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Website · by **denis_berthier** » Mon Aug 29, 2022 10:48 am

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#20958 in mith's collection of 63137 min-expand T&E(3) puzzles

Code: Select all: +-------+-------+-------+ ! 1 . . ! . . 6 ! . 8 . ! ! . . . ! . . . ! 2 . . ! ! 6 . . ! . 7 2 ! . 1 4 ! +-------+-------+-------+ ! 2 7 5 ! . . . ! . . . ! ! 3 6 9 ! . . . ! . . . ! ! 8 4 1 ! . 6 7 ! . . . ! +-------+-------+-------+ ! . 8 . ! . 2 1 ! 6 7 . ! ! . 1 . ! . . 8 ! . 4 . ! ! . . . ! . 4 . ! 1 . 8 ! +-------+-------+-------+ 1....6.8.......2..6...72.14275......369......841.67....8..2167..1...8.4.....4.1.8;4357;362565 SER = 10.2

[Edit]:added number in title

by **DEFISE** » Tue Aug 30, 2022 9:39 am

After basics:

Code: Select all: |----------------------------------------------------------------------| | 1 2359 234 | 3459 359* 6 | 7 8 359* | | 4579 359 3478 | 134589 13589 3459* | 2 359* 6 | | 6 359 38 | 3589* 7 2 | 359* 1 4 | |----------------------------------------------------------------------| | 2 7 5 | 3489 389 349 | 48 6 1 | | 3 6 9 | 12458 158 45 | 48 25 7 | | 8 4 1 | 25 6 7 | 359 2359 2359 | |----------------------------------------------------------------------| | 459 8 34 | 359* 2 1 | 6 359* | | 579 1 2367 | 67 359* 8 | 359* 4 2359 | | 579 2359 2367 | 67 4 359* | 1 2359* 8 | |----------------------------------------------------------------------|

Tridaggon anti-diag: 3,5,9 in B2,B3,B8,B9 (cells tagged *)
3 guardians : 4r2c6, 8r3c4, 2r9c8.

Each of these 3 partial whips from 2r1c3 see one different guardian :

1) r1n4{c3 c4}
2) b1{4r1c3 HP:47p46}- c3n8{r2 r3}
3) c2n2{r1 r9}- r8n2{c3 c9}

So 2r1c3 is false.

N.B: we can also say that the following partial braid (from 2r1c3) sees the 3 guardians:
Partial S2-braid[5]: r1n4{c3 c4}- b1{4r1c3 HP:47p46}- c3n8{r2 r3}- c2n2{r1 r9}- r8n2{c3 c9}

After removing 2r1c3 the puzzle is solvable in W8.

by **eleven** » Tue Aug 30, 2022 3:35 pm

Code: Select all: +-------------------------+-------------------------+-------------------------+ | 1 2359 234 | 3459 359 6 | 7 8 359 | | 4579 359 *3478 | 134589 13589 3459 | 2 359 6 | | 6 359 38 | 3589 7 2 | 359 1 4 | +-------------------------+-------------------------+-------------------------+ | 2 7 5 | 3489 389 349 | 48 6 1 | | 3 6 9 | 12458 158 45 | 48 25 7 | | 8 4 1 | 25 6 7 | 359 2359 2359 | +-------------------------+-------------------------+-------------------------+ | 459 8 34 | 359 2 1 | 6 7 359 | | 579 1 #2367 |#67 359 8 | 359 4 2359 | | 579 2359 #2367 |#67 4 359 | 1 2359 8 | +-------------------------+-------------------------+-------------------------+

UR 67r89c34 => r2c3=7, hidden pair 18r2c45

Code: Select all: +----------------------+----------------------+----------------------+ | 1 2359 234 | 3459 359 6 | 7 8 359 | | 459 359 7 |#18 #18 3459 | 2 359 6 | | 6 359 8 | 359 7 2 | 359 1 4 | +----------------------+----------------------+----------------------+ | 2 7 5 | 389 389 39 | 48 6 1 | | 3 6 9 |#12458 #158 45 |*48 25 7 | | 8 4 1 | 25 6 7 | 359 2359 2359 | +----------------------+----------------------+----------------------+ | 459 8 34 | 359 2 1 | 6 7 359 | | 579 1 236 | 67 359 8 | 359 4 2359 | | 579 2359 236 | 67 4 359 | 1 2359 8 | +----------------------+----------------------+----------------------+

