The New Sudoku Players' Forum

by **Leren** » Sat Sep 18, 2021 9:37 am

Code: Select all: *-----------* |.4.|5..|.1.| |...|.3.|..6| |2..|9..|3..| |---+---+---| |.1.|7..|..9| |4..|.1.|.8.| |...|..6|...| |---+---+---| |3..|6..|...| |..2|.4.|..7| |.7.|.8.|.4.| *-----------* .4.5...1.....3...62..9..3...1.7....94...1..8......6...3..6.......2.4...7.7..8..4.

by **Cenoman** » Sat Sep 18, 2021 1:23 pm

Code: Select all: +------------------+-------------------+-------------------+ | 9 4 3 | 5 6 28 | 7 1 28 | | 7 58 158 | 48 3 ea1248# | d248 9 6 | | 2 6 18 | 9 7 148* | 3 5 48* | +------------------+-------------------+-------------------+ | 6 1 58 | 7 25 48* | c24 3 9 | | 4 2 7 | 3 1 9 | 6 8 5 | | 58 3 9 | 48* 25 6 | b124# 7 124* | +------------------+-------------------+-------------------+ | 3 58 4 | 6 9 7 | 158 2 18 | | 58 9 2 | 1 4 3 | 58 6 7 | | 1 7 6 | 2 8 5 | 9 4 3 | +------------------+-------------------+-------------------+

5-link oddagon (4)r36, c69, b5; two guardians (#)
(4)r2c6 == r6c7 - (4=2)r4c7 - r2c7 = (2)r2c6 => -18 r2c6; ste

by **SteveG48** » Sat Sep 18, 2021 4:38 pm

Code: Select all: *--------------------------------------------------------------* | 9 4 3 | 5 6 2-8 | 7 1 aeg28 | | 7 b58 158 |bg48 3 1248 |bfg24-8 9 6 | | 2 6 18 | 9 7 148 | 3 5 e48 | *-------------------+--------------------+---------------------| | 6 1 58 | 7 25 48 | 24 3 9 | | 4 2 7 | 3 1 9 | 6 8 5 | | 58 3 9 | 48 25 6 | 124 7 124 | *-------------------+--------------------+---------------------| | 3 c58 4 | 6 9 7 | 158 2 d18 | | 58 9 2 | 1 4 3 | 58 6 7 | | 1 7 6 | 2 8 5 | 9 4 3 | *--------------------------------------------------------------*

(8=2)r1c9 - (2=485)r2c247 - (5=8)r7c2 - r7c9 = r13c9 - 8r2c7 = (28)b3p34|(48)r2c47 => -8 r1c6,r2c7 ; stte

Or,

Code: Select all: *------------------------------------------------------------* | 9 4 3 | 5 6 c28 | 7 1 28 | | 7 5-8 15-8 |ad48 3 c124-8 |a248 9 6 | | 2 6 18 | 9 7 c148 | 3 5 48 | *-------------------+--------------------+-------------------| | 6 1 58 | 7 25 b48 |b24 3 9 | | 4 2 7 | 3 1 9 | 6 8 5 | | 58 3 9 | 48 25 6 | 124 7 124 | *-------------------+--------------------+-------------------| | 3 58 4 | 6 9 7 | 158 2 18 | | 58 9 2 | 1 4 3 | 58 6 7 | | 1 7 6 | 2 8 5 | 9 4 3 | *------------------------------------------------------------*

