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Website · by **denis_berthier** » Sat Nov 19, 2022 5:46 am

.
Similar to #10033 in my approach. Will they also be similar for you?

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 8 ! 9 . 2 ! ! 7 . . ! . . . ! 6 1 . ! ! . . . ! . . 1 ! 4 . . ! +-------+-------+-------+ 1.3.56....5718..6.68.7.3......8.5...3.5.67...87.31.5.6....789.27.....61......14..;2403;32666 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 23479 13479 ! ! 3 1249 5 ! 249 6 7 ! 128 2489 1489 ! ! 8 7 249 ! 3 1 249 ! 5 249 6 ! +-------------------+-------------------+-------------------+ ! 45 1346 146 ! 456 7 8 ! 9 35 2 ! ! 7 2349 2489 ! 2459 2349 249 ! 6 1 358 ! ! 259 2369 2689 ! 2569 239 1 ! 4 3578 3578 ! +-------------------+-------------------+-------------------+ 164 candidates.

by **totuan** » Sat Nov 19, 2022 5:10 pm

Code: Select all: *--------------------------------------------------------------------* | 1 A249 3 |B249 5 6 | 278 78-249 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 23479 13479 | | 3 1-249 5 |C249 6 7 | 128 2489 1489 | | 8 7 249 | 3 1 249 | 5 C249 6 | |----------------------+----------------------+----------------------| | 45 1346 146 | 456 7 8 | 9 35 2 | | 7 2349 2489 | 2459 2349 249 | 6 1 358 | | 259 2369 2689 | 2569 239 1 | 4 3578 3578 | *--------------------------------------------------------------------*

My path for this one:
01 & 02: Tridagon (249)B1245 => r5c2=1, RT (249)ABC => r1c8<>249, some singles

Code: Select all: *-----------------------------------------------------------* | 1 #249 3 |#249 5 6 | 278 78 4789 | | 249 5 7 | 1 8 249 | 23 6 349 | | 6 8 249 | 7 249 3 | 1 249 5 | |-------------------+-------------------+-------------------| | 249 2469 2469 | 8 249 5 | 37 37 1 | | 3 1 5 |#249 6 7 | 28 249 489 | | 8 7 249 | 3 1 249 | 5 249 6 | |-------------------+-------------------+-------------------| | 45 346 1 |*46 7 8 | 9 35 2 | | 7 %2349 %249-8 | 5 %2349 %249 | 6 1 38 | | 259 2369 2689 |*269 239 1 | 4 3578 378 | *-----------------------------------------------------------*

03: Look at: RT (249)r1c24/r5c4 and (249)R8C4 => whichever digit in r1c2 then in r8c3 => r8c3<>8, some singles

Code: Select all: *-----------------------------------------------------------* | 1 249A 3 |%249 5 6 | 27 8 479 | |#249 5 7 | 1 8 #249 | 23 6 349 | | 6 8 #249 | 7 249 3 | 1 249 5 | |-------------------+-------------------+-------------------| | 249 #249 6 | 8 *249 5 | 37 37 1 | | 3 1 5 |%249 6 7 | 8 249 49 | | 8 7 #249 | 3 1 249A | 5 249 6 | |-------------------+-------------------+-------------------| | 45 346 1 | 46 7 8 | 9 35 2 | | 7 3-249 249A | 5 2349 #249 | 6 1 8 | | 259 2369 8 | 269 239 1 | 4 357 37 | *-----------------------------------------------------------*

04: Look at: (249)B4 => whichever digit in r6c3 then in r4c5
=> whichever digit x in r1c2 and RT (249)r1c24/r5c4 => x in r8c3 => r6c3<>x => r4c5<>x => r6c6=x
=> whichever digit x in r1c2 then in r6c6 & r8c3 => remote pair in (#) cells => r8c2<>249, some singles

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

05: RT (249) r1c24/r5c4 => r5c4<>2, r5c8=2
06: 2’s r3c3=r3c5-r4c5=r4c12 => r6c3<>2
07: Using eleven’s move on previous puzzle

: Oddagon (49) on (*) => r4c2<>2, stte

Thanks for the puzzle!
totuan

by **marek stefanik** » Sat Nov 19, 2022 8:21 pm

Totuan's solution is very clean despite only using one of the remote triples from the TH.
My solution will also showcase one of the remaining two.