UR 18r25c56 => r5c7=8

Code: Select all: +-------------------+-------------------+-------------------+ | 1 2359 234 | 3459 #359 6 | 7 8 #359 | | 459 359 7 | 18 18 #359+4 | 2 #359 6 | | 6 359 8 |#359 7 2 |#359 1 4 | +-------------------+-------------------+-------------------+ | 2 7 5 | 389 389 39 | 4 6 1 | | 3 6 9 | 124-5 1-5 a45 | 8 b25 7 | | 8 4 1 | 25 6 7 | 359 2359 2359 | +-------------------+-------------------+-------------------+ | 459 8 34 |#359 2 1 | 6 7 #359 | | 579 1 236 | 67 #359 8 |#359 4 2359 | | 579 2359 236 | 67 4 #359 | 1 #359+2 8 | +-------------------+-------------------+-------------------+

Tridagon 359 (#): 4r2c6 = 2r9c8
(5=4)r5c6 - 4r2c6 == 2r9c8 - (2=5)r5c8 => -5r5c45

Code: Select all: +-------------------+-------------------+-------------------+ | 1 2359 234 | 3459 359 6 | 7 8 359 | | 459 359 7 | 1 8 3459 | 2 359 6 | | 6 359 8 | 359 7 2 | 359 1 4 | +-------------------+-------------------+-------------------+ | 2 7 5 |#8 39 39 |#4 6 1 | | 3 6 9 |#2-4 1 45 |#8 25 7 | | 8 4 1 | 25 6 7 | 359 2359 2359 | +-------------------+-------------------+-------------------+ | 459 8 34 | 359 2 1 | 6 7 359 | | 579 1 236 | 67 359 8 | 359 4 2359 | | 579 2359 236 | 67 4 359 | 1 2359 8 | +-------------------+-------------------+-------------------+

UR1 48r45c47 => -4r5c4

Code: Select all: +-------------------+-------------------+-------------------+ | 1 2359 23 | 4 #359 6 | 7 8 #359 | | 4 359 7 | 1 8 #359 | 2 #39 6 | | 6 359 8 |#39 7 2 |#359 1 4 | +-------------------+-------------------+-------------------+ | 2 7 5 | 8 39 39 | 4 6 1 | | 3 6 9 | 2 1 4 | 8 5 7 | | 8 4 1 | 5 6 7 | 39 239 239 | +-------------------+-------------------+-------------------+ | 59 8 4 |#39 2 1 | 6 7 #359 | | 579 1 236 | 67 #359 8 |#359 4 2359 | | 579 23 236 | 67 4 #359 | 1 39-2 8 | +-------------------+-------------------+-------------------+

Same tridagon => r9c8=2
w-wing or skyscraper to finish.

Website · by **denis_berthier** » Tue Aug 30, 2022 4:08 pm

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Thanks for your solutions. I hadn't thought of trying uniqueness.

I (SudoRules speaking) have found a solution in W4 + OR2FW3 (what I consider easy for a puzzle in T&E(3):

Code: Select all: Resolution state after Singles and whips[1]: +----------------------+----------------------+----------------------+ ! 1 2359 2347 ! 3459 359 6 ! 3579 8 3579 ! ! 4579 359 3478 ! 134589 13589 3459 ! 2 3569 35679 ! ! 6 359 38 ! 3589 7 2 ! 359 1 4 ! +----------------------+----------------------+----------------------+ ! 2 7 5 ! 13489 1389 349 ! 3489 369 1369 ! ! 3 6 9 ! 12458 158 45 ! 4578 25 1257 ! ! 8 4 1 ! 2359 6 7 ! 359 2359 2359 ! +----------------------+----------------------+----------------------+ ! 459 8 34 ! 359 2 1 ! 6 7 359 ! ! 579 1 2367 ! 35679 359 8 ! 359 4 2359 ! ! 579 2359 2367 ! 35679 4 359 ! 1 2359 8 ! +----------------------+----------------------+----------------------+ 184 candidates