(8=42)r2c47 - (2=48)r4c67 - 8r123c6 = 8r2c4 => -8 r2c236 ; stte

by **P.O.** » Sat Sep 18, 2021 5:41 pm

Code: Select all: after singles: 6789 4 3 5 267 278 2789 1 28 15789 589 15789 1248 3 12478 245789 2579 6 2 568 15678 9 67 1478 3 57 458 568 1 568 7 b-2+5 2×3458 2456 2356 9 4 2×3569 5679 a+2-3 1 b+3-(259) 2567 8 2×35 5789 23589 5789 2×348 b-(25)+9 6 12457 2357 12345 3 589 4 6 2579 12579 12589 259 1258 15689 5689 2 13 4 1359 15689 3569 7 1569 7 1569 123 8 12359 12569 4 1235 depth: 1 candidate: 3 from cells (((4 6 5) (2 3 4 5 8)) ((5 2 4) (2 3 5 6 9)) ((5 9 6) (2 3 5)) ((6 4 5) (2 3 4 8))) ((3 0) (5 4 5) (2 3)) ((2 0) (5 4 5) (2 3)) ((3 1 113) (5 6 5) (2 3 5 9)) singles: ( r4c1b4 n6 r9c3b7 n6 r9c1b7 n1 r6c3b4 n9 r9c7b9 n9 r1c7b3 n7 r2c1b1 n7 r1c1b1 n9 r8c2b7 n9 r1c5b2 n6 r5c3b4 n7 r5c7b6 n6 r2c8b3 n9 r6c8b6 n7 r8c6b8 n3 r7c8b9 n2 r7c6b8 n7 r7c5b8 n9 r9c6b8 n5 r5c6b5 n9 r9c4b8 n2 r8c4b8 n1 r5c9b6 n5 r5c4b5 n3 r3c8b3 n5 r3c5b2 n7 r3c2b1 n6 r9c9b9 n3 r5c2b4 n2 r8c8b9 n6 r6c2b4 n3 r4c8b6 n3 ) 9 4 3 5 6 f+2-8 7 1 28 7 58 158 48 3 a-1×248 248 9 6 2 6 c-1+8 9 7 b+148 3 5 48 6 1 d5-8 7 25 e24+8 24 3 9 4 2 7 3 1 9 6 8 5 58 3 9 48 25 6 124 7 124 3 58 4 6 9 7 158 2 18 58 9 2 1 4 3 58 6 7 1 7 6 2 8 5 9 4 3 depth: 3 candidate: 2 from start ((1 0) (2 6 2) (1 2 4 8)) ((1 0) (3 6 2) (1 4 8)) ((8 1 9) (3 3 1) (1 8)) ((8 2 1) (4 6 5) (2 4 8)) ((2 3 9) (1 6 2) (2 8)) ste.

by **jco** » Sat Sep 18, 2021 6:01 pm

Code: Select all: .------------------------------------------. | 9 4 3 | 5 6 28 | 7 1 28 | | 7 b58 18-5|b48 3 1248 |b248 9 6 | | 2 6 18 | 9 7 148 | 3 5 48 | |-------------+--------------+-------------| | 6 1 a58 | 7 25 a48 |a24 3 9 | | 4 2 7 | 3 1 9 | 6 8 5 | | 58 3 9 | 48 25 6 | 124 7 124 | |-------------+--------------+-------------| | 3 58 4 | 6 9 7 | 158 2 18 | | 58 9 2 | 1 4 3 | 58 6 7 | | 1 7 6 | 2 8 5 | 9 4 3 | '------------------------------------------'

(5=842)r4c367 - (2=485)r2c247 => -5 r3c2; ste

by **Ngisa** » Sat Sep 18, 2021 9:14 pm

Code: Select all: +-------------------+--------------------+-------------------+ | 9 4 3 | 5 6 28 | 7 1 28 | | 7 58 f158 | 48 3 e1248 |d248 9 6 | | 2 6 f18 | 9 7 148 | 3 5 48 | +-------------------+--------------------+-------------------+ | 6 1 f58 | 7 b25 48 |c24 3 9 | | 4 2 7 | 3 1 9 | 6 8 5 | | 8-5 3 9 | 48 a25 6 | 124 7 124 | +-------------------+--------------------+-------------------+ | 3 58 4 | 6 9 7 | 158 2 18 | | 58 9 2 | 1 4 3 | 58 6 7 | | 1 7 6 | 2 8 5 | 9 4 3 | +-------------------+--------------------+-------------------+

(5=2)r6c5 - r4c5 = r4c7 - r2c7 = (2-1)r2c6 = (185)r234c3 => - 5r6c1; stte

Clement

Website · by **denis_berthier** » Mon Sep 20, 2021 3:45 am

.

