The New Sudoku Players' Forum

by **m_b_metcalf** » Fri May 06, 2022 8:38 am

This was the hardest 17-clue symmetric puzzle that I found. A long slog with a few bumps:

Code: Select all: . . . . 9 . 7 . 2 . 3 5 . . . . . . . 4 . . . . . . . . . . . . 7 . 5 . 6 . . . . . 8 . . . . . 3 . . . . . 8 . . . 6 . . . . . . . 9 . . . . 4 7 . . . . . . 3 . 17 clues, diagonal symmetry

Mike

by **rjamil** » Fri May 06, 2022 10:07 am

Code: Select all: ....9.7.2.35.......4............7.5.6.....8.....3.....8...6.......9....47......3.

Two steps:

Code: Select all: +---------------+--------------+--------------+ | 1 68 68 | 5 9 3 | 7 4 2 | | 29 3 5 | 4 (7) [1]2|[1]9 (8) 6 | | 29 4 7 | 8 [1]2 6 | 3 [1]9 5 | +---------------+--------------+--------------+ | 3 128 1289 | 6 [1]28 7 | 4 5 19 | | 6 7 129 |[1]2 (4) 5 | 8 29-1 3 | | 4 5 128 | 3 [1]28 9 | 12 6 7 | +---------------+--------------+--------------+ | 8 129 3 | 7 6 4 | 5 129 19 | | 5 126 126 | 9 3 8 | 126 7 4 | | 7 69 4 | 12 5 12 | 69 3 8 | +---------------+--------------+--------------+

1) Grouped Empty Rectangle: ERI 1 @ b3r2c8 ERI 1 @ b2r2c5 ERI 1 @ b5r5c5 => -1 @ r5c8; and

Code: Select all: +---------------+-------------+--------------+ | 1 68 68 | 5 9 3 | 7 4 2 | | 29 3 5 | 4 7 12 |*19 8 6 | | 29 4 7 | 8 12 6 | 3 +19 5 | +---------------+-------------+--------------+ | 3 128 1289 | 6 128 7 | 4 5 19 | | 6 7 129 | 12 4 5 | 8 29 3 | | 4 5 128 | 3 128 9 | 12 6 7 | +---------------+-------------+--------------+ | 8 129 3 | 7 6 4 | 5 +129 *19 | | 5 126 126 | 9 3 8 | 126 7 4 | | 7 69 4 | 12 5 12 | 6-9 3 8 | +---------------+-------------+--------------+

2) W-Wing: 19 @ r7c9 r2c7 SL between 1 @ r3c8 and 1 @ r7c8 => -9 @ r9c7; stte

R. Jamil

by **shye** » Fri May 06, 2022 1:49 pm

Code: Select all: .---------------.-------------.--------------. | 1 68 68 | 5 9 3 | 7 4 2 | | 29 3 5 | 4 7 *12 | 9-1 8 6 | | 29 4 7 | 8 *12 6 | 3 #19 5 | :---------------+-------------+--------------: | 3 128 1289 | 6 *128 7 | 4 5 19 | | 6 7 129 |*12 4 5 | 8 #129 3 | | 4 5 128 | 3 *128 9 |#12 6 7 | :---------------+-------------+--------------: | 8 129 3 | 7 6 4 | 5 129 19 | | 5 126 126 | 9 3 8 | 126 7 4 | | 7 69 4 | 12 5 12 | 69 3 8 | '---------------'-------------'--------------'

almost y-wing
[(1=9)r3c8 - (9=2)r5c8 - (2=1)r6c7] = 1r5c8 - 1b5p4 = 1b5p28 - 1b2p8 = 1b2p6
=> -1r2c7 stte

by **SteveG48** » Fri May 06, 2022 2:45 pm

Code: Select all: *------------------------------------------------------------* | 1 68 68 | 5 9 3 | 7 4 2 | | 29 3 5 | 4 7 g12 |ab9-1 8 6 | | 29 4 7 | 8 12 6 | 3 b19 5 | *-------------------+-------------------+--------------------| | 3 128 1289 | 6 128 7 | 4 5 19 | | 6 7 129 |d12 4 5 | 8 c129 3 | | 4 5 128 | 3 128 9 | b12 6 7 | *-------------------+-------------------+--------------------| | 8 129 3 | 7 6 4 | 5 129 19 | | 5 126 126 | 9 3 8 | 126 7 4 | | 7 69 4 |e12 5 f12 | 69 3 8 | *------------------------------------------------------------*

