The New Sudoku Players' Forum

by **coloin** » Wed Feb 12, 2025 8:05 pm

Code: Select all: +---+---+---+ |87.|.65|...| |4..|9.8|7..| |.9.|47.|8..| +---+---+---+ |.48|...|...| |7.9|...|.64| |65.|.94|..8| +---+---+---+ |...|.5.|...| |9..|...|..1| |56.|...|.82| +---+---+---+ JS

Not sure if this is similar to other puzzles ... but it scores highly

by **Cenoman** » Wed Feb 12, 2025 10:45 pm

Looks like already seen puzzles...
lcls [HP(56)r23c3, locked (6)r23c9]. At this resolution state, an impossible pattern and a deadly pattern are effective:

Code: Select all: +-----------------------+---------------------------+--------------------------+ | 8 7 b123* | b123* 6 5 | c12349 c12349 9-3 | | 4 123* 56# | 9 123* 8 | 7 d1235 356# | | 123* 9 56# | 4 7 123* | 8 d1235 356# | +-----------------------+---------------------------+--------------------------+ | 123* 4 8 | 123567 123* 12367 | 12359 123579 579-3 | | 7 123* 9 | 12358 1238 123* | 1235 6 4 | | 6 5 a123* | 123+7* 9 4 | 123 37-12 8 | +-----------------------+---------------------------+--------------------------+ | 123 1238 12347 | 123678 5 123679 | 3469 3479 79-3 | | 9 238 2347 | 23678 2348 2367 | 3456 3457 1 | | 5 6 1347 | 137 134 1379 | 349 8 2 | +-----------------------+---------------------------+--------------------------+

1. Tridagon (123)b1245 (*), having a single guardian => +7 r6c4;
2. Remote Triple (123)r16c3,r1c4 with Empty Rectangle (12)b3 => -12 r6c8;
3. UR(56)r23c39 (#), using internals => -3 r147c9; 25 placements

Code: Select all: +--------------------+-------------------+------------------+ | 8 7 f1-23 | a23* 6 5 | 4 12 9 | | 4 123 56 | 9 ba123* 8 | 7 125 36 | | 123 9 56 | 4 7 123 | 8 125 36 | +--------------------+-------------------+------------------+ | d123 4 8 | 23 c123 6 | 9 7 5 | | 7 123 9 | 5 8 123 | 12 6 4 | | 6 5 e12 | 7 9 4 | 12 3 8 | +--------------------+-------------------+------------------+ | 123 123 4 | 8 5 23 | 6 9 7 | | 9 8 a23* | 6 a23* 7 | 5 4 1 | | 5 6 7 | 1 4 9 | 3 8 2 | +--------------------+-------------------+------------------+

4. Almost Remote Pair (23):
(23)[r1c4 = r2c5 - r8c5 = r8c3] = (1)r2c5 - r4c5 = r4c1 - r6c3 = (1)r1c3 => -23 r1c3; ste

Thanks for the puzzle.

by **coloin** » Wed Feb 12, 2025 10:53 pm

ah yes .. i missed the simple tridagon 7@r6c4.. :roll:

Trying to find puzzles without these initially ...

by **coloin** » Thu Feb 13, 2025 7:27 pm

Maybe this one doesnt have the initial tridagon

Code: Select all: +---+---+---+ |...|...|...| |4.7|9.8|5.6| |.5.|64.|..9| +---+---+---+ |.86|5.7|.9.| |7.9|4..|.5.| |54.|...|...| +---+---+---+ |...|...|2.1| |87.|...|965| |...|..6|...| +---+---+---+ Living Ston LS

by **marek stefanik** » Sat Feb 15, 2025 9:46 am

Code: Select all: ,-------------------,-------------------,--------------------, | 69 69 b#1238 |b#123–7 57 1235 | 1348 12348 2348 | | 4 *123 7 | 9 *123 8 | 5 b123 6 | |*123 5 b123–8 | 6 4 *123 | 1378 12378 9 | :-------------------+-------------------+--------------------: |*123 8 6 | 5 *123 7 | 134 9 234 | | 7 *123 9 | 4 68 *123 | 1368 5 238 | | 5 4 a#123 |#1238 689 1239 | 13678 12378 2378 | :-------------------+-------------------+--------------------: | 369 369 345 | 378 5789 3459 | 2 3478 1 | | 8 7 1234 |a123 b123 b1234 | 9 6 5 | | 1239 1239 12345 | 12378 5789 6 | 3478 3478 3478 | '-------------------'-------------------'--------------------'