First, some easy cleaning with short bivalue-chains:

Code: Select all: hidden-pairs-in-a-column: c4{n6 n7}{r8 r9} ==> r9c4≠9, r9c4≠5, r9c4≠3, r8c4≠9, r8c4≠5, r8c4≠3 hidden-pairs-in-a-column: c7{n4 n8}{r4 r5} ==> r5c7≠7, r5c7≠5, r4c7≠9, r4c7≠3 singles ==> r5c9=7, r1c7=7, r4c9=1, r4c8=6, r2c9=6, r6c4≠3, r6c4≠9 biv-chain[3]: r7c3{n3 n4} - c1n4{r7 r2} - r2n7{c1 c3} ==> r2c3≠3 biv-chain[4]: r3c3{n8 n3} - r7c3{n3 n4} - c1n4{r7 r2} - r2n7{c1 c3} ==> r2c3≠8 hidden-single-in-a-block ==> r3c3=8 hidden-pairs-in-a-block: b2{n1 n8}{r2c4 r2c5} ==> r2c5≠9, r2c5≠5, r2c5≠3, r2c4≠9, r2c4≠5, r2c4≠4, r2c4≠3 +-------------------+-------------------+-------------------+ ! 1 2359 234 ! 3459 359 6 ! 7 8 359 ! ! 4579 359 47 ! 18 18 3459 ! 2 359 6 ! ! 6 359 8 ! 359 7 2 ! 359 1 4 ! +-------------------+-------------------+-------------------+ ! 2 7 5 ! 3489 389 349 ! 48 6 1 ! ! 3 6 9 ! 12458 158 45 ! 48 25 7 ! ! 8 4 1 ! 25 6 7 ! 359 2359 2359 ! +-------------------+-------------------+-------------------+ ! 459 8 34 ! 359 2 1 ! 6 7 359 ! ! 579 1 2367 ! 67 359 8 ! 359 4 2359 ! ! 579 2359 2367 ! 67 4 359 ! 1 2359 8 ! +-------------------+-------------------+-------------------+

Here's now the tridagon part, with an anti-tridagon with 2 guardians, leading to 5 easy eliminations, based on 5 different pairs of partial-whips:

Code: Select all: OR2-anti-tridagon[12] (type antidiag) for digits 3, 5 and 9 in blocks: b2, with cells: r1c5, r2c6, r3c4 b3, with cells: r1c9, r2c8, r3c7 b8, with cells: r8c5, r9c6, r7c4 b9, with cells: r8c7, r9c8, r7c9 with 2 guardians: n4r2c6 n2r9c8 OR2-forcing-whip-elim[3] based on OR2-anti-tridagon[12] for n2r9c8 and n4r2c6: || n2r9c8 - || n4r2c6 - partial-whip[2]: r5c6{n4 n5} - r5c8{n5 n2} - ==> r6c8≠2 OR2-forcing-whip-elim[3] based on OR2-anti-tridagon[12] for n2r9c8 and n4r2c6: || n2r9c8 - || n4r2c6 - partial-whip[2]: r1n4{c4 c3} - r1n2{c3 c2} - ==> r9c2≠2 hidden-single-in-a-column ==> r1c2=2 naked-pairs-in-a-column: c3{r1 r7}{n3 n4} ==> r9c3≠3, r8c3≠3, r2c3≠4 naked-single ==> r2c3=7 OR2-forcing-whip-elim[3] based on OR2-anti-tridagon[12] for n2r9c8 and n4r2c6: || n2r9c8 - partial-whip[1]: r5n2{c8 c4} - || n4r2c6 - partial-whip[1]: r5c6{n4 n5} - ==> r5c4≠5 OR2-forcing-whip-elim[3] based on OR2-anti-tridagon[12] for n2r9c8 and n4r2c6: || n2r9c8 - partial-whip[1]: r5c8{n2 n5} - || n4r2c6 - partial-whip[1]: r5c6{n4 n5} - ==> r5c5≠5 naked-pairs-in-a-column: c5{r2 r5}{n1 n8} ==> r4c5≠8 OR2-forcing-whip-elim[3] based on OR2-anti-tridagon[12] for n4r2c6 and n2r9c8: || n4r2c6 - || n2r9c8 - partial-whip[2]: r5c8{n2 n5} - r5c6{n5 n4} - ==> r4c6≠4

