The New Sudoku Players' Forum

Website · by **denis_berthier** » Fri Nov 18, 2022 5:31 am

.
This puzzle has something special.
Even the SER takes a long time to be computed.

Code: Select all: +-------+-------+-------+ ! 1 . 3 ! . 5 6 ! . . . ! ! . 5 7 ! 1 8 . ! . 6 . ! ! 6 8 . ! 7 . 3 ! . . . ! +-------+-------+-------+ ! . . . ! 8 . 5 ! . . . ! ! 3 . 5 ! . 6 7 ! . . . ! ! 8 7 . ! 3 1 . ! 5 . 6 ! +-------+-------+-------+ ! . . . ! . 7 . ! 9 3 2 ! ! 7 . . ! . . . ! 6 1 . ! ! . . . ! . . 1 ! 4 . . ! +-------+-------+-------+ 1.3.56....5718..6.68.7.3......8.5...3.5.67...87.31.5.6....7.9327.....61......14..;2403;32703 SER = 11.6

Code: Select all: Resolution state after Singles and whips[1]: +-------------------+-------------------+-------------------+ ! 1 249 3 ! 249 5 6 ! 278 24789 4789 ! ! 249 5 7 ! 1 8 249 ! 23 6 349 ! ! 6 8 249 ! 7 249 3 ! 12 2459 1459 ! +-------------------+-------------------+-------------------+ ! 249 12469 12469 ! 8 249 5 ! 1237 2479 13479 ! ! 3 1249 5 ! 249 6 7 ! 128 2489 1489 ! ! 8 7 249 ! 3 1 249 ! 5 249 6 ! +-------------------+-------------------+-------------------+ ! 45 146 1468 ! 456 7 48 ! 9 3 2 ! ! 7 2349 2489 ! 2459 2349 2489 ! 6 1 58 ! ! 259 2369 2689 ! 2569 239 1 ! 4 578 578 ! +-------------------+-------------------+-------------------+ 161 candidates.

by **shye** » Fri Nov 18, 2022 7:14 am

.
not sure i found what you had in mind, but enjoyed the solve regardless

249 tridagon in b1245, +1r5c2
then after singles and hidden 13 pair:

Code: Select all: .-----------------.-----------------.----------------. | 1 A249 3 |B249 5 6 | 7 8-249 489 | | 249 5 7 | 1 8 249 | 23 6 349 | | 6 8 249 | 7 249 3 | 12 2459 1459 | :-----------------+-----------------+----------------: | 249 2469 2469 | 8 249 5 | 13 7 13 | | 3 1 5 |C249 6 7 | 8 249 49 | | 8 7 249 | 3 1 249 | 5 C249 6 | :-----------------+-----------------+----------------: | 45 46 1 | 456 7 8 | 9 3 2 | | 7 2349 2489 | 2459 2349 249 | 6 1 58 | | 259 2369 2689 | 2569 239 1 | 4 58 7 | '-----------------'-----------------'----------------'

r1c2,r1c4,r5c4 form a remote triple using the tridagon, label as ABC
C in b6 must be in p8
-ABCr1c8
many singles

Code: Select all: .----------------.----------------.------------. | 1 A49+2 3 |B249 5 6 | 7 8 C49 | |B49 5 7 | 1 8 49 | 2 6 3 | | 6 8 C249 | 7 249 3 | 1 49 5 | :----------------+----------------+------------: | 249 249 6 | 8 249 5 | 3 7 1 | | 3 1 5 |C249 6 7 | 8 249 49 | | 8 7 249 | 3 1 249 | 5 C249 6 | :----------------+----------------+------------: | 5 46 1 |a46 7 8 | 9 3 2 | | 7 2349 A249 | 5 *2349 *249 | 6 1 8 | | 29 2369 8 |a269 239 1 | 4 5 7 | '----------------'----------------'------------'

C in r1 is in c9
A in c4 is locked to b8, places A in r8
C in c3 is in r3
B in b1 is in p4
A is now the only value able to be 2, +2r1c2 stte

by **Cenoman** » Fri Nov 18, 2022 9:34 pm

Code: Select all: +------------------------+-----------------------+-------------------------+ | 1 249* 3 | 249* 5 6 | 278 24789 4789 | | 249* 5 7 | 1 8 249* | 23 6 349 | | 6 8 249* | 7 249* 3 | 12 2459 1459 | +------------------------+-----------------------+-------------------------+ | 249* 12469 12469 | 8 249* 5 | 1237 2479 13479 | | 3 249+1* 5 | 249* 6 7 | 128 2489 1489 | | 8 7 249* | 3 1 249* | 5 249 6 | +------------------------+-----------------------+-------------------------+ | 45 146 1468 | 456 7 48 | 9 3 2 | | 7 2349 2489 | 2459 2349 2489 | 6 1 58 | | 259 2369 2689 | 2569 239 1 | 4 578 578 | +------------------------+-----------------------+-------------------------+

