The New Sudoku Players' Forum

by **champagne** » Wed Dec 03, 2025 4:49 pm

This puzzle skfr 11.0 is still 9.7 after TH, with a high potential for eliminations with the digits of the TH
Specialists should find a nice path to go to the end

.............89..17...3.....4.8..6.5.67.4581.5.8..1.746.4..8.5787....16..15...4.8;239

Code: Select all: 12349 23589 12369 |124567 12567 2467 |23579 23489 2369 234 235 236 |24567 8 9 |2357 234 1 7 2589 1269 |12456 3 246 |259 2489 269 ------------------------------------------------------ 1239 4 1239 |8 279 237 |6 239 5 239 6 7 |239 4 5 |8 1 239 5 239 8 |2369 269 1 |239 7 4 ------------------------------------------------------ 6 239 4 |1239 129 8 |239 5 7 8 7 239 |23459 259 234 |1 6 239 239 1 5 |23679 2679 2367 |4 239 8

by **rjamil** » Wed Dec 03, 2025 7:13 pm

Don't know Thor Hammer, Tridagon & Oddagon covered by POM, but, here is several triple-digit POM solution:

Code: Select all: +---------------------+---------------------+--------------------+ | 12349 23589 12369 | 124567 12567 2467 | 23579 23489 2369 | | 234 235 236 | 24567 8 9 | 2357 234 1 | | 7 2589 1269 | 12456 3 246 | 259 2489 269 | +---------------------+---------------------+--------------------+ | 1239 4 1239 | 8 279 237 | 6 239 5 | | 239 6 7 | 239 4 5 | 8 1 239 | | 5 239 8 | 2369 269 1 | 239 7 4 | +---------------------+---------------------+--------------------+ | 6 239 4 | 1239 129 8 | 239 5 7 | | 8 7 239 | 23459 259 234 | 1 6 239 | | 239 1 5 | 23679 2679 2367 | 4 239 8 | +---------------------+---------------------+--------------------+

1) #VT: (4 198 29 7 8 9 6 2 51)
Triple-digit POM: 2 @ r1c123456789 r2c123478 r3c2346789 r4c13568 r5c149 r6c2457 r7c2457 r8c34569 r9c14568
and POM: 3 @ r1c123789 r2c12378 r3c5 r4c1368 r5c149 r6c247 r7c247 r8c3469 r9c1468
and POM: 9 @ r1c123789 r2c6 r3c23789 r4c1358 r5c149 r6c2457 r7c2457 r8c3459 r9c1458
Digit 2 not in 119 Templates => -2 @ r1c1 r2c1

Triple-digit POM: 3 @ r1c123789 r2c12378 r3c5 r4c1368 r5c149 r6c247 r7c247 r8c3469 r9c1468
and POM: 2 @ r1c23456789 r2c23478 r3c2346789 r4c13568 r5c149 r6c2457 r7c2457 r8c34569 r9c14568
and POM: 9 @ r1c123789 r2c6 r3c23789 r4c1358 r5c149 r6c2457 r7c2457 r8c3459 r9c1458
Digit 3 not in 15 Templates => -3 @ r1c1 r2c1 r7c4

Triple-digit POM: 3 @ r1c23789 r2c2378 r3c5 r4c1368 r5c149 r6c247 r7c27 r8c3469 r9c1468
and POM: 5 @ r1c2457 r2c247 r3c247 r4c9 r5c6 r6c1 r7c8 r8c45 r9c3
and POM: 8 @ r1c28 r2c5 r3c28 r4c4 r5c7 r6c3 r7c6 r8c1 r9c9
Digit 3 not in 13 Templates => -3 @ r1c8

Triple-digit POM: 4 @ r1c1468 r2c148 r3c468 r4c2 r5c5 r6c9 r7c3 r8c46 r9c7
and POM: 2 @ r1c23456789 r2c23478 r3c2346789 r4c13568 r5c149 r6c2457 r7c2457 r8c34569 r9c14568
and POM: 8 @ r1c28 r2c5 r3c28 r4c4 r5c7 r6c3 r7c6 r8c1 r9c9
Digit 4 not in 5 Templates => -4 @ r1c8