Code: Select all: Resolution state after Singles and whips[1]: +----------------------+----------------------+----------------------+ ! 6789 4 3 ! 5 267 278 ! 2789 1 28 ! ! 15789 589 15789 ! 1248 3 12478 ! 245789 2579 6 ! ! 2 568 15678 ! 9 67 1478 ! 3 57 458 ! +----------------------+----------------------+----------------------+ ! 568 1 568 ! 7 25 23458 ! 2456 2356 9 ! ! 4 23569 5679 ! 23 1 2359 ! 2567 8 235 ! ! 5789 23589 5789 ! 2348 259 6 ! 12457 2357 12345 ! +----------------------+----------------------+----------------------+ ! 3 589 4 ! 6 2579 12579 ! 12589 259 1258 ! ! 15689 5689 2 ! 13 4 1359 ! 15689 3569 7 ! ! 1569 7 1569 ! 123 8 12359 ! 12569 4 1235 ! +----------------------+----------------------+----------------------+ 217 candidates.

Code: Select all: hidden-pairs-in-a-column: c2{n2 n3}{r5 r6} ==> r6c2≠9, r6c2≠8, r6c2≠5, r5c2≠9, r5c2≠6, r5c2≠5 naked-pairs-in-a-row: r5{c2 c4}{n2 n3} ==> r5c9≠3, r5c9≠2, r5c7≠2, r5c6≠3, r5c6≠2 naked-single ==> r5c9=5 naked-single ==> r5c6=9 hidden-single-in-a-column ==> r7c5=9 hidden-single-in-a-block ==> r7c6=7 whip[1]: r7n1{c9 .} ==> r8c7≠1, r9c7≠1, r9c9≠1 whip[1]: r7n2{c9 .} ==> r9c7≠2, r9c9≠2 naked-single ==> r9c9=3 whip[1]: b8n5{r9c6 .} ==> r4c6≠5 naked-pairs-in-a-row: r1{c6 c9}{n2 n8} ==> r1c7≠8, r1c7≠2, r1c5≠2, r1c1≠8 whip[1]: c5n2{r6 .} ==> r4c6≠2, r5c4≠2, r6c4≠2 naked-single ==> r5c4=3 naked-single ==> r5c2=2 naked-single ==> r6c2=3 naked-single ==> r8c4=1 naked-single ==> r9c4=2 naked-single ==> r9c6=5 naked-single ==> r8c6=3 hidden-single-in-a-block ==> r4c8=3 hidden-single-in-a-column ==> r8c8=6 naked-single ==> r9c7=9 naked-single ==> r1c7=7 naked-single ==> r1c5=6 naked-single ==> r1c1=9 naked-single ==> r3c5=7 naked-single ==> r3c8=5 naked-single ==> r7c8=2 naked-single ==> r2c8=9 naked-single ==> r6c8=7 naked-single ==> r5c7=6 naked-single ==> r5c3=7 hidden-single-in-a-block ==> r2c1=7 hidden-single-in-a-column ==> r9c1=1 naked-single ==> r9c3=6 hidden-single-in-a-block ==> r3c2=6 hidden-single-in-a-block ==> r4c1=6 hidden-single-in-a-column ==> r8c2=9 hidden-single-in-a-column ==> r6c3=9

;;; THIS IS WHERE THE OTHER SOLUTIONS START FROM
;;; From this point, the solution is totally trivial:

Code: Select all: finned-x-wing-in-columns: n8{c2 c9}{r7 r2} ==> r2c7≠8 whip[1]: c7n8{r8 .} ==> r7c9≠8 naked-single ==> r7c9=1 hidden-single-in-a-block ==> r6c7=1 finned-x-wing-in-columns: n4{c7 c4}{r2 r4} ==> r4c6≠4 stte

by **RSW** » Fri Sep 24, 2021 9:38 pm

Code: Select all: +------------+------------+-----------+ | 9 4 3 | 5 6 28 | 7 1 28 | | 7 58 c158 | 48 3 d1248 |e248 9 6 | | 2 6 18 | 9 7 148 | 3 5 48 | +------------+------------+-----------+ | 6 1 b58 | 7 a25 48 |*4-2 3 9 | | 4 2 7 | 3 1 9 | 6 8 5 | | 58 3 9 | 48 25 6 | 124 7 124 | +------------+------------+-----------+ | 3 58 4 | 6 9 7 | 158 2 18 | | 58 9 2 | 1 4 3 | 58 6 7 | | 1 7 6 | 2 8 5 | 9 4 3 | +------------+------------+-----------+

(2=5)r4c5 - (5)r4c3 = (5-1)r2c3 = (1-2)r2c6 = (2)r2c7 => -2r4c7; stte

Leren's Puzzles 69