- Code: Select all
+---+---+---+
|1..|...|...|
|.25|...|...|
|.87|...|.56|
+---+---+---+
|...|8..|.95|
|...|.4.|6.8|
|...|..9|47.|
+---+---+---+
|...|.98|76.|
|...|4.7|5.9|
|..9|56.|.84|
+---+---+---+ Which Hazel
Which Hazel
6 posts
• Page 1 of 1
Which Hazel
by coloin » Sun Oct 27, 2024 12:52 pm
- coloin
- Posts: 2477
- Joined: 05 May 2005
- Location: Devon
Re: Which Hazel
by eleven » Sun Oct 27, 2024 5:04 pm
Nice monster hazel, full of impossible patterns.
Impossible patterns:
If r6c5<>5, then 7r4c5
6r6c4 leads to a tridagon
6r4c6 to 9r3c4 and the starred impossible pattern.
=> 5r6c5, singles HP78
tridagon => 6r6c4, singles triple
Impossible pattern => 4r7c3
Oddagon 23: 1r6c9 => 1r5c3&r9c7 => 1r4c6 killing all extra candidates
=> -1r6c9, stte
- Code: Select all
*---------------------------------------------------------------------------*
| 1 3469 346 | 23679 23578 23456 | 2389 234 237 |
| 3469 2 5 | 13679 1378 1346 | 1389 134 137 |
| 349 8 7 | b1239 *123 1234 | *1239 5 6 |
|--------------------------+--------------------------+---------------------|
| 23467 13467 12346 | 8 a1237 b1236 | *123 9 5 |
| 23579 13579 123 | *1237 4 1235 | 6 *123 8 |
| 23568 1356 12368 | *1236 123+5 9 | 4 7 *123 |
|--------------------------+--------------------------+---------------------|
| 2345 1345 1234 | *123 9 8 | 7 6 *123 |
| 2368 136 12368 | 4 *123 7 | 5 *123 9 |
| 237 137 9 | 5 6 *123 | *123 8 4 |
*---------------------------------------------------------------------------*
Impossible patterns:
If r6c5<>5, then 7r4c5
6r6c4 leads to a tridagon
6r4c6 to 9r3c4 and the starred impossible pattern.
Hidden Text: Show
=> 5r6c5, singles HP78
- Code: Select all
+----------------------+-----------------------+----------------------+
| 1 3469 346 | 2369 78 5 | 2389 234 237 |
| 3469 2 5 | 1369 78 1346 | 1389 134 137 |
| 349 8 7 | 1239 123 1234 | 1239 5 6 |
+----------------------+-----------------------+----------------------+
| 23467 13467 12346 | 8 *123 1236 | *123 9 5 |
| 59 59 123 | 7 4 *123 | 6 *123 8 |
| 2368 136 12368 | *123+6 5 9 | 4 7 *123 |
+----------------------+-----------------------+----------------------+
| 2345 1345 1234 | *123 9 8 | 7 6 *123 |
| 2368 136 12368 | 4 *123 7 | 5 *123 9 |
| 237 137 9 | 5 6 *123 | *123 8 4 |
+----------------------+-----------------------+----------------------+
tridagon => 6r6c4, singles triple
- Code: Select all
+----------------------+-----------------------+----------------------+
| 1 3469 346 | 239 78 5 | 2389 234 237 |
| 349 2 5 | 139 78 6 | 1389 134 137 |
| 39 8 7 | 1239 123 4 | 1239 5 6 |
+----------------------+-----------------------+----------------------+
| 467 467 46 | 8 *123 *123 | *123 9 5 |
| 59 59 *123 | 7 4 *123 | 6 *123 8 |
| 238 13 1238 | 6 5 9 | 4 7 *123 |
+----------------------+-----------------------+----------------------+
| 2345 1345 *123+4 | *123 9 8 | 7 6 *123 |
| 2368 136 12368 | 4 *123 7 | 5 *123 9 |
| 237 137 9 | 5 6 *123 | *123 8 4 |
+----------------------+-----------------------+----------------------+
Impossible pattern => 4r7c3
Hidden Text: Show
- Code: Select all
+----------------+-----------------+-----------------+
| 1 6 3 | 29 78 5 | 89 4 27 |
| 4 2 5 | 139 78 6 | 89 13 137 |
| 9 8 7 | 123 123 4 | 123 5 6 |
+----------------+-----------------+-----------------+
| 7 4 6 | 8 *23+1 d123 | *23+1 9 5 |
