The New Sudoku Players' Forum

Website · by **denis_berthier** » Thu Sep 01, 2022 3:45 am

.
If you liked the puzzle there: http://forum.enjoysudoku.com/many-tridagon-eliminations-t40287.html, you'll like the following.

Code: Select all: #45728 in mith's database of 63,137 min-expand puzzles +-------+-------+-------+ ! . 2 3 ! . 5 . ! 7 . 9 ! ! . 5 . ! . . . ! . 3 2 ! ! 7 . 9 ! 2 3 . ! . . . ! +-------+-------+-------+ ! 2 3 . ! . . 4 ! . 7 5 ! ! . 4 . ! . . . ! . 9 . ! ! 9 . . ! . . . ! 3 . 4 ! +-------+-------+-------+ ! . . . ! . 4 5 ! . . 7 ! ! . 9 2 ! . 6 7 ! . . . ! ! . 7 4 ! 1 2 . ! . . . ! +-------+-------+-------+ .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

Code: Select all: Resolution state after Singles and whips[1]: +-------------------+-------------------+-------------------+ ! 1468 2 3 ! 468 5 168 ! 7 168 9 ! ! 1468 5 168 ! 46789 1789 1689 ! 168 3 2 ! ! 7 168 9 ! 2 3 168 ! 14568 14568 168 ! +-------------------+-------------------+-------------------+ ! 2 3 168 ! 689 189 4 ! 168 7 5 ! ! 168 4 15678 ! 35678 178 12368 ! 1268 9 168 ! ! 9 168 15678 ! 5678 178 1268 ! 3 1268 4 ! +-------------------+-------------------+-------------------+ ! 1368 168 168 ! 389 4 5 ! 12689 1268 7 ! ! 1358 9 2 ! 38 6 7 ! 1458 1458 138 ! ! 3568 7 4 ! 1 2 389 ! 5689 568 368 ! +-------------------+-------------------+-------------------+ 174 candidates

[Edit]: added number in the name

by **DEFISE** » Thu Sep 01, 2022 9:47 am

After basics :

Code: Select all: |-------------------------------------------------------------| | 1468* 2 3 | 468 5 168 | 7 168* 9 | | 1468 5 168* | 46789 1789 1689 | 168* 3 2 | | 7 168* 9 | 2 3 168 | 45 45 168* | |-------------------------------------------------------------| | 2 3 168* | 689 189 4 | 168* 7 5 | | 168* 4 57 | 35678 178 12368 | 1268 9 168* | | 9 168* 57 | 5678 178 1268 | 3 1268* 4 | |-------------------------------------------------------------| | 1368 168 168 | 389 4 5 | 12689 1268 7 | | 1358 9 2 | 38 6 7 | 1458 1458 138 | | 3568 7 4 | 1 2 389 | 5689 568 368 | |-------------------------------------------------------------|

Tridagon diag: 1,6,8 in B1,B3,B4,B6 (cells tagged with *)
2 guardians : 4r1c1, 2r6c8

This partial whip from 9r9c6 see 2r6c8:
r7n9{c4 c7}- r7n2{c7 c8}

And this partial S3-whip also from 9r9c6 see 4r1c1:
b2n9{r2c6 NT:168p369}- r1c4{n6 n4}

So 9r9c6 is false. Then the puzzle is solvable in W7 :