There are 3 guardians, but they are all at the rectangle (#).
The 8-loop (*) has no guardians.
If b15* or b24* were restricted to the same two digits, it would break one of the other boxes.
Consequently, each of 123 can appear at the rectangle at most once.

The digit in r6c3, let's call it a, must appear in b2* and is in c4 and r8 forced into b8. So a must take r8c4.
The 1|2|3 in r13c3, let's call it b, must appear in b5* and in r8 b is forced into c56. In c4 b must then take r1c4.
Therefore in b1 b takes r3c3 and in b3 r2c8. –7r1c4, –8r3c3

Code: Select all: ,-------------------,------------------,--------------------, | 69 69 8 |b123 7 5 | 134 1234 234 | | 4 *123 7 | 9 *123 8 | 5 b123 6 | |*123 5 b123 | 6 4 *123 | 78 78 9 | :-------------------+------------------+--------------------: |*123 8 6 | 5 *123 7 | 134 9 234 | | 7 *123 9 | 4 68 *123 | 1368 5 238 | | 5 4 a123 | 1238 689 1239 | 13678 78–123 2378 | :-------------------+------------------+--------------------: | 369 369 345 | 378 589 349 | 2 3478 1 | | 8 7 1234 |a123 123 1234 | 9 6 5 | | 1239 1239 12345 | 12378 589 6 | 3478 3478 3478 | '-------------------'------------------'--------------------'

Another property of the 8-loop is that each digit can appear on it at most 3 times.
In b12, only b appears outside the 8-loop.
The remaining two digits must do so in b45, which forces them into r6c346.
Together with br2c8, each of 123 sees r6c8. –123r6c8

Code: Select all: ,---------------,--------------,--------------, | 69 69 8 |b12 7 5 | 34 12 34 | | 4 *123 7 | 9 *123 8 | 5 b12 6 | |*123 5 b23–1| 6 4 *123 | 7 8 9 | :---------------+--------------+--------------: |*123 8 6 | 5 *123 7 | 134 9 234 | | 7 *123 9 | 4 6 *123 | 13 5 8 | | 5 4 a3–12| 8 9 1–23| 6 7 23 | :---------------+--------------+--------------: | 36 36 5 | 7 8 9 | 2 4 1 | | 8 7 12 |a3 12 4 | 9 6 5 | | 129 129 4 | 12 5 6 | 8 3 7 | '---------------'--------------'--------------'

In r8c4, we see that a=3, so r6c3=3.
1r6 is forced into r6c6, outside the 8-loop. It must then appear on the 8-loop in b1. –1r3c3, stte

Marek

by **totuan** » Fri Feb 21, 2025 6:37 pm

For Living Ston puzzle:

Code: Select all: *--------------------------------------------------------------------* | 69 69 #1238 | 1237 7-5 #123+5 | 1348 12348 2348 | | 4 #123 7 | 9 #123 8 | 5 123 6 | |#123 5 #1238 | 6 4 #123 | 1378 12378 9 | |----------------------+----------------------+----------------------| |#123 8 6 | 5 #123 7 | 134 9 234 | | 7 #123 9 | 4 68 #123 | 1368 5 238 | | 5 4 #123 |#123+8 689 1239 | 13678 12378 2378 | |----------------------+----------------------+----------------------| | 369 369 345 | 378 5789 3459 | 2 3478 1 | | 8 7 #123+4 | 123 #123A 1234 | 9 6 5 | | 1239 1239 12345 | 12378 5789 6 | 3478 3478 3478 | *--------------------------------------------------------------------*

My path for this one, using impossible patterns – as usual

Impossible pattern(123) #-marked cells – like twin => (5)r1c6=(8)r6c4=(4)r8c3
01: Present as diagram: => r1c5<>5, some singles

