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Website · by **denis_berthier** » Mon Sep 05, 2022 4:49 am

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This is #42693 in mith's list of 63137 min-expand puzzles in T&E(3).
Selected for its high number of direct anti-tridagon eliminations.
(For more seasoned tridagon players.)

Code: Select all: +-------+-------+-------+ ! 1 . . ! 4 . 6 ! 7 8 . ! ! 4 . . ! 1 . . ! . 6 3 ! ! 6 . . ! . . 3 ! 4 . 1 ! +-------+-------+-------+ ! . . . ! 8 . 7 ! . 3 . ! ! . . . ! . . 4 ! . . . ! ! . . 8 ! 6 3 . ! 1 7 . ! +-------+-------+-------+ ! . 9 4 ! 7 6 . ! . . . ! ! 7 . 2 ! . 4 . ! . . . ! ! 8 6 1 ! . . . ! . 4 7 ! +-------+-------+-------+ 1..4.678.4..1...636....34.1...8.7.3......4.....863.17..9476....7.2.4....861....47;8928;212137 SER = 10.4

Code: Select all: Resolution state after Singles and whips[1]: +-------------------+-------------------+-------------------+ ! 1 235 359 ! 4 259 6 ! 7 8 259 ! ! 4 2578 579 ! 1 25789 259 ! 259 6 3 ! ! 6 2578 579 ! 259 25789 3 ! 4 259 1 ! +-------------------+-------------------+-------------------+ ! 259 145 56 ! 8 1259 7 ! 2569 3 24569 ! ! 2359 1357 3567 ! 259 1259 4 ! 25689 259 25689 ! ! 259 45 8 ! 6 3 259 ! 1 7 2459 ! +-------------------+-------------------+-------------------+ ! 35 9 4 ! 7 6 1258 ! 2358 125 258 ! ! 7 35 2 ! 359 4 1589 ! 35689 159 5689 ! ! 8 6 1 ! 2359 259 259 ! 2359 4 7 ! +-------------------+-------------------+-------------------+ 164 candidates.

by **Leren** » Mon Sep 05, 2022 5:44 am

Code: Select all: *------------------------------------------* | 1 25 3 | 4 *259 6 | 7 8 *259 | | 4 258 79 | 1 78 *29 |*259 6 3 | | 6 258 79 |*259 78 3 | 4 *259 1 | |-----------+-------------+----------------| | 29 1 5 | 8 *29 7 |#6-259 3 4 | | 3 7 6 |*259 1 4 | 2589 *259 2589 | | 29 4 8 | 6 3 *259 | 1 7 *259 | |-----------+-------------+----------------| | 5 9 4 | 7 6 18 | 3 12 28 | | 7 3 2 | 59 4 18 | 589 159 6 | | 8 6 1 | 3 259 259 | 59 4 7 | *------------------------------------------*

Resolution state after the Single Guardian Trigadon 259b2356 and basics. Solves with a few simple chains thereafter.

Hodoku, which does not do Trigadons, had a score of 27,592 for this puzzle. With the 6 added as a clue in r4c7, the score dropped to 1384.

Leren

by **P.O.** » Mon Sep 05, 2022 7:59 am

just a remark, from a template point of view, this type of puzzle, the "tridagon profile" requires most of the time at most a combination of 4 templates to be solved, evaluating their difficulty with SER does not seem to make much sense, the SER >= 10.0 which don't have that profile don't give in so easily, i wonder if the tridagon rule should be integrated into the SER hierarchy at what level it would be.

Code: Select all: 1....6.8.......2..6...72.14275......369......841.67....8..2167..1...8.4.....4.1.8 ;4357;362565 SER = 10.2 4-templates #VT:(4 6 138 8 116 4 10 6 116) 1.345..8945........983....5.....39.8.39...17...4....2...18......4593.8......15... ;3557;85092 SER = 11.0 4-templates #VT:(7 99 8 4 4 380 117 6 4) .23.5.7.9.5.....327.923....23...4.75.4.....9.9.....3.4....45..7.92.67....7412.... ;9598;223333 SER = 10.4 3-templates #VT:(111 2 4 4 8 131 4 262 3) 1.3.56.....7..9.........5....4...6.8..6.48.95......42..4.89..62.....59.4.6..2485. ;811;24505 SER = 11.7 3-templates #VT:(72 17 84 4 5 4 68 14 10) ...45........8.1.379.231....6739..18.........91..6..3.3.....8.7.7...836.68...3.91 ;4815 73447 SER = 11.0 4-templates #VT:(6 114 2 84 90 10 10 4 6) 1..4.678.4..1...636....34.1...8.7.3......4.....863.17..9476....7.2.4....861....47 ;8928;212137 SER = 10.4 4-templates #VT:(4 64 5 2 184 4 4 8 75)

by **Leren** » Mon Sep 05, 2022 8:29 am

Another remark. It seems to me that a trigadon can't go away just because one or more of the 3 digits has been removed in the trigadon cells. A corollary seems to be that you could have one with some of the trigadon cells being clues.