Single(s): 9r9c7, 9r7c4, 9r4c5, 9r2c6, 3r7c1
Hidden pairs: 45c7r38 => -1r8c7 -8r8c7
whip[6]: c5n8{r5 r2}- c3n8{r2 r7}- c7n8{r7 r5}- r5n2{c7 c6}- r5n3{c6 c4}- r8c4{n3 .} => -8r4c4
Single(s): 6r4c4
whip[7]: r4n8{c7 c3}- c2n8{r6 r3}- c9n8{r3 r5}- r4c7{n8 n1}- r2c7{n1 n6}- r5n6{c7 c1}
- b1n6{r1c1 .} => -8r7c7
whip[7]: r4n1{c7 c3}- c2n1{r6 r3}- r2n1{c1 c5}- r1n1{c6 c8}- r6n1{c8 c6}- r6n2{c6 c8}- r7n2{c8 .} => -1r7c7
whip[4]: r5n6{c7 c1}- r9n6{c1 c9}- r7c7{n6 n2}- c8n2{r7 .} => -6r6c8
Single(s): 6r6c2
whip[7]: r4c7{n8 n1}- r4c3{n1 n8}- r7n8{c3 c2}- r3c2{n8 n1}- r2n1{c1 c5}- r6n1{c5 c6}- r6n2{c6 .} => -8r6c8
Box/Line: 8r6b5 => -8r5c4 -8r5c5 -8r5c6
whip[7]: r4c7{n1 n8}- r4c3{n8 n1}- r7n1{c3 c2}- r8n1{c1 c9}- r5c9{n1 n6}- r3c9{n6 n8}- r3c2{n8 .} => -1r6c8
Single(s): 2r6c8, 2r5c6, 3r5c4, 8r8c4, 4r1c4, 7r2c4, 5r6c4, 7r6c3, 5r5c3, 3r9c6, 4r2c1, 7r5c5, 2r7c7, 3r8c9
Box/Line: 1b9c8 => -1r1c8
whip[5]: r2n6{c3 c7}- r1c8{n6 n8}- r3c9{n8 n1}- r3c2{n1 n8}- r7n8{c2 .} => -6r7c3
STTE

by **Cenoman** » Thu Sep 01, 2022 9:01 pm

After lcls, 33 solved cells, 162 candidates

Code: Select all: +---------------------+-------------------------+-----------------------+ | *1468 2 3 | 468 5 168 | 7 *168 9 | | 1468 5 *168 | 46789 1789 1689 | *168 3 2 | | 7 *168 9 | 2 3 168 | 45 45 *168 | +---------------------+-------------------------+-----------------------+ | 2 3 *168 | 689 189 4 | *168 7 5 | | *168 4 57 | 35678 178 12368 | 1268 9 *168 | | 9 *168 57 | 5678 178 1268 | 3 *1268 4 | +---------------------+-------------------------+-----------------------+ | 1368 168 168 | 389 4 5 | 12689 1268 7 | | 1358 9 2 | 38 6 7 | 1458 1458 138 | | 3568 7 4 | 1 2 389 | 5689 568 368 | +---------------------+-------------------------+-----------------------+

TH (168)b1346*, having two guardians: 4r1c1, 2r6c8
1. (168=2)r136c6 - (2)r6c8 == (4)r1c1 - (4=168)r2c137 => -168 r2c6; lcls, 5 placements

2. (89=3)r78c4 - r5c4 = (3-2)r5c6 = r6c6 - (2)r6c8 == (4)r1c1 - r1c4 = (4-7)r2c4 = r2c5 - (7=189)r456c5 => -89 r4c4; lcls, 1 placement

3. (8)r78c4 = r9c6 - (8=162)r136c6 - (2)r6c8 == (4)r1c1 - r1c4 = r2c4 - (4=3698)r1478c4 => -8 r256c4

4. (2)r5c6 = r6c6 - (2)r6c8 == (4)r1c1 - (4=168)b2p139 => -168 r5c6

Resulting resolution state (39 solved cells, 119 candidates), hence a total of 37 eliminations (each of these could be shown eliminated by a chain containing the node (2)r6c8 == (4)r1c1)

Code: Select all: +---------------------+--------------------+----------------------+ | 1468 2 3 | 48 5 168 | 7 168 9 | | 1468 5 168 | 47 178 9 | 168 3 2 | | 7 168 9 | 2 3 168 | 45 45 168 | +---------------------+--------------------+----------------------+ | 2 3 18 | 6 9 4 | 18 7 5 | | 168 4 57 | 357 178 23 | 1268 9 168 | | 9 168 57 | 57 18 128 | 3 1268 4 | +---------------------+--------------------+----------------------+ | 3 168 168 | 9 4 5 | 1268 1268 7 | | 158 9 2 | 38 6 7 | 45 1458 138 | | 568 7 4 | 1 2 38 | 9 568 368 | +---------------------+--------------------+----------------------+

