two EL13c179-OR3-relations with respective lists of guardians:
n3r3c4 n3r2c4 n3r8c4 and n3r2c4 n3r2c8 n3r8c4 .

EL13c179-OR3-whip[1]: OR3{{n3r8c4 n3r2c4 n3r3c4 | .}} ==> r5c4≠3
naked-triplets-in-a-block: b1{r1c2 r3c1 r3c2}{n6 n2 n8} ==> r1c1≠2

At least one candidate of a previous Trid-OR2-relation between candidates n2r1c1 n3r2c8 has just been eliminated.
There remains a Trid-OR1-relation between candidates: n3r2c8

Trid-ORk-relation with only one candidate => r2c8=3
hidden-single-in-a-block ==> r3c4=3

At least one candidate of a previous EL14c30-OR4-relation between candidates n3r3c8 n4r1c4 n2r1c1 n3r8c4 has just been eliminated.
There remains an EL14c30-OR1-relation between candidates: n4r1c4

EL14c30-ORk-relation with only one candidate => r1c4=4

The end is trivial, in BC3.
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