Code: Select all: .-------------------.-----------------.--------------------. | 1 A#249 3 |A#249 5 6 | 278 24789 4789 | |B#249 5 7 | 1 8 B#249 | 23 6 349 | | 6 8 C#249 | 7 C#249 3 | 12 2459 1459 | :-------------------+-----------------+--------------------: |#249 12469 12469 | 8 C#249 5 | 1237 23479 13479 | | 3 1–249 5 |A#249 6 7 | 128 2489 1489 | | 8 7 #249 | 3 1 B#249 | 5 249 6 | :-------------------+-----------------+--------------------: | 45 1346 146 | 456 7 8 | 9 35 2 | | 7 2349 2489 | 2459 2349 249 | 6 1 358 | | 259 2369 2689 | 2569 239 1 | 4 3578 3578 | '-------------------'-----------------'--------------------'

TH[11] => -249r5c2, RTs 249A 249B 249C

Code: Select all: .-----------------.-----------------.------------------. | 1 A249 3 |A249 5 6 | 278 78–249 4789 | | 249 5 7 | 1 8 249 | 23 6 349 | | 6 8 249 | 7 249 3 | 12 2459 1459 | :-----------------+-----------------+------------------: | 249 2469 2469 | 8 249 5 | 137 37 137 | | 3 1 5 |A249 6 7 |#28 #2489 #489 | | 8 7 249 | 3 1 249 | 5 #249 6 | :-----------------+-----------------+------------------: | 45 346 1 | 456 7 8 | 9 35 2 | | 7 2349 2489 | 2459 2349 249 | 6 1 358 | | 259 2369 2689 | 2569 239 1 | 4 3578 3578 | '-----------------'-----------------'------------------'

249b6A \ r15c8 => -249r1c8

Code: Select all: .-----------------.----------------.-----------------. | 1 249 3 | 249 5 6 | 278 78 4789 | |B249 5 7 | 1 8 B249 | 23 6 349 | | 6 8 249 | 7 249 3 | 1 249 5 | :-----------------+----------------+-----------------: | 249 2469 2469 | 8 249 5 | 37 37 1 | | 3 1 5 | 249 6 7 | 28 249 489 | | 8 7 249 | 3 1 B249 | 5 249 6 | :-----------------+----------------+-----------------: |#45 346 1 | 46 7 8 | 9 35 2 | | 7 #2349 #2489 | 5 #2349 #249 | 6 1 38 | |#259 2369 2689 | 269 239 1 | 4 3578 378 | '-----------------'----------------'-----------------'

(2|4|9)r79c1 is in B forced into c6 and then in r8 into c5. => -3r8c5

Code: Select all: .-----------------.---------------.----------------. | 1 A249 3 |A249 5 6 | 278 78 4789 | | 249 5 7 | 1 8 249 | 23 6 349 | | 6 8 249 | 7 249 3 | 1 249 5 | :-----------------+---------------+----------------: | 249 2469 2469 | 8 249 5 | 37 37 1 | | 3 1 5 |A249 6 7 | 28 249 489 | | 8 7 249 | 3 1 249 | 5 249 6 | :-----------------+---------------+----------------: | 45 346 1 |#46 7 8 | 9 35 2 | | 7 3–249 2489 | 5 #249 #249 | 6 1 38 | | 259 269 2689 |#269 3 1 | 4 578 78 | '-----------------'---------------'----------------'

249b8A \ r8c24 => -249r8c2

Code: Select all: .---------------.---------------.------------. | 1 249 3 | 249 5 6 | 7 8 49 | |B*49 5 7 | 1 8 B*49 | 2 6 3 | | 6 8 249 | 7 *249 3 | 1 49 5 | :---------------+---------------+------------: | 29–4 249 6 | 8 *249 5 | 3 7 1 | | 3 1 5 | 249 6 7 | 8 249 49 | | 8 7 249 | 3 1 B249 | 5 249 6 | :---------------+---------------+------------: | 5 46 1 | 46 7 8 | 9 3 2 | | 7 3 #249 | 5 #29–4#249 | 6 1 8 | |#29 269 8 | 269 3 1 | 4 5 7 | '---------------'---------------'------------'

49r2 \ B => –49r6c6
(2|9)r9c1 is in B forced into c6 and then in r8 into c5 as before. => -4r8c5
4r2c5 \ r4c1b2 => -4r4c1, stte