Complete solution of the puzzle:
After the first three steps above, using the TH pattern, the resolution state is:

Code: Select all: +---------------------+---------------------+----------------------+ | 1468 2 3 | 48 5 168 | 7 168 9 | | 1468 5 168 | 47 178 9 | 168 3 2 | | 7 168 9 | 2 3 168 | 45 45 168 | +---------------------+---------------------+----------------------+ | 2 3 18 | 6 9 4 | 18 7 5 | | 168 4 *57 | *57+3 178 1238 | 1268 9 168 | | 9 168 *57 | *57 18 128 | 3 168+2 4 | +---------------------+---------------------+----------------------+ | 3 168 168 | 9 4 5 | 1268 1268 7 | | 158 9 2 | 38 6 7 | 45 1458 138 | | 568 7 4 | 1 2 38 | 9 568 368 | +---------------------+---------------------+----------------------+

4; UR (57)r56c34 using single internal => +3 r5c4; lcls, 11 placements, among which +4r2c1.
5. Hence, TH guardian 4r1c1 is False => +2 r6c8, lcls, 4 placements

Code: Select all: +-------------------+------------------+--------------------+ | c168 2 3 | 4 5 b168 | 7 8-6 9 | | 4 5 *16-8 | 7 a18 9 | *168 3 2 | | 7 d18 9 | 2 3 16-8 | 45 45 168 | +-------------------+------------------+--------------------+ | 2 3 18 | 6 9 4 | 18 7 5 | | 18 4 5 | 3 7 2 | 168 9 168 | | 9 6 7 | 5 18 18 | 3 2 4 | +-------------------+------------------+--------------------+ | 3 18 *168 | 9 4 5 | 2 *168 7 | | 15 9 2 | 8 6 7 | 45 145 3 | | 568 7 4 | 1 2 3 | 9 568 68 | +-------------------+------------------+--------------------+

6. Skyscraper (6)r2c7 = r2c3 - r7c3 = r7c8 => -6 r1c8
7. W-Wing (8=1)r2c5 - r1c6 = r1c1 - (1=8)r3c2 => -8 r2c3, r3c6; ste

by **pjb** » Fri Sep 02, 2022 12:53 am

Similar to Cenoman:
After applying type 2 TH 4 times:

Code: Select all: 1468 2 3 | 468 5 168 | 7 168 9 1468 5 168 | 47 178 9 | 168 3 2 7 168 9 | 2 3 168 | 45 45 168 ------------------------+----------------------+--------------------- 2 3 168 | 68 9 4 | 168 7 5 168 4 57 | 35678 178 12368 | 1268 9 168 9 168 57 | 5678 178 1268 | 3 1268 4 ------------------------+----------------------+--------------------- 3 168 168 | 9 4 5 | 1268 1268 7 158 9 2 | 38 6 7 | 45 1458 138 568 7 4 | 1 2 38 | 9 568 368

Then:
Type 1 unique rectangle of 45 at r38c78 => -45 r8c8
Type 3 unique rectangle of 57 at r56c34 => -68 r1c4 =>

Code: Select all: *168 2 3 | 4 5 168 | 7 *168 9 4 5 *168 | 7 18 9 |*168 3 2 7 *168 9 | 2 3 168 | 5 4 *168 ------------------------+----------------------+--------------------- 2 3 *168 | 68 9 4 |*168 7 5 *168 4 57 | 3568 178 1238 | 1268 9 *168 9 *168 57 | 568 178 128 | 3 *2-168 4 ------------------------+----------------------+--------------------- 3 168 168 | 9 4 5 | 268 268 7 5 9 2 | 38 6 7 | 4 18 138 68 7 4 | 1 2 38 | 9 5 368

Then type 1 TH => -168 r6c8
Finally (6)r1c1 = (6)r9c1 - (6)r7c3 = (6)r7c8 => -6 r1c8; stte