| 5 9 c12 | 7 4 123 | 6 *23+1 8 |
| 8 3 b12 | 6 5 9 | 4 7 a12 |
+----------------+-----------------+-----------------+
| 23 5 4 | 123 9 8 | 7 6 b123 |
| 6 1 8 | 4 *23 7 | 5 *23 9 |
| 23 7 9 | 5 6 123 | c123 8 4 |
+----------------+-----------------+-----------------+
Oddagon 23: 1r6c9 => 1r5c3&r9c7 => 1r4c6 killing all extra candidates
=> -1r6c9, stte
- eleven
- Posts: 3136
- Joined: 10 February 2008
Re: Which Hazel
by totuan » Sun Oct 27, 2024 5:56 pm
- Code: Select all
*--------------------------------------------------------------------*
| 1 3469 346 | 23679 23578 23456 | 2389 234 237 |
| 3469 2 5 | 13679 1378 1346 | 1389 134 137 |
| 349 8 7 |*1239 #123 1234 |#123+9 5 6 |
|----------------------+----------------------+----------------------|
| 23467 13467 12346 | 8 1237 123+6A |#123A 9 5 |
| 23579 13579 123 |#123+7A 4 1235 | 6 #123A 8 |
| 23568 1356 12368 |#123+6 #123+5A 9 | 4 7 #123A |
|----------------------+----------------------+----------------------|
| 2345 1345 1234 |#123A 9 8 | 7 6 #123A |
| 2368 136 12368 | 4 #123A 7 | 5 #123A 9 |
| 237 137 9 | 5 6 #123A |#123A 8 4 |
*--------------------------------------------------------------------*
The same as eleven’s, just present for first move as diagram.
- Tridagon (123) A marked cells => (6)r4c6=(57)r5c4,r6c5
- Impossible Partern (123) # marked cells => (6)r6c4=(57)r5c4,r6c5=(9)r3c7
- AALS (12369)r467c4 => (123)r467c4=(9)r3c4=(6)r6c4
Present as diagram: => r5c4=7
- Code: Select all
(57)r5c4,r6c5*
||
|| (123)r367c4-(123=7)r5c4*
|| ||
(9)r3c7--(9)r3c4
|| ||
|| (6)r6c4
|| |
(6)r6c4----(6)r4c6==(57)r5c4,r6c5*
Thanks for your nice puzzle!
totuan
- totuan
- Posts: 232
- Joined: 25 May 2010
- Location: vietnam
Re: Which Hazel
by Cenoman » Mon Oct 28, 2024 3:53 pm
Another way, using only tridagon impossible pattern and its remote triple sub-pattern.
Originally, the puzzle has two tridagons (123)b6, b8, b9, b5-cells tagged (#) and (^) resp.
1. +5 r5c6 => -7 r5c4 => +6 r4c6 AND RT(123)r9c6, r49c7 [tridagon (123)b5p348, b6,b8,b9 having a single guardian 6r4c6]
+6 r4c6 => +9 r3c4 AND Empty Rectangle (1,2,3)b2 [(6)r4c6 - (6=123)r567c4 => -123 r123c4 ]
Then (1,2,3): r49c7 =RT= r9c6 - r123c6 =ER= r3c5 => -123 r3c7; +9 r3c7; contradiction => r5c6 <> 5; lcls, 3 placements
2. Tridagon (123)b5p267, b6,b8,b9 having a single guardian => +6 r6c4 AND RT(123)r6c9, r7c49; lcls, 2 placements (note Empty Rectangle (1,2,3)b4) =>
(1,2,3)r7c49 =RT= r6c9 - r6c123 =ER= r5c3 => -123 r7c3; +4 r7c3; lcls; 18 placements
3. End with simple steps:
3a. Finned XW(1)r4c56 = r4c7 - r9c7 = r9c6 => -1 r5c6
3b. M2-Wing: (1=3)r2c8 - r2c9 = (3-1)r7c9 = (1)r7c4 => -1 r2c4
3c. Bivalue oddagon (23)r58, c58, b5 => +1 r5c8; ste
Hidden Text: Show
1. +5 r5c6 => -7 r5c4 => +6 r4c6 AND RT(123)r9c6, r49c7 [tridagon (123)b5p348, b6,b8,b9 having a single guardian 6r4c6]
- Code: Select all
+-------------------------+-----------------------+---------------------+
| 1 3469 346 | 679-23 5 C234-6 | 8 234 237 |
| 3469 2 5 | 679-13 8 C134-6 | 139 134 137 |
| 349 8 7 | 9-123 D123 C1234 | 9-123 5 6 |
+-------------------------+-----------------------+---------------------+
| 2346 1346 12346 | 8 7 a123+6 | A123* 9 5 |
| 79 79 123 | b123 4 5 | 6 123 8 |
| 23568 1356 12368 | b1236 123 9 | 4 7 123 |
+-------------------------+-----------------------+---------------------+