The end is standard business in W4:

Code: Select all: naked-pairs-in-a-block: b5{r4c5 r4c6}{n3 n9} ==> r4c4≠9, r4c4≠3 finned-x-wing-in-columns: n3{c3 c4}{r7 r1} ==> r1c5≠3 whip[4]: c5n5{r1 r8} - c4n5{r7 r6} - r1n5{c4 c9} - c7n5{r3 .} ==> r2c6≠5 biv-chain[5]: c6n5{r9 r5} - r5c8{n5 n2} - r9n2{c8 c3} - r9n6{c3 c4} - r9n7{c4 c1} ==> r9c1≠5 finned-swordfish-in-rows: n5{r5 r9 r2}{c8 c6 c2} ==> r3c2≠5 whip[1]: b1n5{r2c2 .} ==> r2c8≠5 biv-chain[2]: r3n5{c7 c4} - c5n5{r1 r8} ==> r8c7≠5 whip[4]: c3n3{r7 r1} - r3c2{n3 n9} - c4n9{r3 r1} - r1n4{c4 .} ==> r7c4≠3 whip[1]: c4n3{r3 .} ==> r2c6≠3 t-whip[3]: c1n4{r7 r2} - r2c6{n4 n9} - c4n9{r1 .} ==> r7c1≠9 finned-x-wing-in-rows: n9{r7 r1}{c9 c4} ==> r3c4≠9 biv-chain[3]: r7n9{c4 c9} - r8c7{n9 n3} - b8n3{r8c5 r9c6} ==> r9c6≠9 biv-chain[3]: r9c6{n3 n5} - r5n5{c6 c8} - c8n2{r5 r9} ==> r9c8≠3 biv-chain[4]: b8n3{r8c5 r9c6} - c6n5{r9 r5} - r6c4{n5 n2} - c9n2{r6 r8} ==> r8c9≠3 biv-chain[3]: r8n3{c7 c5} - r9n3{c6 c2} - r2n3{c2 c8} ==> r3c7≠3 t-whip[4]: r3n9{c2 c7} - c7n5{r3 r6} - c8n5{r5 r9} - c2n5{r9 .} ==> r2c2≠9 z-chain[4]: r5n5{c8 c6} - r9n5{c6 c2} - r2c2{n5 n3} - c8n3{r2 .} ==> r6c8≠5 naked-pairs-in-a-column: c8{r2 r6}{n3 n9} ==> r9c8≠9 whip[1]: r9n9{c2 .} ==> r8c1≠9 x-wing-in-columns: n5{c6 c8}{r5 r9} ==> r9c2≠5 singles ==> r2c2=5, r2c8=3, r6c8=9 naked-pairs-in-a-row: r1{c5 c9}{n5 n9} ==> r1c4≠9, r1c4≠5 hidden-single-in-a-column ==> r7c4=9 x-wing-in-columns: n5{c4 c7}{r3 r6} ==> r6c9≠5 biv-chain[3]: b6n2{r6c9 r5c8} - c8n5{r5 r9} - r7c9{n5 n3} ==> r6c9≠3 stte