Phil

Website · by **denis_berthier** » Fri Sep 02, 2022 4:36 am

Cenoman wrote:TH (168)b1346*, having two guardians: 4r1c1, 2r6c8
1. (168=2)r136c6 - (2)r6c8 == (4)r1c1 - (4=168)r2c137 => -168 r2c6; lcls, 5 placements
2. (89=3)r78c4 - r5c4 = (3-2)r5c6 = r6c6 - (2)r6c8 == (4)r1c1 - r1c4 = (4-7)r2c4 = r2c5 - (7=189)r456c5 => -89 r4c4; lcls, 1 placement
3. (8)r78c4 = r9c6 - (8=162)r136c6 - (2)r6c8 == (4)r1c1 - r1c4 = r2c4 - (4=3698)r1478c4 => -8 r256c4
4. (2)r5c6 = r6c6 - (2)r6c8 == (4)r1c1 - (4=168)b2p139 => -168 r5c6
Resulting resolution state (39 solved cells, 119 candidates), hence a total of 37 eliminations (each of these could be shown eliminated by a chain containing the node (2)r6c8 == (4)r1c1)

It doesn't really matter much, but I count 3+2+3+3 = 11 direct eliminations with TH. The other ones are circumstantial consequences of them.
.

Website · by **denis_berthier** » Fri Sep 02, 2022 9:20 am

.
Starting from the resolution state after Whips[1]:

Code: Select all: hidden-pairs-in-a-column: c3{n5 n7}{r5 r6} ==> r6c3≠8, r6c3≠6, r6c3≠1, r5c3≠8, r5c3≠6, r5c3≠1 hidden-pairs-in-a-row: r3{n4 n5}{c7 c8} ==> r3c8≠8, r3c8≠6, r3c8≠1, r3c7≠8, r3c7≠6, r3c7≠1 t-whip[4]: c6n3{r5 r9} - r8c4{n3 n8} - r7c4{n8 n9} - r4c4{n9 .} ==> r5c6≠6 whip[4]: r2n7{c4 c5} - c5n9{r2 r4} - r4c4{n9 n8} - c5n8{r4 .} ==> r2c4≠6 t-whip[5]: c6n2{r6 r5} - r5n3{c6 c4} - r8c4{n3 n8} - r7c4{n8 n9} - r4c4{n9 .} ==> r6c6≠6 whip[1]: c6n6{r3 .} ==> r1c4≠6 +-------------------+-------------------+-------------------+ ! 1468 2 3 ! 48 5 168 ! 7 168 9 ! ! 1468 5 168 ! 4789 1789 1689 ! 168 3 2 ! ! 7 168 9 ! 2 3 168 ! 45 45 168 ! +-------------------+-------------------+-------------------+ ! 2 3 168 ! 689 189 4 ! 168 7 5 ! ! 168 4 57 ! 35678 178 1238 ! 1268 9 168 ! ! 9 168 57 ! 5678 178 128 ! 3 1268 4 ! +-------------------+-------------------+-------------------+ ! 1368 168 168 ! 389 4 5 ! 12689 1268 7 ! ! 1358 9 2 ! 38 6 7 ! 1458 1458 138 ! ! 3568 7 4 ! 1 2 389 ! 5689 568 368 ! +-------------------+-------------------+-------------------+