Is that right ? Leren

Website · by **denis_berthier** » Mon Sep 05, 2022 10:36 am

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I don't have much time now, so just a quick answer.

Templates have never been considered as a pattern-based approach, because combining them is mainly a heavy computational burden.

By the very definition of its levels, SER is unable of making a difference between T&E(1), T&E(2) or T&E(3). SER is (relatively) useful as it is and I can't see any point in adding any exotic pattern to it. One of its main problem is the discrepancies introduced by its uniqueness rules.

Adding a single clue (e.g. a backdoor) - or deleting a single candidate - can have a drastic effect on a puzzle. Nothing new here.

Leren, your question about deleting some of the tridagon candidates remains open as of today. I had planned to analyse it in my tridagon thread, but I have been busy with other things.
Notice however that:
- all the min-expand puzzles in mith's 63,137 collection have (at least) one anti-tridagon pattern with all 3 candidates in all 2 cells;
- allowing missing candidates (together with more than a single guardian) is likely to drastically increase the computational complexity.

by **DEFISE** » Mon Sep 05, 2022 11:05 am

After basics :

Code: Select all: |-----------------------------------------------------------| | 1 235 359 | 4 259 6 | 7 8 259 | | 4 2578 579 | 1 78 259 | 259 6 3 | | 6 2578 579 | 259 78 3 | 4 259 1 | |-----------------------------------------------------------| | 259 145 56 | 8 1259 7 | 2569 3 24569 | | 2359 1357 3567 | 259 1259 4 | 25689 259 25689 | | 259 45 8 | 6 3 259 | 1 7 2459 | |-----------------------------------------------------------| | 35 9 4 | 7 6 18 | 2358 125 258 | | 7 35 2 | 359 4 18 | 35689 159 5689 | | 8 6 1 | 2359 259 259 | 359 4 7 | |-----------------------------------------------------------|

Tridagon (2,5,9) in B2p267, B3p348, B5p249, B6p159
3 gardians : 1r4c5, 6r4c7, 4r6c9

I consider this chain from 3r7c1 (= right elements of a partial g-braid[5] from 3r7c1):
3r7c1 -> 5r456c1 -> 6r4c3* -> 4r6c2* -> 1r4c2*
Each of the 3 gardians is seen by a candidate tagged with *. So 3r7c1 is false.

Then the puzzle is solvable in W6 but with a lot steps.
Here is a much shorter solution in W10:

Single(s): 5r7c1, 3r8c2, 3r1c3, 3r5c1, 3r7c7, 3r9c4
whip[6]: r1n9{c9 c5}- r5n9{c5 c4}- r8c4{n9 n5}- r9c5{n5 n2}- b5n2{r4c5 r6c6}- r6c1{n2 .} => -9r6c9
whip[9]: r6c2{n5 n4}- r6c9{n4 n2}- c7n2{r4 r2}- r2c6{n2 n9}- r1n9{c5 c9}- r3c8{n9 n5}- r3c4{n5 n2}- r5c4{n2 n9}- r5c8{n9 .} => -5r6c6
Naked pairs: 29r6c16 => -2r6c9
whip[10]: r6n5{c9 c2}- c2n4{r6 r4}- r4n1{c2 c5}- r4n5{c5 c7}- r9c7{n5 n9}- b3n9{r2c7 r3c8}- r5c8{n9 n2}- b5n2{r5c4 r6c6}-
c6n9{r6 r2}- r1n9{c5 .} => -5r1c9
whip[9]: r1c2{n5 n2}- r1c9{n2 n9}- r1c5{n9 n5}- c6n5{r2 r9}- r8c4{n5 n9}- c8n9{r8 r5}- c5n9{r5 r4}- r4n1{c5 c2}- c2n4{r4 .} => -5r6c2
Single(s): 4r6c2, 5r6c9, 4r4c9
whip[3]: r1c9{n9 n2}- r7n2{c9 c8}- r5c8{n2 .} => -9r3c8
whip[6]: c4n2{r3 r5}- c4n5{r5 r8}- c8n5{r8 r3}- c8n2{r3 r7}- c9n2{r7 r1}- r1n9{c9 .} => -9r3c4
Single(s): 9r3c3
Naked pairs: 25r3c48 => -2r3c2 -5r3c2
Xwing in columns: 9c48r58 => -9r5c5 -9r5c7 -9r5c9 -9r8c7 -9r8c9
STTE

by **Cenoman** » Mon Sep 05, 2022 1:03 pm

After lcls (34 solved cells, 153 candidates)