| 2345 1345 1234 | b123 9 8 | 7 6 123 |
| 2368 136 12368 | 4 123 7 | 5 123 9 |
| 237 137 9 | 5 6 B123* | A123* 8 4 |
+-------------------------+-----------------------+---------------------+
+6 r4c6 => +9 r3c4 AND Empty Rectangle (1,2,3)b2 [(6)r4c6 - (6=123)r567c4 => -123 r123c4 ]
Then (1,2,3): r49c7 =RT= r9c6 - r123c6 =ER= r3c5 => -123 r3c7; +9 r3c7; contradiction => r5c6 <> 5; lcls, 3 placements
- Code: Select all
+------------------------+---------------------+---------------------+
| 1 3469 346 | 239 78 5 | 2389 234 237 |
| 349 2 5 | 139 78 6 | 1389 134 137 |
| 39 8 7 | 1239 123 4 | 1239 5 6 |
+------------------------+---------------------+---------------------+
| 467 467 46 | 8 123 123 | 123 9 5 |
| 59 59 d123 | 7 4 123 | 6 123 8 |
| c238 c13 c1238 | 6 5 9 | 4 7 b123* |
+------------------------+---------------------+---------------------+
| 2345 1345 4-123 | a123* 9 8 | 7 6 a123* |
| 2368 136 12368 | 4 123 7 | 5 123 9 |
| 237 137 9 | 5 6 123 | 123 8 4 |
+------------------------+---------------------+---------------------+
2. Tridagon (123)b5p267, b6,b8,b9 having a single guardian => +6 r6c4 AND RT(123)r6c9, r7c49; lcls, 2 placements (note Empty Rectangle (1,2,3)b4) =>
(1,2,3)r7c49 =RT= r6c9 - r6c123 =ER= r5c3 => -123 r7c3; +4 r7c3; lcls; 18 placements
Hidden Text: Show
3a. Finned XW(1)r4c56 = r4c7 - r9c7 = r9c6 => -1 r5c6
3b. M2-Wing: (1=3)r2c8 - r2c9 = (3-1)r7c9 = (1)r7c4 => -1 r2c4
Hidden Text: Show
Cenoman
- Cenoman
- Posts: 2959
- Joined: 21 November 2016
- Location: France
Re: Which Hazel
by shye » Tue Oct 29, 2024 12:37 am
like in Magic Jim, this puzzle has two near-tridagons. i found it easier to treat this as two puzzles based on the placements in b5, as the logic is symmetrical and following it through will show which path fails
5 and 7 must be diagonally apart to avoid breaking 123 ALS in r5/c5, then to avoid a tridagon 6 is placed on the same side
label tridagon RT as ABC, in each puzzle A/B is placed in b2/b4 and gives another RT eliminating 123 from r3c7/r7c3 (and placing 9/4)
now by looking at the givens and placements, we can see that puzzle 1 has too many digits to place in b2 and not enough cells
so puzzle 2 is the correct path and we can fill 7r5c4, 6r6c4, 5r6c5, 4r7c3 and the hidden quad in b4
the puzzle solves with the aforementioned RT
A in r7 is in c1
A+2, stte
- Code: Select all
Puzzle 1 Puzzle 2
+-------------+-------------+-------------+ +-------------+-------------+-------------+
| . . . | . . . | . . . | | . . . | . . . | . . . |
| . . . | . . . | . . . | | . . . | . . . | . . . |
| . . . | . 123 . | . . . | | . . . | . 123 . | . . . |
+-------------+-------------+-------------+ +-------------+-------------+-------------+
| . . . | . 7 6 | 123 . . | | . . . | . 123 123 | 123 . . |
| . . 123 | 123 . 5 | . 123 . | | . . 123 | 7 . 123 | . 123 . |
| . . . | 123 123 . | . . 123 | | . . . | 6 5 . | . . 123 |
+-------------+-------------+-------------+ +-------------+-------------+-------------+
| . . . | 123 . . | . . 123 | | . . . | 123 . . | . . 123 |
| . . . | . 123 . | . 123 . | | . . . | . 123 . | . 123 . |
| . . . | . . 123 | 123 . . | | . . . | . . 123 | 123 . . |
+-------------+-------------+-------------+ +-------------+-------------+-------------+