Code: Select all: OR2-anti-tridagon[12] (type antidiag) for digits 1, 6 and 8 in blocks: b1, with cells: r1c1, r2c3, r3c2 b3, with cells: r1c8, r2c7, r3c9 b4, with cells: r5c1, r4c3, r6c2 b6, with cells: r5c9, r4c7, r6c8 with 2 guardians: n4r1c1 n2r6c8 OR2-forcing-whip-elim[4] based on OR2-anti-tridagon[12] for n2r6c8 and n4r1c1: || n2r6c8 - partial-whip[1]: r5n2{c7 c6} - || n4r1c1 - partial-whip[2]: r1c4{n4 n8} - b8n8{r7c4 r9c6} - ==> r5c6≠8 OR2-forcing-whip-elim[4] based on OR2-anti-tridagon[12] for n4r1c1 and n2r6c8: || n4r1c1 - partial-whip[1]: r1c4{n4 n8} - || n2r6c8 - partial-whip[2]: c7n2{r5 r7} - r7n9{c7 c4} - ==> r7c4≠8 z-chain[4]: b8n8{r8c4 r9c6} - r9n9{c6 c7} - c7n5{r9 r3} - c7n4{r3 .} ==> r8c7≠8 OR2-forcing-whip-elim[4] based on OR2-anti-tridagon[12] for n4r1c1 and n2r6c8: || n4r1c1 - partial-whip[1]: r1c4{n4 n8} - || n2r6c8 - partial-whip[2]: r5n2{c7 c6} - r5n3{c6 c4} - ==> r5c4≠8 OR2-forcing-whip-elim[4] based on OR2-anti-tridagon[12] for n4r1c1 and n2r6c8: || n4r1c1 - partial-whip[1]: r2n4{c1 c4} - || n2r6c8 - partial-whip[2]: c7n2{r5 r7} - r7n9{c7 c4} - ==> r2c4≠9 OR2-forcing-whip-elim[5] based on OR2-anti-tridagon[12] for n2r6c8 and n4r1c1: || n2r6c8 - partial-whip[1]: c7n2{r5 r7} - || n4r1c1 - partial-whip[3]: r1c4{n4 n8} - b8n8{r8c4 r9c6} - b8n9{r9c6 r7c4} - ==> r7c7≠9 singles ==> r9c7=9, r7c4=9, r4c5=9, r2c6=9, r7c1=3 hidden-pairs-in-a-column: c7{n4 n5}{r3 r8} ==> r8c7≠1 OR2-forcing-whip-elim[5] based on OR2-anti-tridagon[12] for n2r6c8 and n4r1c1: || n2r6c8 - partial-whip[2]: r5n2{c7 c6} - r5n3{c6 c4} - || n4r1c1 - partial-whip[2]: r1c4{n4 n8} - r4c4{n8 n6} - ==> r5c4≠6 OR2-forcing-whip-elim[5] based on OR2-anti-tridagon[12] for n2r6c8 and n4r1c1: || n2r6c8 - partial-whip[1]: r5n2{c7 c6} - || n4r1c1 - partial-whip[3]: r1c4{n4 n8} - b8n8{r8c4 r9c6} - c6n3{r9 r5} - ==> r5c6≠1 z-chain[5]: r5n6{c9 c1} - r9n6{c1 c9} - r9n3{c9 c6} - r5c6{n3 n2} - b6n2{r5c7 .} ==> r6c8≠6 OR2-forcing-whip-elim[5] based on OR2-anti-tridagon[12] for n4r1c1 and n2r6c8: || n4r1c1 - partial-whip[1]: r1c4{n4 n8} - || n2r6c8 - partial-whip[3]: r5n2{c7 c6} - c6n3{r5 r9} - r8c4{n3 n8} - ==> r6c4≠8, r4c4≠8 singles ==> r4c4=6, r6c2=6 naked-pairs-in-a-row: r6{c3 c4}{n5 n7} ==> r6c5≠7 z-chain[4]: c2n8{r7 r3} - c9n8{r3 r5} - r5n6{c9 c7} - c7n2{r5 .} ==> r7c7≠8 z-chain[4]: c2n1{r7 r3} - c9n1{r3 r5} - r5n6{c9 c7} - c7n2{r5 .} ==> r7c7≠1 z-chain[5]: c1n4{r2 r1} - b1n6{r1c1 r2c3} - r2c7{n6 n1} - r4n1{c7 c3} - b4n8{r4c3 .} ==> r2c1≠8 z-chain[5]: c1n4{r2 r1} - b1n6{r1c1 r2c3} - r2c7{n6 n8} - r4n8{c7 c3} - b4n1{r4c3 .} ==> r2c1≠1 OR2-forcing-whip-elim[4] based on OR2-anti-tridagon[12] for n2r6c8 and n4r1c1: || n2r6c8 - || n4r1c1 - partial-whip[3]: r2c1{n4 n6} - b7n6{r9c1 r7c3} - c7n6{r7 r5} - ==> r5c7≠2 singles ==> r6c8=2, r5c6=2, r5c4=3, r8c4=8, r1c4=4, r2c4=7, r6c4=5, r6c3=7, r5c3=5, r9c6=3, r8c9=3, r5c5=7, r2c1=4, r7c7=2 whip[1]: b9n1{r8c8 .} ==> r1c8≠1 finned-x-wing-in-rows: n6{r7 r2}{c3 c8} ==> r1c8≠6 singles ==> r1c8=8, r9c9=8, r5c1=8, r4c3=1, r4c7=8 biv-chain[3]: b3n1{r2c7 r3c9} - r3c2{n1 n8} - b2n8{r3c6 r2c5} ==> r2c5≠1 stte