Code: Select all: +-----------------------+----------------------+------------------------+ | 1 235 359 | 4 259* 6 | 7 8 259* | | 4 2578 579 | 1 78 259* | 259* 6 3 | | 6 2578 579 | 259* 78 3 | 4 259* 1 | +-----------------------+----------------------+------------------------+ | 29-5 b145 B56 | 8 a1259* 7 | A2569* 3 24569 | | 239-5 137-5 367-5 | 259* 1259 4 | 25689 259* 25689 | | 29-5 zb45 8 | 6 3 259* | 1 7 y2459* | +-----------------------+----------------------+------------------------+ | 35 9 4 | 7 6 18 | 2358 125 258 | | 7 35 2 | 359 4 18 | 35689 159 5689 | | 8 6 1 | 2359 259 259 | 359 4 7 | +-----------------------+----------------------+------------------------+

1. TH (259)b2356 (*) having three guardians: 2r4c5, 6r4c7, 4r6c9
(1)r4c5 - (1=45)r46c2
(6)r4c7 - (6=5)r4c3
(4)r6c9 - (4=5)r6c2
=> -5 b4p14567; lcls, 6 placements (25 eliminations, 122 candidates)
(Maybe could it be called TH-Death Blossom ?? :lol:

)

Code: Select all: +--------------------+---------------------+------------------------+ | 1 25 3 | 4 259 6 | 7 8 259 | | 4 2578* 579 | 1 78* 259 | 259 6 3 | | 6 2578* 579 | 259 78* 3 | 4 259 1 | +--------------------+---------------------+------------------------+ | 29 145 56 | 8 1259 7 | 2569 3 24569 | | 3 1+7 67 | 259 1259 4 | 25689 259 25689 | | 29 45 8 | 6 3 259 | 1 7 2459 | +--------------------+---------------------+------------------------+ | 5 9 4 | 7 6 18 | 3 12 28 | | 7 3 2 | 59 4 18 | 5689 159 5689 | | 8 6 1 | 3 259 259 | 59 4 7 | +--------------------+---------------------+------------------------+

SE rating ~ 8.9 I agree with François

Then the puzzle is solvable [...] with a lot steps.

That's true with chain techniques. Here, uniqueness helps:
2. UR (78)r23c25 using single external => +7 r5c2, lcls, 9 placements

Code: Select all: +------------------+--------------------+----------------------+ | 1 25 3 | 4 X25-9 6 | 7 8 z59(2) | | 4 258 79 | 1 78 Ww59(2) | 59+2 6 3 | | 6 258 79 | a25-9* 78 3 | 4 a259* 1 | +------------------+--------------------+----------------------+ | 29 1 5 | 8 29 7 | 6 3 4 | | 3 7 6 | a259* 1 4 | e589-2 a259* 2589 | | 29 4 8 | 6 3 x259 | 1 7 y259 | +------------------+--------------------+----------------------+ | 5 9 4 | 7 6 18 | 3 b12 c28 | | 7 3 2 | Z59 4 18 | d589 159 6 | | 8 6 1 | 3 Y259 259 | 59 4 7 | +------------------+--------------------+----------------------+

3. [XW(2)r5c4 = r3c4 - r3c8*=*r5c8] = r7c8 - (2=8)r7c9 - r8c7 = (8)r5c7 => -2 r5c7; 1 placement (+2 r2c7)

End with two W-Wings:
4. (9=5)r2c6 - r6c6 = r6c9 - (5=9)r1c9 => -9 r1c5
5. (9=5)r2c6 - r1c5 = r9c5 - (5=9)r8c4 => -9 r3c4, -9 r9c6; ste

Website · by **denis_berthier** » Tue Sep 06, 2022 3:59 am

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A solution in SFin+W5+OR3FW7, starting from the resolution state after whips[1], with 7 direct OR3-FW eliminations.