by **Cenoman** » Tue Aug 30, 2022 9:08 pm

Code: Select all: +-----------------------+--------------------------+----------------------+ | 1 b2359 b234 | 3459 359 6 | 7 8 359 | | 4579 b359 3478 | 134589 13589 3459 | 2 359 6 | | 6 b359 8-3 | 3589 7 2 | 359 1 4 | +-----------------------+--------------------------+----------------------+ | 2 7 5 | 3489 389 349 | 48 6 1 | | 3 6 9 | 12458 158 45 | 48 25 7 | | 8 4 1 | 25 6 7 | 359 2359 2359 | +-----------------------+--------------------------+----------------------+ | 459 8 a34 | 359 2 1 | 6 7 359 | | 579 1 2367 | 67 359 8 | 359 4 2359 | | 579 2359 2367 | 67 4 359 | 1 2359 8 | +-----------------------+--------------------------+----------------------+

1. (3=4)r7c3 - (4=2593)b1p2357 => -3 r3c3; lcls, 1 placement

Code: Select all: +-----------------------+-----------------------+----------------------+ | 1 2359 234 | a3459 359 6 | 7 8 359 | | 4579 359 347 | *18 *18 359-4 | 2 359 6 | | 6 359 8 | 359 7 2 | 359 1 4 | +-----------------------+-----------------------+----------------------+ | 2 7 5 | *3489 389 349 | *48 6 1 | | 3 6 9 | *12458 b*158 c45 | *48 25 7 | | 8 4 1 | 25 6 7 | 359 2359 2359 | +-----------------------+-----------------------+----------------------+ | 459 8 34 | 359 2 1 | 6 7 359 | | 579 1 2367 | 67 359 8 | 359 4 2359 | | 579 2359 2367 | 67 4 359 | 1 2359 8 | +-----------------------+-----------------------+----------------------+

2. MUG (148)r2c45, r4c47, r5c457 using mixed external-internal:
(4)r1c4 == (5)r5c5 - (5=4)r5c6 => -4 r2c6; lcls, 1 placement

Code: Select all: +----------------------+---------------------+----------------------+ | 1 2359 23 | 4 *359 6 | 7 8 *359 | | 47 359 47 | 18 18 *359 | 2 *359 6 | | 6 359 8 | *359 7 2 | *359 1 4 | +----------------------+---------------------+----------------------+ | 2 7 5 | 389 389 349 | 48 6 1 | | 3 6 9 | 1258 158 45 | 48 25 7 | | 8 4 1 | 25 6 7 | 359 2359 2359 | +----------------------+---------------------+----------------------+ | 459 8 34 | *359 2 1 | 6 7 *359 | | 579 1 2367 | 67 *359 8 | *359 4 2359 | | 579 23 2367 | 67 4 *359 | 1 *359+2 8 | +----------------------+---------------------+----------------------+

3. TH (359)b2389 having a single internal => +2 r9c8; lcls, 23 placements
(or tridagon, if you prefer that name)

Code: Select all: +-----------------+-------------------+-------------------+ | 1 2 3 | 4 *59 6 | 7 8 *59 | | 4 59 7 | 1 8 359 | 2 39 6 | | 6 59 8 | 39 7 2 | *359 1 4 | +-----------------+-------------------+-------------------+ | 2 7 5 | 8 39 39 | 4 6 1 | | 3 6 9 | 2 1 4 | 8 5 7 | | 8 4 1 | 5 6 7 | 39 39 2 | +-----------------+-------------------+-------------------+ | 59 8 4 | 39 2 1 | 6 7 359 | | 7 1 2 | 6 39-5 8 | *59 4 359 | | 59 3 6 | 7 4 59 | 1 2 8 | +-----------------+-------------------+-------------------+

4. Kite (5)r1c5 = r1c9 - r3c7 = r8c7 => -5 r8c5; ste

The New Sudoku Players' Forum

#20958, easy puzzle (for one in T&E(3))

#20958, easy puzzle (for one in T&E(3))

Re: easy puzzle (for one in T&E(3))

Re: easy puzzle (for one in T&E(3))

Re: easy puzzle (for one in T&E(3))

Re: easy puzzle (for one in T&E(3))