Triple-digit POM: 9 @ r1c123789 r2c6 r3c23789 r4c1358 r5c149 r6c2457 r7c2457 r8c3459 r9c1458
and POM: 2 @ r1c23456789 r2c23478 r3c2346789 r4c13568 r5c149 r6c2457 r7c2457 r8c34569 r9c14568
and POM: 3 @ r1c2379 r2c2378 r3c5 r4c1368 r5c149 r6c247 r7c27 r8c3469 r9c1468
Digit 9 not in 30 Templates => -9 @ r1c1

Triple-digit POM: 9 @ r1c23789 r2c6 r3c23789 r4c1358 r5c149 r6c2457 r7c2457 r8c3459 r9c1458
and POM: 2 @ r1c23456789 r2c23478 r3c2346789 r4c13568 r5c149 r6c2457 r7c2457 r8c34569 r9c14568
and POM: 8 @ r1c28 r2c5 r3c28 r4c4 r5c7 r6c3 r7c6 r8c1 r9c9
Digit 9 not in 36 Templates => -9 @ r1c8

Code: Select all: +-----------------+-------------------+-----------------+ | 1 2359 2369 | 24567 2567 2467 | 2379 8 2369 | | 4 235 236 | 2567 8 9 | 237 23 1 | | 7 8 269 | 1 3 26 | 5 4 269 | +-----------------+-------------------+-----------------+ | 239 4 1 | 8 279 237 | 6 239 5 | | 239 6 7 | 239 4 5 | 8 1 239 | | 5 239 8 | 2369 269 1 | 239 7 4 | +-----------------+-------------------+-----------------+ | 6 239 4 | 29 1 8 | 239 5 7 | | 8 7 239 | 23459 259 234 | 1 6 239 | | 239 1 5 | 23679 2679 2367 | 4 239 8 | +-----------------+-------------------+-----------------+

2) #VT: (1 60 12 2 3 8 6 1 13)
Triple-digit POM: 2 @ r1c2345679 r2c23478 r3c369 r4c1568 r5c149 r6c2457 r7c247 r8c34569 r9c14568
and POM: 3 @ r1c2379 r2c2378 r3c5 r4c168 r5c149 r6c247 r7c27 r8c3469 r9c1468
and POM: 9 @ r1c2379 r2c6 r3c39 r4c158 r5c149 r6c2457 r7c247 r8c3459 r9c1458
Digit 2 not in 2 Templates => -2 @ r1c3 r1c4 r1c5 r1c6 r1c9 r2c3 r2c4 r2c8 r3c3 r3c9 r4c5 r4c6 r4c8 r5c1 r5c4 r6c2 r6c4 r6c7 r7c2 r7c7 r8c4 r8c5 r8c6 r8c9 r9c1 r9c4 r9c5 r9c6
Digit 2 in all 2 Templates => 2 @ r3c6 r4c1 r5c9 r6c5 r7c4 r8c3 r9c8

Triple-digit POM: 2 @ r1c27 r2c27 r3c6 r4c1 r5c9 r6c5 r7c4 r8c3 r9c8
and POM: 5 @ r1c245 r2c24 r3c7 r4c9 r5c6 r6c1 r7c8 r8c45 r9c3
and POM: 9 @ r1c2379 r2c6 r3c39 r4c58 r5c14 r6c247 r7c27 r8c459 r9c145
Digit 2 not in 1 Template => -2 @ r1c7 r2c2
Digit 2 in all 1 Template => 2 @ r1c2 r2c7

Triple-digit POM: 3 @ r1c379 r2c238 r3c5 r4c68 r5c14 r6c247 r7c27 r8c469 r9c146
and POM: 1 @ r1c1 r2c9 r3c4 r4c3 r5c8 r6c6 r7c5 r8c7 r9c2
and POM: 2 @ r1c2 r2c7 r3c6 r4c1 r5c9 r6c5 r7c4 r8c3 r9c8
Digit 3 not in 3 Templates => -3 @ r2c2 r8c4