by **Leren** » Tue Sep 06, 2022 6:26 am

With my newly minted Type 1 Trigadon code: first basics and then this:

Code: Select all: *------------------------------------------------------* | 1468 2 3 | 468 5 168 | 7 168 9 | | 1468 5 168 | 46789 189-7 1689 | 168 3 2 | | 7 168 9 | 2 3 168 | 45 45 168 | |---------------+---------------------+----------------| | 2 3 168 | 689 189 4 | 168 7 5 | | 168 4 *57 |*3568-7 x78 12368 | 1268 9 168 | | 9 168 *57 |*568-7 x178 1268 | 3 1268 4 | |---------------+---------------------+----------------| | 1368 168 168 | 389 4 5 | 12689 1268 7 | | 1358 9 2 | 38 6 7 | 1458 1458 138 | | 3568 7 4 | 1 2 389 | 5689 568 368 | *------------------------------------------------------*

UR based AIC: r5c5 {7} = UR = r6c5 {7} => - 7 r2c5, r56c4. 3 placements and pointing triple;

Code: Select all: *----------------------------------------------------* |*168 2 3 | 4 5 168 | 7 *168 9 | | 4 5 *168 | 7 189 1689 |*168 3 2 | | 7 *168 9 | 2 3 168 | 45 45 *168 | |----------------+---------------+-------------------| | 2 3 *168 | 689 189 4 |*168 7 5 | |*168 4 57 | 3568 178 1238 | 1268 9 *168 | | 9 *168 57 | 568 178 128 | 3 *2-168 4 | |----------------+---------------+-------------------| | 1368 168 168 | 389 4 5 | 12689 1268 7 | | 1358 9 2 | 38 6 7 | 1458 1458 138 | | 3568 7 4 | 1 2 389 | 5689 568 368 | *----------------------------------------------------*

Type 1 Trigadon - Digits 168 in Boxes 1346.

Finishes off with a Skyscraper, a W Wing and basics. Works for me, no bugs .. yet

What's a Type 2 Trigadon and what's an Anti-Trigadon ?

Leren

Website · by **denis_berthier** » Tue Sep 06, 2022 6:33 am

Leren wrote:What's a Type 2 Trigadon and what's an Anti-Trigadon ?

http://forum.enjoysudoku.com/the-tridagon-rule-t39859.html
I'm making no difference between types 1 and 2.
Anti-tridagons:
http://forum.enjoysudoku.com/the-tridagon-rule-t39859-95.html
are the basis for ORk-Forcing-Whips:
http://forum.enjoysudoku.com/or-k-forcing-whips-t40189.html
a very powerful tool for puzzles in T&E(3).

by **Leren** » Tue Sep 06, 2022 9:38 am

Hi Denis, thanks for clarifying what an Anti-Trigagon is. It will take some time to understanding it fully but I''m patient.

Leren

The New Sudoku Players' Forum

#45728, still more tridagon eliminations.

#45728, still more tridagon eliminations.

Re: still more tridagon eliminations.

Re: still more tridagon eliminations.

Re: still more tridagon eliminations.

Re: still more tridagon eliminations.

Re: still more tridagon eliminations.

Re: #45728, still more tridagon eliminations.

Re: #45728, still more tridagon eliminations.

Re: #45728, still more tridagon eliminations.