1. TH(249)b1245 having a single guardian => +1 r5c2; lcls, 7 placements

Code: Select all: +----------------------+----------------------+--------------------+ | 1 249* 3 | 249* 5 6 | 7 489 489 | | 249 5 7 | 1 8 249 | 23 6 349 | | 6 8 249 | 7 249 3 | 12 459 1459 | +----------------------+----------------------+--------------------+ | 249 2469 2469 | 8 249 5 | 13 7 13 | | 3 1 5 | 249* 6 7 | 8 249 49 | | 8 7 249 | 3 1 249 | 5 249 6 | +----------------------+----------------------+--------------------+ | 45 46 1 | 456 7 8 | 9 3 2 | | 7 2349 2489 | 2459 2349 249 | 6 1 58 | | 259 2369 2689 | 2569 239 1 | 4 58 7 | +----------------------+----------------------+--------------------+

2. RT(249)r1c2, r1c4, r5c4
Note that 2r1c2 and 2r1c4 are conjugates => +2 r1c24, -2 r5c4; 1 placement

Code: Select all: +----------------------+----------------------+--------------------+ | 1 a249* 3 | a249* 5 6 | 7 8-49 489 | | 249 5 7 | 1 8 249 | 23 6 349 | | 6 8 249 | 7 249 3 | 12 459 1459 | +----------------------+----------------------+--------------------+ | 249 2469 2469 | 8 249 5 | 13 7 13 | | 3 1 5 | b49* 6 7 | 8 2 c49 | | 8 7 249 | 3 1 249 | 5 d49 6 | +----------------------+----------------------+--------------------+ | 45 46 1 | 456 7 8 | 9 3 2 | | 7 2349 2489 | 2459 2349 249 | 6 1 58 | | 259 2369 2689 | 2569 239 1 | 4 58 7 | +----------------------+----------------------+--------------------+

3. RT(249)r1c2, r1c4, r5c4
(4,9): r1c24 == r5c4 - r5c9 = r6c8 => -49r1c8; 13 placements

Code: Select all: +---------------------+---------------------+-----------------+ | 1 24-9 3 | 249 5 6 | 7 8 F49 | | A49 5 7 | 1 8 49 | 2 6 3 | | 6 8 249 | 7 b249 3 | 1 c49 5 | +---------------------+---------------------+-----------------+ |Ba249 a249 6 | 8 Ca249 5 | 3 7 1 | | 3 1 5 |Df49 6 7 | 8 2 Ee49 | | 8 7 a249 | 3 1 249 | 5 d49 6 | +---------------------+---------------------+-----------------+ | 5 h46 1 | g46 7 8 | 9 3 2 | | 7 2349 29-4 | 5 a2349 249 | 6 1 8 | | 29 2369 8 | 269 239 1 | 4 5 7 | +---------------------+---------------------+-----------------+

4. (4): [r6c3 = r4c12 - r4c5 = r8c5] = r3c5 - r3c8 = r6c8 - r5c9 = r5c4 - r7c4 = r7c2 => -4 r8c3; (=> -4 r14c2)

5. (9=4)r2c1 - r4c1 = r4c5 - (4=9)r5c4 - r5c9 = (9)r1c9 => -9r1c2; ste

by **eleven** » Fri Nov 18, 2022 11:11 pm

Same with oddagon finish:

Code: Select all: +-------------------+-------------------+-------------------+ | 1 *49+2 3 | 249 5 6 | 7 8 *49 | |*49 5 7 | 1 8 49 | 2 6 3 | | 6 8 249 | 7 249 3 | 1 49 5 | +-------------------+-------------------+-------------------+ |*49+2 49-2 6 | 8 249 5 | 3 7 1 | | 3 1 5 | 49 6 7 | 8 2 *49 | | 8 7 *49+2 | 3 1 249 | 5 *49 6 | +-------------------+-------------------+-------------------+ | 5 46 1 | 46 7 8 | 9 3 2 | | 7 2349 249 | 5 2349 249 | 6 1 8 | | 29 2369 8 | 269 239 1 | 4 5 7 | +-------------------+-------------------+-------------------+

oddagon 49, guardians 2r1c2,r4c1,r6c3 => -2r4c2, stte

Website · by **denis_berthier** » Sat Nov 19, 2022 5:37 am

.
Thanks for your solutions. Interesting to see RP, RT and oddagons at work.