Code: Select all: (5)r1c6* || (8)r6c4-(68=9)r56c5-r6c6=(9-5)r7c6=(5)r1c6* || (4)r8c3-r8c6=(4-5)r7c6=(5)r1c6*

Prove for impossible pattern:

Hidden Text: Show

Code: Select all: A=(1|2|3) *-----------------------------------------------------------* | . . 1238 | . . 123 | . . . | | . 123 . | . 123 . | . . . | | 123 . 1238 | . . 123 | . . . | |-------------------+-------------------+-------------------| | 123 . . | . 123 . | . . . | | . 123 . | . . 123 | . . . | | . . 123 | 123 . . | . . . | |-------------------+-------------------+-------------------| | . . . | . . . | . . . | | . . 123 | . 123A . | . . . | | . . . | . . . | . . . | *-----------------------------------------------------------* Let A=1 => r24c5<>1, r13c6=1 => r6c4=1 => r13c3=1 => r2c2,r3c1<>1 *-----------------------------------------------------------* | . . 1238 | . . 123 | . . . | | . e23 . | . d23 . | . . . | |f23 . 1238 | . . 123 | . . . | |-------------------+-------------------+-------------------| |g23+1 . . | . c23 . | . . . | | . a23+1 . | . . b23 | . . . | | . . 23 | 1 . . | . . . | |-------------------+-------------------+-------------------| | . . . | . . . | . . . | | . . 23 | . 1 . | . . . | | . . . | . . . | . . . | *-----------------------------------------------------------* Oddagon(23) abcde => r5c2=1 => r4c1<>1 => Oddagon(23) cdefg => impossibe The same for A=(2|3)

Code: Select all: *--------------------------------------------------------------------* | 69 69 #*123+8 |#*123 7 5 | 1348 12348 2348 | | 4 #*123 7 | 9 #*123 8 | 5 123 6 | |#*123 5 1238 | 6 4 #*123 | 1378 12378 9 | |----------------------+-----------------------+---------------------| |#*123 8 6 | 5 #*123 7 | 134 9 234 | | 7 #*123 9 | 4 68 #*123 | 1368 5 238 | | 5 4 #*123 |#*123+8 689 *123+9 | 13678 12378 2378 | |----------------------+-----------------------+---------------------| | 369 369 345 | 378 589 349 | 2 3478 1 | | 8 7 *123+4 | 123 *123 1234 | 9 6 5 | | 1239 1239 12345 | 12378 589 6 | 3478 3478 3478 | *--------------------------------------------------------------------*

Tridagon(123) #-marked cells => (8)r1c3=(8)r6c4
Impossible pattern *-marked cells => (8)r1c3=(9)r6c6=(4)r8c3
Note: If r6c5=9 => r6c6<>9 and r8c3<>4 by (49)C6
02: (8)r1c3==(8)r6c4-(68=9)r6c5-(49)r6c6,r8c3==(8)r1c3 => r1c3=8

Prove for impossible pattern

Hidden Text: Show

Code: Select all: A=(1|2|3) *-----------------------------------------------------------* | . . 123 | 123 . . | . . . | | . 123 . | . 123 . | . . . | | 123 . . | . . 123 | . . . | |-------------------+-------------------+-------------------| | 123 . . | . 123 . | . . . | | . 123 . | . . 123 | . . . | | . . 123 | . . 123 | . . . | |-------------------+-------------------+-------------------| | . . . | . . . | . . . | | . . 123 | . 123A . | . . . | | . . . | . . . | . . . | *-----------------------------------------------------------* Let A=1 => r24c5<>1 => r56c6=1, r3c6<>1 => r1c4=1 => r6c3=1 => r5c6=1 *-----------------------------------------------------------* | . . 23 | 1 . . | . . . | | . a23+1 . | . b23 . | . . . | |f23+1 . . | . . g23 | . . . | |-------------------+-------------------+-------------------| |d23 . . | . c23 . | . . . | | . e23 . | . . 1 | . . . | | . . 1 | . . 23 | . . . | |-------------------+-------------------+-------------------| | . . . | . . . | . . . | | . . 23 | . 1 . | . . . | | . . . | . . . | . . . | *-----------------------------------------------------------* Oddagon(23) abcde => r2c1=1 => r3c1<>1 => oddagon(23)bcdfg => impossible The same for A=(2|3)