5 and 7 must be diagonally apart to avoid breaking 123 ALS in r5/c5, then to avoid a tridagon 6 is placed on the same side
- Code: Select all
Puzzle 1 Puzzle 2
+-------------+-------------+-------------+ +-------------+-------------+-------------+
| . . . | x x . | . . . | | . . . | . x x | . . . |
| . . . | x x . | . . . | | . . . | . x x | . . . |
| . . . | x B123 . |-123 . . | | . . . | . B123 x | . . . |
+-------------+-------------+-------------+ +-------------+-------------+-------------+
| . . . | . 7 6 |A123 . . | | x x x | . 123 123 | 123 . . |
| x x A123 | 123 . 5 | . 123 . | | x x A123 | 7 . 123 | . 123 . |
| x x x | 123 123 . | . . 123 | | . . . | 6 5 . | . . A123 |
+-------------+-------------+-------------+ +-------------+-------------+-------------+
| . . . | 123 . . | . . 123 | | . . -123 |B123 . . | . . C123 |
| . . . | . 123 . | . 123 . | | . . . | . 123 . | . 123 . |
| . . . | . . B123 |C123 . . | | . . . | . . 123 | 123 . . |
+-------------+-------------+-------------+ +-------------+-------------+-------------+
label tridagon RT as ABC, in each puzzle A/B is placed in b2/b4 and gives another RT eliminating 123 from r3c7/r7c3 (and placing 9/4)
- Code: Select all
Puzzle 1 Puzzle 2
+-------------+-------------+-------------+ +-------------+-------------+-------------+
| . . . | # # . | . . . | | . . . | . . . | . . . |
| . . . | # # . | . . . | | . . 5 | . . . | . . . |
| . 8 7 | . . . | 9 5 6 | | . . 7 | . . . | . . . |
+-------------+-------------+-------------+ +-------------+-------------+-------------+
| . . . | . . 6 | . . . | | # # . | . . . | . . . |
| . . . | . . 5 | . . . | | # # . | . . . | . . . |
| . . . | . . 9 | . . . | | . . . | . 5 9 | 4 7 . |
+-------------+-------------+-------------+ +-------------+-------------+-------------+
| . . . | . . 8 | . . . | | . . 4 | . . . | . . . |
| . . . | . . 7 | . . . | | . . . | . . . | . . . |
| . . . | . . . | . . . | | . . 9 | . . . | . . . |
+-------------+-------------+-------------+ +-------------+-------------+-------------+
now by looking at the givens and placements, we can see that puzzle 1 has too many digits to place in b2 and not enough cells
so puzzle 2 is the correct path and we can fill 7r5c4, 6r6c4, 5r6c5, 4r7c3 and the hidden quad in b4
- Code: Select all
,-----------,---------------,---------------,
| 1 6 3 | 29 78 5 | 89 4 27 |
| 4 2 5 | 139 78 6 | 89 13 137 |
| 9 8 7 | 123 123 4 | 123 5 6 |
:-----------+---------------+---------------:
| 7 4 6 | 8 123 123 | 123 9 5 |
| 5 9 12 | 7 4 123 | 6 123 8 |
| 8 3 12 | 6 5 9 | 4 7 A1+2 |
:-----------+---------------+---------------:
|a3+2 5 4 |B123 9 8 | 7 6 C123 |
| 6 1 8 | 4 23 7 | 5 23 9 |
| 23 7 9 | 5 6 123 | 123 8 4 |
'-----------'---------------'---------------'
the puzzle solves with the aforementioned RT
A in r7 is in c1
A+2, stte
-
shye - Posts: 311
- Joined: 12 June 2021
Re: Which Hazel
by coloin » Tue Oct 29, 2024 12:19 pm
Marvelous solving all !
very elegant too ...
shye wrote:like in Magic Jim, this puzzle has two near-tridagons. i found it easier to treat this as two puzzles based on the placements in b5, as the logic is symmetrical and following it through will show which path fails
very elegant too ...
- coloin
- Posts: 2477
- Joined: 05 May 2005
- Location: Devon
6 posts
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