Triple-digit POM: 3 @ r1c379 r2c38 r3c5 r4c68 r5c14 r6c247 r7c27 r8c69 r9c146
and POM: 1 @ r1c1 r2c9 r3c4 r4c3 r5c8 r6c6 r7c5 r8c7 r9c2
and POM: 6 @ r1c34569 r2c34 r3c39 r4c7 r5c2 r6c4 r7c1 r8c8 r9c456
Digit 3 not in 1 Template => -3 @ r1c7 r1c9 r2c3 r4c8 r5c4 r6c2 r6c4 r7c7 r8c6 r9c1 r9c6
Digit 3 in all 1 Template => 3 @ r1c3 r4c6 r5c1 r6c7 r7c2 r8c9 r9c4

Triple-digit POM: 4 @ r1c46 r2c1 r3c8 r4c2 r5c5 r6c9 r7c3 r8c46 r9c7
and POM: 5 @ r1c45 r2c24 r3c7 r4c9 r5c6 r6c1 r7c8 r8c45 r9c3
and POM: 9 @ r1c79 r2c6 r3c39 r4c58 r5c4 r6c24 r7c7 r8c45 r9c15
Digit 4 not in 1 Template => -4 @ r1c6 r8c4
Digit 4 in all 1 Template => 4 @ r1c4

Triple-digit POM: 5 @ r1c5 r2c24 r3c7 r4c9 r5c6 r6c1 r7c8 r8c45 r9c3
and POM: 1 @ r1c1 r2c9 r3c4 r4c3 r5c8 r6c6 r7c5 r8c7 r9c2
and POM: 2 @ r1c2 r2c7 r3c6 r4c1 r5c9 r6c5 r7c4 r8c3 r9c8
Digit 5 not in 1 Template => -5 @ r2c4 r8c5
Digit 5 in all 1 Template => 5 @ r1c5 r8c4

Triple-digit POM: 6 @ r1c69 r2c34 r3c39 r4c7 r5c2 r6c4 r7c1 r8c8 r9c56
and POM: 1 @ r1c1 r2c9 r3c4 r4c3 r5c8 r6c6 r7c5 r8c7 r9c2
and POM: 2 @ r1c2 r2c7 r3c6 r4c1 r5c9 r6c5 r7c4 r8c3 r9c8
Digit 6 not in 1 Template => -6 @ r1c9 r2c4 r3c3 r9c6
Digit 6 in all 1 Template => 6 @ r1c6 r3c9 r6c4 r9c5

Triple-digit POM: 7 @ r1c7 r2c4 r3c1 r4c5 r5c3 r6c8 r7c9 r8c2 r9c6
and POM: 1 @ r1c1 r2c9 r3c4 r4c3 r5c8 r6c6 r7c5 r8c7 r9c2
and POM: 2 @ r1c2 r2c7 r3c6 r4c1 r5c9 r6c5 r7c4 r8c3 r9c8
Digit 7 in all 1 Template => 7 @ r1c7 r4c5; stte

R. Jamil

by **totuan** » Wed Dec 03, 2025 8:03 pm

Code: Select all: *-----------------------------------------------------------------------------* | 12349 23589 12369 | 124567 12567 2467 | 23579 23489 2369 | | 234 235 236 | 24567 8 9 | 2357 234 1 | | 7 2589 1269 | 12456 3 246 | 259 2489 269 | |-------------------------+-------------------------+-------------------------| | 1239 4 *239+1 | 8 279 237 | 6 *239 5 | |*239 6 7 | 239 4 5 | 8 1 *239 | | 5 *239 8 | 2369 269 1 |*239 7 4 | |-------------------------+-------------------------+-------------------------| | 6 *239 4 | 1239 129 8 |*239 5 7 | | 8 7 *239 | 23459 259 234 | 1 6 *239 | |*239 1 5 | 23679 2679 2367 | 4 *239 8 | *-----------------------------------------------------------------------------*