Code: Select all: hidden-pairs-in-a-column: c6{n1 n8}{r7 r8} ==> r8c6≠9, r8c6≠5, r7c6≠5, r7c6≠2 whip[1]: r7n2{c9 .} ==> r9c7≠2 hidden-pairs-in-a-column: c5{n7 n8}{r2 r3} ==> r3c5≠9, r3c5≠5, r3c5≠2, r2c5≠9, r2c5≠5, r2c5≠2 biv-chain[3]: r4c3{n6 n5} - r6c2{n5 n4} - b6n4{r6c9 r4c9} ==> r4c9≠6 +-------------------+-------------------+-------------------+ ! 1 235 359 ! 4 259 6 ! 7 8 259 ! ! 4 2578 579 ! 1 78 259 ! 259 6 3 ! ! 6 2578 579 ! 259 78 3 ! 4 259 1 ! +-------------------+-------------------+-------------------+ ! 259 145 56 ! 8 1259 7 ! 2569 3 2459 ! ! 2359 1357 3567 ! 259 1259 4 ! 25689 259 25689 ! ! 259 45 8 ! 6 3 259 ! 1 7 2459 ! +-------------------+-------------------+-------------------+ ! 35 9 4 ! 7 6 18 ! 2358 125 258 ! ! 7 35 2 ! 359 4 18 ! 35689 159 5689 ! ! 8 6 1 ! 2359 259 259 ! 359 4 7 ! +-------------------+-------------------+-------------------+

The Tridagon part, with 7 direct OR3-FW eliminations:

Code: Select all: OR3-anti-tridagon[12] (type diag) for digits 2, 9 and 5 in blocks: b2, with cells: r1c5, r2c6, r3c4 b3, with cells: r1c9, r2c7, r3c8 b5, with cells: r4c5, r6c6, r5c4 b6, with cells: r4c7, r6c9, r5c8 with 3 guardians: n1r4c5 n6r4c7 n4r6c9 OR3-forcing-whip-elim[4] based on OR3-anti-tridagon[12] for n1r4c5, n4r6c9 and n6r4c7: || n1r4c5 - partial-whip[1]: r5n1{c5 c2} - || n4r6c9 - partial-whip[1]: r6c2{n4 n5} - || n6r4c7 - partial-whip[1]: r4c3{n6 n5} - ==> r5c2≠5 OR3-forcing-whip-elim[4] based on OR3-anti-tridagon[12] for n1r4c5, n6r4c7 and n4r6c9: || n1r4c5 - || n6r4c7 - partial-whip[1]: r4c3{n6 n5} - || n4r6c9 - partial-whip[2]: r4n4{c9 c2} - r4n1{c2 c5} - ==> r4c5≠5 OR3-forcing-whip-elim[5] based on OR3-anti-tridagon[12] for n4r6c9, n6r4c7 and n1r4c5: || n4r6c9 - partial-whip[1]: r6c2{n4 n5} - || n6r4c7 - partial-whip[1]: r4c3{n6 n5} - || n1r4c5 - partial-whip[2]: r5n1{c5 c2} - r5n7{c2 c3} - ==> r5c3≠5 OR3-forcing-whip-elim[6] based on OR3-anti-tridagon[12] for n4r6c9, n6r4c7 and n1r4c5: || n4r6c9 - partial-whip[1]: r6c2{n4 n5} - || n6r4c7 - partial-whip[1]: r4c3{n6 n5} - || n1r4c5 - partial-whip[3]: r5n1{c5 c2} - r5n7{c2 c3} - r5n3{c3 c1} - ==> r5c1≠5 OR3-forcing-whip-elim[6] based on OR3-anti-tridagon[12] for n1r4c5, n4r6c9 and n6r4c7: || n1r4c5 - partial-whip[1]: r5n1{c5 c2} - || n4r6c9 - partial-whip[2]: r6c2{n4 n5} - r8c2{n5 n3} - || n6r4c7 - partial-whip[2]: r5n6{c9 c3} - r5n7{c3 c2} - ==> r5c2≠3 OR3-forcing-whip-elim[7] based on OR3-anti-tridagon[12] for n4r6c9, n6r4c7 and n1r4c5: || n4r6c9 - partial-whip[1]: r6c2{n4 n5} - || n6r4c7 - partial-whip[1]: r4c3{n6 n5} - || n1r4c5 - partial-whip[4]: r5n1{c5 c2} - r5n7{c2 c3} - r5n3{c3 c1} - r7c1{n3 n5} - ==> r6c1≠5 OR3-forcing-whip-elim[7] based on OR3-anti-tridagon[12] for n6r4c7, n1r4c5 and n4r6c9: || n6r4c7 - partial-whip[1]: r5n6{c9 c3} - || n1r4c5 - partial-whip[2]: r5n1{c5 c2} - r5n7{c2 c3} - || n4r6c9 - partial-whip[3]: r6c2{n4 n5} - c1n5{r4 r7} - c1n3{r7 r5} - ==> r5c3≠3

The end is easy for this kind of puzzle.