Marek

by **Cenoman** » Sat Nov 19, 2022 10:48 pm

Same start as other players:

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 23479 13479 | | 3 249+1* 5 | 249* 6 7 | 128 2489 1489 | | 8 7 249* | 3 1 249* | 5 249 6 | +------------------------+----------------------+-------------------------+ | 45 1346 146 | 456 7 8 | 9 35 2 | | 7 2349 2489 | 2459 2349 249 | 6 1 358 | | 259 2369 2689 | 2569 239 1 | 4 3578 3578 | +------------------------+----------------------+-------------------------+

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

Code: Select all: +----------------------+----------------------+-----------------------+ | 1 a249* 3 | a249* 5 6 | 278 78-249 4789 | | 249 5 7 | 1 8 249 | 23 6 349 | | 6 8 249 | 7 249 3 | 12 2459 1459 | +----------------------+----------------------+-----------------------+ | 249 2469 2469 | 8 249 5 | 137 37 137 | | 3 1 5 | b249* 6 7 | c28 c2489 c489 | | 8 7 249 | 3 1 249 | 5 d249 6 | +----------------------+----------------------+-----------------------+ | 45 346 1 | 456 7 8 | 9 35 2 | | 7 2349 2489 | 2459 2349 249 | 6 1 358 | | 259 2369 2689 | 2569 239 1 | 4 3578 3578 | +----------------------+----------------------+-----------------------+

2. RT(249) r1c24, r5c4: (2,4,9): r1c24 = r5c4 - r5c789 = r6c8 => -249 r1c8; lcls, some placements

Code: Select all: +----------------------+---------------------+----------------------+ | 1 249 3 | 249 5 6 | 278 78 4789 | | 249 5 7 | 1 8 249 | 23 6 349 | | 6 8 249 | 7 249 3 | 1 249 5 | +----------------------+---------------------+----------------------+ | 249 2469 2469 | 8 249 5 | 37 37 1 | | 3 1 5 | 249 6 7 | 28 249 489 | | 8 7 249 | 3 1 249 | 5 249 6 | +----------------------+---------------------+----------------------+ | 45 346 1 | 46 7 8 | 9 35 2 | | 7 2349 2489 | 5 2349 249 | 6 1 38 | | 259 2369 2689 | 269 239 1 | 4 3578 378 | +----------------------+---------------------+----------------------+

3. eleven's variable replacement method: 249 -> xyz, while setting +x r1c2, +y r1c4, +z r5c4 (x, y, z solutions of the above RT cells)

Code: Select all: +----------------------+---------------------+----------------------+ | 1 x 3 | y 5 6 | 278 78 4789 | | yz 5 7 | 1 8 xz | 23 6 349 | | 6 8 yz | 7 xz 3 | 1 xyz 5 | +----------------------+---------------------+----------------------+ | yz+x yz6 249+6 | 8 xy 5 | 37 37 1 | | 3 1 5 | z 6 7 | 28 xyz 489 | | 8 7 xyz | 3 1 xy | 5 xyz 6 | +----------------------+---------------------+----------------------+ | 45 346 1 | x6 7 8 | 9 35 2 | | 7 yz3 yz8+x | 5 yz3 yz | 6 1 3+8 | | 259 2369 269+8 | x6 239 1 | 4 3578 378 | +----------------------+---------------------+----------------------+

Note that r79c4 is Hidden Pair (x6) => +x r8c3; +8 r9c3, +8r8c9, +6r4c3, +x r4c1 => +x r6c6 (hidden singles)
With singles only, the following resolution state is reached:

Code: Select all: +----------------------+---------------------+----------------------+ | 1 x 3 | y 5 6 | 7 8 49 | | y 5 7 | 1 8 z | 2 6 3 | | 6 8 z | 7 x 3 | 1 y 5 | +----------------------+---------------------+----------------------+ | x z 6 | 8 y 5 | 3 7 1 | | 3 1 5 | z 6 7 | 8 x 49 | | 8 7 y | 3 1 x | 5 z 6 | +----------------------+---------------------+----------------------+ | 5 46 1 | x6 7 8 | 9 3 2 | | 7 3 x | 5 z y | 6 1 8 | | 29 269 8 | x6 3 1 | 4 5 7 | +----------------------+---------------------+----------------------+