01: Tridagon(239) *-marked cells => r4c3=1, some singles

Code: Select all: *--------------------------------------------------------------------* | 1 23589 2369 | 24567 2567 2467 | 23579 48 2369 | | 4 235 236 | 2567 8 9 | 2357 23 1 | | 7 2589 269 | 1 3 246 | 259 48 269 | |----------------------+----------------------+----------------------| |*239 4 1 | 8 279 237 | 6 239 5 | |*239 6 7 |*239 4 5 | 8 1 *239 | | 5 *239A 8 |*239+6 269 1 |*239 7 4 | |----------------------+----------------------+----------------------| | 6 *239 4 |*239 1 8 |*239 5 7 | | 8 7 *239 | 23459 259 234 | 1 6 *239 | |*239 1 5 | 23679 2679 2367 | 4 *239 8 | *--------------------------------------------------------------------*

02: Impossible pattern(239) *-marked cells => r6c4=6, some singles

Code: Select all: *--------------------------------------------------------------------* | 1 23589 239 | 2457 2567 2467 | 23579 48 2369 | | 4 *235 6 | 257 8 9 |*2357 %23 1 | | 7 2589 29 | 1 3 246 | 259 48 269 | |----------------------+----------------------+----------------------| | 239 4 1 | 8 279 237 | 6 #29-3 5 | | 239 6 7 |#29-3 4 5 | 8 1 239 | | 5 #*29-3 8 | 6 29 1 |*239 7 4 | |----------------------+----------------------+----------------------| | 6 239 4 | 239 1 8 |#29-3 5 7 | | 8 7 239 | 23459 259 234 | 1 6 239 | |#29-3 1 5 | 2379 2679 2367 | 4 239 8 | *--------------------------------------------------------------------*

Note: #-marked cells contain the same digit
03: (X-wing: 3’s *-marked cells)=(3)r2c8 => 3’s at #-marked cell must be eliminated, some singles

Add:
Digits 2&3 in R2 must see to one of #-marked cells => 2’s & 3’s at #-marked cells must be eliminated => #-marked cells contain digit 9’s, stte
Not necessaries for steps 4&5

Prove for the same digit at #-marked cells:

Hidden Text: Show

Code: Select all: *--------------------------------------------------------------------* | 1 23589 239 | 2457 2567 2467 | 23579 48 2369 | | 4 235 6 | 257 8 9 | 2357 23 1 | | 7 2589 29 | 1 3 246 | 259 48 269 | |----------------------+----------------------+----------------------| | 239 4 1 | 8 279 237 | 6 239 5 | | 239 6 7 |b239 4 5 | 8 1 a239 | | 5 X239 8 | 6 29 1 | 239 7 4 | |----------------------+----------------------+----------------------| | 6 239 4 |c239 1 8 |d239 5 7 | | 8 7 239 | 23459 259 234 | 1 6 239 | |X239 1 5 | 2379 2679 2367 | 4 239 8 | *--------------------------------------------------------------------* Let X be the digit in r6c2 01: r6c2=X => r9c1=X by C1 02: r6c2,r9c1=X => X’s: abcd => r8c9<>X => in B9 r7c7=X *--------------------------------------------------------------------* | 1 23589 239 | 2457 2567 2467 | 23579 48 2369 | | 4 235 6 | 257 8 9 | 2357 23 1 | | 7 2589 29 | 1 3 246 | 259 48 269 | |----------------------+----------------------+----------------------| |b239 4 1 | 8 279 237 | 6 a239 5 | |c239 6 7 |d239 4 5 | 8 1 #239 | | 5 X239 8 | 6 29 1 | 239 7 4 | |----------------------+----------------------+----------------------| | 6 f239 4 |e239 1 8 |X239 5 7 | | 8 7 g239 | 23459 259 234 | 1 6 h239 | |X239 1 5 | 2379 2679 2367 | 4 i239 8 | *--------------------------------------------------------------------* 03: If r6c2,r9c1,r7c7=X and r4c8<>X => in B6 r5c9=X => Oddagon: abcdefghi => impossible => r4c8=X => in B5 r5c4=X

Code: Select all: *--------------------------------------------------------------------* | 1 23589 239 | 2457 256 2467 | 2579 48 369-2 | | 4 #235 6 |b257 8 9 | a57 a23 1 | | 7 2589 29 | 1 3 246 | 259 48 69-2 | |----------------------+----------------------+----------------------| |*29 4 1 | 8 7 3 | 6 *9-2 5 | | 3 6 7 |c29 4 5 | 8 1 d29% | | 5 *29 8 | 6 29 1 | 3 7 4 | |----------------------+----------------------+----------------------| | 6 239 4 | 239 1 8 | 29 5 7 | | 8 7 239 | 23459 259 24 | 1 6 239% | | 29 1 5 | 2379 269 267 | 4 239% 8 | *--------------------------------------------------------------------*