What I had in mind was actually different.
The start is the same as all of you:

Code: Select all: Resolution state after Singles and whips[1]: +-------------------+-------------------+-------------------+ ! 1 249 3 ! 249 5 6 ! 278 24789 4789 ! ! 249 5 7 ! 1 8 249 ! 23 6 349 ! ! 6 8 249 ! 7 249 3 ! 12 2459 1459 ! +-------------------+-------------------+-------------------+ ! 249 12469 12469 ! 8 249 5 ! 1237 2479 13479 ! ! 3 1249 5 ! 249 6 7 ! 128 2489 1489 ! ! 8 7 249 ! 3 1 249 ! 5 249 6 ! +-------------------+-------------------+-------------------+ ! 45 146 1468 ! 456 7 48 ! 9 3 2 ! ! 7 2349 2489 ! 2459 2349 2489 ! 6 1 58 ! ! 259 2369 2689 ! 2569 239 1 ! 4 578 578 ! +-------------------+-------------------+-------------------+ 161 candidates. tridagon for digits 2, 4 and 9 in blocks: b4, with cells: r5c2 (target cell), r6c3, r4c1 b5, with cells: r5c4, r6c6, r4c5 b1, with cells: r1c2, r3c3, r2c1 b2, with cells: r1c4, r3c5, r2c6 ==> r5c2≠2,4,9 singles ==> r5c2=1, r7c3=1, r7c6=8 hidden-pairs-in-a-row: r4{n1 n3}{c7 c9} ==> r4c9≠9, r4c9≠7, r4c9≠4, r4c7≠7, r4c7≠2 singles ==> r4c8=7, r9c9=7, r1c7=7, r5c7=8 whip[1]: b6n2{r6c8 .} ==> r1c8≠2, r3c8≠2 +----------------+----------------+----------------+ ! 1 249 3 ! 249 5 6 ! 7 489 489 ! ! 249 5 7 ! 1 8 249 ! 23 6 349 ! ! 6 8 249 ! 7 249 3 ! 12 459 1459 ! +----------------+----------------+----------------+ ! 249 2469 2469 ! 8 249 5 ! 13 7 13 ! ! 3 1 5 ! 249 6 7 ! 8 249 49 ! ! 8 7 249 ! 3 1 249 ! 5 249 6 ! +----------------+----------------+----------------+ ! 45 46 1 ! 456 7 8 ! 9 3 2 ! ! 7 2349 2489 ! 2459 2349 249 ! 6 1 58 ! ! 259 2369 2689 ! 2569 239 1 ! 4 58 7 ! +----------------+----------------+----------------+

After this, no ordinary whip[≤ 12] can give any elimination. But eleven replacement does wonders:

Code: Select all: ***** STARTING ELEVEN''S REPLACEMENT TECHNIQUE FOR GENERAL TRIDAGON in resolution state: ***** RELEVANT DIGIT REPLACEMENTS WILL BE NECESSARY AT THE END, based on the original givens. Trying in block 5 +-------------------+-------------------+-------------------+ ! 1 249 3 ! 249 5 6 ! 7 2489 2489 ! ! 249 5 7 ! 1 8 249 ! 2349 6 2349 ! ! 6 8 249 ! 7 249 3 ! 1249 2459 12459 ! +-------------------+-------------------+-------------------+ ! 249 2469 2469 ! 8 9 5 ! 13 7 13 ! ! 3 1 5 ! 4 6 7 ! 8 249 249 ! ! 8 7 249 ! 3 1 2 ! 5 249 6 ! +-------------------+-------------------+-------------------+ ! 2459 2469 1 ! 24569 7 8 ! 249 3 249 ! ! 7 2349 2489 ! 2459 2349 249 ! 6 1 58 ! ! 2459 23469 24689 ! 24569 2349 1 ! 249 58 7 ! +-------------------+-------------------+-------------------+ singles ==> r6c3=9, r6c8=4 whip[1]: r3n9{c7 .} ==> r2c9≠9, r2c7≠9, r1c9≠9, r1c8≠9 naked-pairs-in-a-row: r3{c3 c5}{n2 n4} ==> r3c9≠4, r3c9≠2, r3c8≠2, r3c7≠4, r3c7≠2 finned-x-wing-in-rows: n9{r1 r8}{c2 c4} ==> r9c4≠9, r7c4≠9 whip[1]: b8n9{r8c6 .} ==> r8c2≠9 biv-chain[2]: c6n4{r8 r2} - r3n4{c5 c3} ==> r8c3≠4 biv-chain[3]: r2n9{c1 c6} - r1c4{n9 n2} - r3n2{c5 c3} ==> r2c1≠2 whip[1]: r2n2{c9 .} ==> r1c9≠2, r1c8≠2 stte

The New Sudoku Players' Forum

#10033 in 63137 mn-expands

#10033 in 63137 mn-expands

Re: #10033 in 63137 mn-expands

Re: #10033 in 63137 mn-expands

Re: #10033 in 63137 mn-expands

Re: #10033 in 63137 mn-expands