Code: Select all: *--------------------------------------------------------------------* | 69 69 8 |#123 7 5 | 134 1234 234 | | 4 #123 7 | 9 #123 8 | 5 #123A 6 | |#123 5 #123 | 6 4 #123 | 78 %78 9 | |----------------------+----------------------+----------------------| |#123 8 6 | 5 #123 7 | 134 9 234 | | 7 #123 9 | 4 *68 #123 | 1368 5 238 | | 5 4 #123 |#123+8 *689 1239 | 13678 #123+78 2378 | |----------------------+----------------------+----------------------| | 369 369 345 |%378 *589 349 | 2 %3478 1 | | 8 7 1234 | 123 123 1234 | 9 6 5 | | 1239 1239 12345 | 12378 589 6 | 3478 3478 3478 | *--------------------------------------------------------------------*

Impossible pattern(123) #-marked cells => (8)r6c4=(78)r6c8
03: (8)r6c4=r56c5-r7c5=(78)r7c48,r3c8-(78)r6c8==(8)r6c4 => r6c4=8, some singles

Impossible pattern – the same proving as above.

Hidden Text: Show

Code: Select all: *-----------------------------------------------------------* | 69 69 8 | 123 7 5 | 134 1234 234 | | 4 #123 7 | 9 #123 8 | 5 #123 6 | |#123 5 #123 | 6 4 #123 | 78 78 9 | |-------------------+-------------------+-------------------| |#123 8 6 | 5 #123 7 | 134 9 234 | | 7 #123 9 | 4 6 #123 | 138 5 238 | | 5 4 #123 | 8 9 #123 | 6 #123+7 237 | |-------------------+-------------------+-------------------| | 36 36 45 | 7 58 9 | 2 48 1 | | 8 7 #12 | 123 #123 4 | 9 6 5 | | 129 129 45 | 12 58 6 | 3478 3478 3478 | *-----------------------------------------------------------*

04: Impossible pattern(123) #-marked cells => r6c8=7, some singles then ER-6.6 and easy to finish.

Prove for impossible pattern:

Hidden Text: Show

Code: Select all: A=(1|2|3) *-----------------------------------------------------------* | . . . | . . . | . . . | | . 123 . | . 123 . | . 123 . | | 123 . 123 | . . 123 | . . . | |-------------------+-------------------+-------------------| | 123 . . | . 123A . | . . . | | . 123 . | . . 123 | . . . | | . . 123 | . . 123 | . 123 . | |-------------------+-------------------+-------------------| | . . . | . . . | . . . | | . . 123 | . 123 . | . . . | | . . . | . . . | . . . | *-----------------------------------------------------------* Let A=1 => r56c6<>1 => r3c6=1 => r2c2=1 => r6c3=1 *-----------------------------------------------------------* | . . . | . . . | . . . | | . 1 . | . j23 . | . k23 . | |f23 . g23 | . . 1 | . . . | |-------------------+-------------------+-------------------| |e23 . . | . 1 . | . . . | | . d23 . | . . c23 | . . . | | . . 1 | . . b23 | . a23 . | |-------------------+-------------------+-------------------| | . . . | . . . | . . . | | . . h23 | . i23 . | . . . | | . . . | . . . | . . . | *-----------------------------------------------------------* Oddagon(23) abcdefghijk => impossible. The same for A=(2|3)

Another view for marek’s second move, using a special impossible pattern

Code: Select all: *--------------------------------------------------------------------* | 69 69 8 |#123 7 5 | 134 1234 234 | | 4 #123 7 | 9 #123 8 | 5 #123A 6 | |#123 5 #123 | 6 4 #123 | 78 78 9 | |----------------------+----------------------+----------------------| |#123 8 6 | 5 #123 7 | 134 9 234 | | 7 #123 9 | 4 68 #123 | 1368 5 238 | | 5 4 #123 |#1238* 689 #1239* | 13678 #123+78 2378 | |----------------------+----------------------+----------------------| | 369 369 345 | 378 589 349 | 2 3478 1 | | 8 7 #1234* |#123 #123 #1234* | 9 6 5 | | 1239 1239 12345 | 12378 589 6 | 3478 3478 3478 | *--------------------------------------------------------------------*