04: [2’s: abcd]=r2c2-r6c2=r4c1-r4c8=r5c9 => r13c9<>2
05: (2)r5c9=(2-3)r8c9=(3-9)r9c8=r4c8 => r4c8<>2, stte

Thanks for the puzzle!
totuan

by **champagne** » Thu Dec 04, 2025 7:03 am

rjamil wrote:Don't know Thor Hammer, Tridagon & Oddagon covered by POM, but, here is several triple-digit POM solution:
.......
R. Jamil

Hi rjamil,
What you do is not far from my "multifloors analysis.

I run it here only for the digits 239 of the TH threat and got eliminations corresponding to it
I then added the corresponding assignments and restarted the run on the same 239 digits with another group of assignments/eliminations.

Among them, the second step of totuan.

This multifloors analysis is on my side a tool to detect the weaknesses of a PM, but you don't get any idea of the difficlculty of the logic doing the same.

Here, usually, the game is to find such a logic ( using mostly already seen patterns)

The most common first pattern for puzzles having a very high serate rating are

JE (junior exocet) with a small number of clues
and TH (thor hammer) with more clues

but the start can also be MSLS, double JE ....

Having many eliminations in the second run, I expected a nice solution as in totuan path.

PS having a puzzle in canonical morph, we know that the start is 12345678945 with r4c1=2.

by **rjamil** » Thu Dec 04, 2025 11:51 am

Hi champagne,

champagne wrote:Hi rjamil,
What you do is not far from my "multifloors analysis.

Its beyond my capabilities and limitations of my programming skills.

However, thanks for your valuable suggestions.

Code: Select all: ,--------------------,---------------------,---------------------, | 24589 12479 2469 | 23469 24579 23489 | 136789 1689 13679 | | 4589 479 469 | 3469 4579 1 | 36789 689 2 | | 289 1279 3 | 269 279 289 | 16789 4 5 | :--------------------+---------------------+---------------------: | 249 6 7 | 2349 8 2349 | 5 129 149 | | 1 249 8 | 5 249 7 | 2469 3 469 | | 3 5 249 | 1 6 249 | 249 7 8 | :--------------------+---------------------+---------------------: | 249 8 5 | 7 3 249 | 12469 1269 1469 | | 7 249 1 | 8 249 6 | 2349 5 349 | | 6 3 249 | 249 1 5 | 24789 289 479 | '--------------------'---------------------'---------------------'

BTW, the above puzzle state is obtained from YZF_Sudoku 2.0.0.630, after selecting Tools/minlex/Current Puzzle. Then, program gives only one step as follows:

Triplet Oddagon Type 1: 249r58c25,r4c14,r6c36,r7c16,r9c34 => r4c4<>249

R. Jamil

by **champagne** » Thu Dec 04, 2025 2:00 pm

Hi again rjamil.

Your puzzle is nearly morphed to show the classical best appearance for the TH pattern, thanks to the provider.
So, the first elimination is quite easy for anybody aware of the pattern.

Here, after totuan second move, I run again my multifloors analysis with a high suspicion, regarding eliminations, that in this partial PM
(note : 6r13c9 is a bi value)

Code: Select all: |+++++++++++++++|+++++++++++++++|+++++++++++++++| | 239 | | 2639| | | | 23 | | 29 | | 269 | |+++++++++++++++|+++++++++++++++|+++++++++++++++| | 239 | | 239 | | 239 | 239 | 239 | | 239 | 29 | 239 | |+++++++++++++++|+++++++++++++++|+++++++++++++++| | 239 | 239 | 239 | | 239 | | 239 | | 239 | | 239 | |+++++++++++++++|+++++++++++++++|+++++++++++++++|

we have no valid implementation if r2c8=2

so r2c8 = 3 and many other effects can be seen in this pattern.