Code: Select all: singles ==> r5c1=3, r7c1=5, r8c2=3, r1c3=3, r9c4=3, r7c7=3 z-chain[4]: c4n2{r5 r3} - c8n2{r3 r7} - r7c9{n2 n8} - r5n8{c9 .} ==> r5c7≠2 t-whip[4]: r1c2{n2 n5} - c3n5{r3 r4} - r4n6{c3 c7} - c7n2{r4 .} ==> r2c2≠2, r1c9≠2 whip[5]: r1n9{c9 c5} - r9n9{c5 c6} - b5n9{r6c6 r5c4} - c4n2{r5 r3} - b3n2{r3c8 .} ==> r2c7≠9 whip[5]: r2c7{n2 n5} - r1c9{n5 n9} - b2n9{r1c5 r3c4} - r8c4{n9 n5} - b9n5{r8c7 .} ==> r2c6≠2 hidden-single-in-a-row ==> r2c7=2 biv-chain[3]: b3n5{r3c8 r1c9} - r1c2{n5 n2} - b2n2{r1c5 r3c4} ==> r3c4≠5 t-whip[2]: c4n5{r5 r8} - r9n5{c6 .} ==> r5c7≠5 z-chain[3]: b3n5{r3c8 r1c9} - b2n5{r1c5 r2c6} - b5n5{r6c6 .} ==> r5c8≠5 biv-chain[3]: b3n9{r1c9 r3c8} - c8n5{r3 r8} - r8c4{n5 n9} ==> r8c9≠9 z-chain[3]: b3n5{r3c8 r1c9} - r6n5{c9 c6} - r2n5{c6 .} ==> r3c2≠5 z-chain[4]: r1n9{c9 c5} - c6n9{r2 r9} - c6n2{r9 r6} - r6c1{n2 .} ==> r6c9≠9 z-chain[4]: r5c8{n9 n2} - r7n2{c8 c9} - c9n8{r7 r8} - c9n6{r8 .} ==> r5c9≠9 z-chain[4]: r5c8{n9 n2} - r5c4{n2 n5} - r8c4{n5 n9} - b9n9{r8c8 .} ==> r5c7≠9 z-chain[4]: c8n5{r3 r8} - r8c4{n5 n9} - r5n9{c4 c5} - r1n9{c5 .} ==> r3c8≠9 singles ==> r3c8=5, r1c9=9 biv-chain[3]: b2n5{r1c5 r2c6} - b2n9{r2c6 r3c4} - r8c4{n9 n5} ==> r9c5≠5 biv-chain[3]: r9c5{n9 n2} - b2n2{r1c5 r3c4} - b2n9{r3c4 r2c6} ==> r9c6≠9 biv-chain[2]: b8n9{r9c5 r8c4} - c8n9{r8 r5} ==> r5c5≠9 biv-chain[4]: b4n2{r4c1 r6c1} - r6n9{c1 c6} - b2n9{r2c6 r3c4} - b2n2{r3c4 r1c5} ==> r4c5≠2 z-chain[4]: r8c4{n9 n5} - r9c6{n5 n2} - b5n2{r6c6 r5c5} - r5c8{n2 .} ==> r5c4≠9 singles ==> r5c8=9, r8c8=1, r7c8=2, r7c9=8, r7c6=1, r8c6=8, r5c7=8 naked-pairs-in-a-row: r4{c3 c7}{n5 n6} ==> r4c9≠5, r4c2≠5 biv-chain[3]: r5c4{n2 n5} - r8c4{n5 n9} - r9c5{n9 n2} ==> r5c5≠2 biv-chain[3]: c4n5{r8 r5} - r5n2{c4 c9} - c9n6{r5 r8} ==> r8c9≠5 stte

The New Sudoku Players' Forum

#42693, many tridagon eliminations again

#42693, many tridagon eliminations again

Re: #42693, many tridagon eliminations again

Re: #42693, many tridagon eliminations again

Re: #42693, many tridagon eliminations again

Re: #42693, many tridagon eliminations again

Re: #42693, many tridagon eliminations again

Re: #42693, many tridagon eliminations again

Re: #42693, many tridagon eliminations again