Look at box 3: the unsolved pair is 49 => y=4|9; look at row 1 => x=2, +9 r9c1; look at col 1 => y=4; z=9; ste

by **totuan** » Sun Nov 20, 2022 4:50 am

marek stefanik wrote:Totuan's solution is very clean despite only using one of the remote triples from the TH.
My solution will also showcase one of the remaining two.
Code: Select all
.-------------------.-----------------.--------------------. | 1 A#249 3 |A#249 5 6 | 278 24789 4789 | |B#249 5 7 | 1 8 B#249 | 23 6 349 | | 6 8 C#249 | 7 C#249 3 | 12 2459 1459 | :-------------------+-----------------+--------------------: |#249 12469 12469 | 8 C#249 5 | 1237 23479 13479 | | 3 1–249 5 |A#249 6 7 | 128 2489 1489 | | 8 7 #249 | 3 1 B#249 | 5 249 6 | :-------------------+-----------------+--------------------: | 45 1346 146 | 456 7 8 | 9 35 2 | | 7 2349 2489 | 2459 2349 249 | 6 1 358 | | 259 2369 2689 | 2569 239 1 | 4 3578 3578 | '-------------------'-----------------'--------------------'

Very nice observation!
It’s not hard to prove based on main RT, thanks for sharing that.

totuan

Website · by **denis_berthier** » Mon Nov 21, 2022 4:32 am

.
Thanks for your solution. As I said, mine is close to the one for #10033. Using replacement after the tridagon eliminations, a solution is found in BC4:

Code: Select all: 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 hidden-triplets-in-a-row: r4{n1 n3 n7}{c7 c9 c8} ==> r4c9≠9, r4c9≠4, r4c8≠9, r4c8≠4, r4c8≠2, r4c7≠2 biv-chain[3]: b9n7{r9c9 r9c8} - r4c8{n7 n3} - r7c8{n3 n5} ==> r9c9≠5 biv-chain[4]: c9n1{r4 r3} - b3n5{r3c9 r3c8} - r7c8{n5 n3} - r4c8{n3 n7} ==> r4c9≠7 +-------------------+-------------------+-------------------+ ! 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 2469 2469 ! 8 249 5 ! 137 37 13 ! ! 3 1 5 ! 249 6 7 ! 28 2489 489 ! ! 8 7 249 ! 3 1 249 ! 5 249 6 ! +-------------------+-------------------+-------------------+ ! 45 346 1 ! 456 7 8 ! 9 35 2 ! ! 7 2349 2489 ! 2459 2349 249 ! 6 1 358 ! ! 259 2369 2689 ! 2569 239 1 ! 4 3578 378 ! +-------------------+-------------------+-------------------+ ***** STARTING ELEVEN''S REPLACEMENT TECHNIQUE FOR GENERAL TRIDAGON ***** RELEVANT DIGIT REPLACEMENTS WILL BE NECESSARY AT THE END, based on the original givens. Trying in block 5 +-------------------+-------------------+-------------------+ ! 1 249 3 ! 249 5 6 ! 24789 24789 24789 ! ! 249 5 7 ! 1 8 249 ! 2349 6 2349 ! ! 6 8 249 ! 7 249 3 ! 1249 2459 12459 ! +-------------------+-------------------+-------------------+ ! 249 2469 2469 ! 8 9 5 ! 137 37 13 ! ! 3 1 5 ! 4 6 7 ! 2489 2489 2489 ! ! 8 7 249 ! 3 1 2 ! 5 249 6 ! +-------------------+-------------------+-------------------+ ! 2459 23469 1 ! 24569 7 8 ! 249 35 249 ! ! 7 2349 2489 ! 2459 2349 249 ! 6 1 358 ! ! 2459 23469 24689 ! 24569 2349 1 ! 249 3578 378 ! +-------------------+-------------------+-------------------+ singles ==> r6c3=9, r6c8=4 whip[1]: r3n9{c7 .} ==> r2c9≠9, r2c7≠9, r1c9≠9, r1c8≠9, r1c7≠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, r1c7≠2 stte

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#10034 in 63137 min-expands

#10034 in 63137 min-expands

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Re: #10034 in 63137 min-expands

Re: #10034 in 63137 min-expands

Re: #10034 in 63137 min-expands