by **eleven** » Thu Dec 04, 2025 9:20 pm

An alternative move after totuan's second step:

Code: Select all: *------------------------------------------------------------------------* | 1 23589 239 | 2457 2567 2467 | 23579 48 2369 | | 4 235 6 | '257 8 9 | 2357 b23 1 | | 7 2589 29 | 1 3 246 | 259 48 269 | |----------------------+------------------------+------------------------| | c239 4 1 | 8 279 237 | 6 #239 5 | | #239 6 7 | a9-23 4 5 | 8 1 #239 | | 5 *239 8 | 6 '29 1 | *239 7 4 | |----------------------+------------------------+------------------------| | 6 *239 4 | '239 1 8 | *239 5 7 | | 8 7 239 | 23459 259 234 | 1 6 239 | | #239 1 5 | 2379 2679 2367 | 4 #239 8 | *------------------------------------------------------------------------*

Note the possible x-wing (*) in r67.
If r5c4 is 2 or 3 (say x), we have an x-wing there and r2c8 must be x.
The #-marked cells are a possible oddagon.
With x in r5c4 and r2c8, it goes to r4c1, killing x from all oddagon cells.
=> -23r5c4
Solves with x-wing 9 and remote pairs 23 then.

btw. for the impossible pattern r4c1 is not needed.

Hidden Text: Show

by **champagne** » Fri Dec 05, 2025 1:49 am

Hi "eleven",

The 20 cells pattern above has only one implementation, then stte.
I am sure that you have a nice way to write this.

by **marek stefanik** » Fri Dec 05, 2025 10:30 am

eleven wrote:An alternative move after totuan's second step: -23r5c4

That's nice, I missed the 2 elim.
That means we can get a full parity path.

After TH => –239r4c3:

Code: Select all: ,------------------,-------------------,------------------, | 1 23589 2369 | 24567 2567 2467 | 23579 48 2369 | | 4 235 236 | 2567 8 9 | 2357 23 1 | | 7 2589 269 | 1 3 246 | 259 48 269 | :------------------+-------------------+------------------: |!239 4 1 | 8 a279 a237 | 6 !239 5 | | 239 6 7 |c239 4 5 | 8 1 239 | | 5 239! 8 |b6–239 b269 1 | 239! 7 4 | :------------------+-------------------+------------------: | 6 239! 4 |b29–3 1 8 | 239! 5 7 | | 8 7 239 |c45–239 c259 c234 | 1 6 239 | |!239 1 5 |a23679 a267–9a267–3| 4 !239 8 | '------------------'-------------------'------------------'

In r456789, each minirow contains one of 239.
Therefore, rows within the same band have different permutations of the same parity.
Each parity has 3 permutations: {239, 392, 923} or {293, 329, 932}.
If the bands have the same parity, each row has a twin in the other band with the same permutation. However, r5 cannot have a twin among r789.
So they have opposite parities and each pair of rows from r456 x r789 has the same digit in one of the stacks.
r49 have their shared digit in the middle stack (–39r9c56), so do r67 (–239r6c4, –3r7c4).
So r58 share the remaining digit in the middle stack (–239r8c4). Note that we also could have deduced this using TH instead of the other row pairs: r8c3=r4c1≠r5c1, otherwise in the solution we could swap r4c13 and remove all non-TH cells to get a 3-digit TH solution, contradiction.

Code: Select all: ,-----------------,------------------,------------------, | 1 23589 x239 | 2457 2567 2467 | 23579 48 x2369 | | 4 235 6 | 257 8 x9 | 2357 23 1 | | 7 2589 x29 | 1 3 246 | 259 48 x269 | :-----------------+------------------+------------------: | 239 4 1 | 8 279 237 | 6 239 5 | | 239 6 7 |x9–23 4 5 | 8 1 239 | | 5 239 8 | 6 29 1 | 239 7 4 | :-----------------+------------------+------------------: | 6 239 4 | 29 1 8 | 239 5 7 | | 8 7 239 | 45 x9–25 x234 | 1 6 239 | | 239 1 5 | 2379 267 267 | 4 239 8 | '-----------------'------------------'------------------'

The shared digit among r58 is forced into r13 in c39, so in r2 it is left with r2c56, so it must be 9, stte.

by **eleven** » Fri Dec 05, 2025 12:37 pm

Sorry, no, this is a very complex impossible pattern.