Impossible pattern(123) #-marked cells, *-marked cells by triples(123) at R8 & B5.
One guardian => r6c8=78
Prove for impossible pattern by ugly way

Hidden Text: Show

Code: Select all: A=(1|2|3), we prove: (123)r2c8&(123)r6c346 must be triples. *-----------------------------------------------------------* | . . . | 123 . . | . . . | | . 123 . | . 123B . | . #123A . | | 123 . 123 | . . 123 | . . . | |-------------------+-------------------+-------------------| | 123 . . | . 123C . | . . . | | . 123 . | . . 123 | . . . | | . . #123 |#123(8). #123(9)| . 123 . | |-------------------+-------------------+-------------------| | . . . | . . . | . . . | | . . 123(4)| 123 123 123(4)| . . . | | . . . | . . . | . . . | *-----------------------------------------------------------* Let A=1 => r2c25<>1, r3c13=1, r3c6<>1 => r1c4=1 *-----------------------------------------------------------* | . . . | 1 . . | . . . | | . 23 . | . 23B . | . 1A . | | 123 . 123 | . . 23 | . . . | |-------------------+-------------------+-------------------| | 123 . . | . 123C . | . . . | | . 123 . | . . 123 | . . . | | . . 123 | 23(8) . 123(9)| . 123 . | |-------------------+-------------------+-------------------| | . . . | . . . | . . . | | . . 123(4)| 23 123 123(4)| . . . | | . . . | . . . | . . . | *-----------------------------------------------------------* Let B=2 => *-----------------------------------------------------------* | . . . | 1 . . | . . . | | . 3 . | . 2B . | . 1A . | | 12 . 12 | . . 3 | . . . | |-------------------+-------------------+-------------------| | 123 . . | . 13C . | . . . | | . 12 . | . . 12 | . . . | | . . 123 | 23(8) . 12(9) | . 123 . | |-------------------+-------------------+-------------------| | . . . | . . . | . . . | | . . 123(4)| 23 13 12(4) | . . . | | . . . | . . . | . . . | *-----------------------------------------------------------* From here, have two cases: Let C=1 => r6c4=3, r5c6=2 => r5c2=1 => r6c3=2, triples(123) at r2c8,r6c34 => impossible at r6c8. *-----------------------------------------------------------* | . . . | 1 . . | . . . | | . 3 . | . 2B . | . *1A . | | 2 . 1 | . . 3 | . . . | |-------------------+-------------------+-------------------| | 3 . . | . 1C . | . . . | | . 1 . | . . 2 | . . . | | . . *2 |*3 . (9) | . 123 . | |-------------------+-------------------+-------------------| | . . . | . . . | . . . | | . . (4) | 2 3 1 | . . . | | . . . | . . . | . . . | *-----------------------------------------------------------* Let C=3 => r6c3=3, r8c5=1, r8c4=3 *-----------------------------------------------------------* | . . . | 1 . . | . . . | | . 3 . | . 2B . | . *1A . | |d12 . c12 | . . 3 | . . . | |-------------------+-------------------+-------------------| |e12 . . | . 3C . | . . . | | . f12 . | . . 1-2 | . . . | | . . 3 |*2(8) . *12(9) | . 123 . | |-------------------+-------------------+-------------------| | . . . | . . . | . . . | | . . b2(4) | 3 1 a2(4) | . . . | | . . . | . . . | . . . | *-----------------------------------------------------------* 2’s: abcdef => r5c6<>2 => r6c46=2 => triples(123) at r2c8, r6c46 => impossibe at r6c8 The same for other cases.

Thanks for the puzzle!
totuan

The New Sudoku Players' Forum

Jonathan Seagull

Jonathan Seagull

Re: Jonathan Seagull

Re: Jonathan Seagull

Re: Jonathan Seagull

Re: Living Ston

Re: Jonathan Seagull