Code: Select all: |+++++++++++++++|+++++++++++++++|+++++++++++++++| | . . 239 | . . . | . . 639 | | . . . | . . . | . . . | | . . 29 | . . . | . . 69 | |+++++++++++++++|+++++++++++++++|+++++++++++++++| | 239 . . | . . . | . 39 . | | 239 . . | 239 . . | . . 239 | | . 239 . | . 29 . | 239 . . | |+++++++++++++++|+++++++++++++++|+++++++++++++++| | . 239 . | 239 . . | 239 . . | | . . 239 | . . . | . . 239 | | 239 . . | . . . | . 39 . | |+++++++++++++++|+++++++++++++++|+++++++++++++++|

I have only a boring long proof by showing, that bands 23 have only one solution with 9 in r8c3 and r5c9.

by **totuan** » Fri Dec 05, 2025 1:18 pm

Wow…! Nice find – eleven & marek. Based on yours I find other more

The puzzle after tridagon r4c3=1

Code: Select all: *--------------------------------------------------------------------* | 1 23589 2369 | 24567 2567 2467 | 23579 48 2369 | | 4 235 236 | 2567 8 9 | 2357 23 1 | | 7 2589 269 | 1 3 246 | 259 48 269 | |----------------------+----------------------+----------------------| |#29-3 4 1 | 8 279 237 | 6 239 5 | | 239 6 7 | 239 4 5 | 8 1 #29-3 | | 5 239 8 | 2369 #29-6 1 | 239 7 4 | |----------------------+----------------------+----------------------| | 6 239 4 |#29-3 1 8 | 239 5 7 | | 8 7 #29-3 | 23459 259 234 | 1 6 239 | | 239 1 5 | 23679 2679 2367 | 4 #29-3 8 | *--------------------------------------------------------------------*

#-marked cells contain the same digit => -36 at #-marked cells, many singles and downgrate the puzzle to ER-6.7

Prove for the same digit at #-marked cells:

Hidden Text: Show

Code: Select all: *--------------------------------------------------------------------* | 1 23589 2369 | 24567 2567 2467 | 23579 48 2369 | | 4 235 236 | 2567 8 9 | 2357 23 1 | | 7 2589 269 | 1 3 246 | 259 48 269 | |----------------------+----------------------+----------------------| | 239 4 1 | 8 279 237 | 6 239 5 | |b239 6 7 |*239 4 5 | 8 1 a239 | | 5 239 8 | 2369 269 1 | 239 7 4 | |----------------------+----------------------+----------------------| | 6 239 4 |X239 1 8 | 239 5 7 | | 8 7 239 | 23459 259 234 | 1 6 #239 | |c239 1 5 |*23679 *2679 *2367 | 4 d239 8 | *--------------------------------------------------------------------* Let X be the digit in r7c4 01: r7c4=X => X’s: abcd => r8c9<>X => in B9 r9c8=X, in B7 r8c3=X, in B4 r6c1<>X by C1 *--------------------------------------------------------------------* | 1 23589 2369 | 24567 2567 2467 | 23579 48 2369 | | 4 235 236 | 2567 8 9 | 2357 23 1 | | 7 2589 269 | 1 3 246 | 259 48 269 | |----------------------+----------------------+----------------------| |b239 4 1 | 8 279 237 | 6 a239 5 | | 239 6 7 | 239 4 5 | 8 1 g239 | | 5 239 8 | 2369 269 1 |#239 7 4 | |----------------------+----------------------+----------------------| | 6 d239 4 |X239 1 8 |e239 5 7 | | 8 7 X239 | 23459 259 234 | 1 6 f239 | |c239 1 5 | 23679 2679 2367 | 4 X239 8 | *--------------------------------------------------------------------* 02: If r7c4,r8c3,r9c8=X and r6c7=X => in R5 r5c1=X => Oddagon: abcdefg => impossible => r5c9=X => in B4 r4c1=X

totuan

The New Sudoku Players' Forum

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Re: skfr 9.7 after th