9r2c7 = ((12)r26c7)&(9r3c8) - (2|9=1)r5c8 -1r5c4 = r9c4 - r9c6 = 1r2c6 => -1 r2c7 ; stte

by **P.O.** » Fri May 06, 2022 2:59 pm

Code: Select all: after singles and intersections: 1 68 68 5 9 3 7 4 2 29 3 5 4 7 A+12 a+19 8 6 29 4 7 8 12 6 3 19 5 3 128 1289 6 128 7 4 5 19 6 7 129 C×1+2 4 5 8 d+129 3 4 5 128 3 128 9 12 6 7 8 129 3 7 6 4 5 d-129 c+19 5 126 126 9 3 8 126 7 4 7 69 4 C1-2 5 B1+2 b6+9 3 8 1r2c67 => r5c4 <> 1 r2c6=1 - r9c6{n1 n2} - c4n2{r9 r5} r2c7=1 - c7n9{r2 r9} - r7c9{n9 n1} - c8n1{r7 r5} ste.

by **Cenoman** » Fri May 06, 2022 9:02 pm

Code: Select all: +--------------------+------------------+-------------------+ | 1 68 68 | 5 9 3 | 7 4 2 | | 29 3 5 | 4 7 12* | 19* 8 6 | | 29 4 7 | 8 12 6 | 3 19* 5 | +--------------------+------------------+-------------------+ | 3 128 1289 | 6 128 7 | 4 5 1-9 | | 6 7 b129# | a12* 4 5 | 8 a129* 3 | | 4 5 128 | 3 128 9 | 12 6 7 | +--------------------+------------------+-------------------+ | 8 129 3 | 7 6 4 | 5 c129# d19 | | 5 126 126 | 9 3 8 | 126 7 4 | | 7 69 4 | 12* 5 12* | 69 3 8 | +--------------------+------------------+-------------------+

7-link oddagon (1)r259, c468, b3 having two guardians (#):
(9)r5c8 = (9-1)r5c3 == (1)r7c8 - (1=9)r7c9 => -9 r4c9; ste

by **jco** » Sat May 07, 2022 12:03 am

After basics

Code: Select all: .-----------------------------------------------------------. | 1 68 68 | 5 9 3 | 7 4 2 | | 29 3 5 | 4 7 g12 |h19 8 6 | | 29 4 7 | 8 fb12 6 | 3 a19 5 | |-------------------+-------------------+-------------------| | 3 128 1289 | 6 ec128 7 | 4 5 19 | | 6 7 129 |d12 4 5 | 8 29-1 3 | | 4 5 128 | 3 ec128 9 |i12 6 7 | |-------------------+-------------------+-------------------| | 8 129 3 | 7 6 4 | 5 k29-1 19 | | 5 126 126 | 9 3 8 |j126 7 4 | | 7 69 4 | 12 5 12 | 69 3 8 | '-----------------------------------------------------------'

(1)r3c8 = r3c5 - (1)r46c5 = (1*-2)r5c4 = (2)r46c5 - (2)r3c5 = (2-1)r2c6 = (1)r2c7 - (1=2)r6c7 - (2)r8c7 = (2)r7c8 => -1* r5c8, r7c8; ste

by **pjb** » Sat May 07, 2022 2:48 am

Code: Select all: 1 68 68 | 5 9 3 | 7 4 2 29 3 5 | 4 7 12 | 19 8 6 29 4 7 | 8 12 6 | 3 19 5 ------------------------+----------------------+--------------------- 3 128 1289 | 6 128 7 | 4 5 19 6 7 129 | 12 4 5 | 8 129 3 4 5 128 | 3 128 9 | 12 6 7 ------------------------+----------------------+--------------------- 8 129 3 | 7 6 4 | 5 129 19 5 126 126 | 9 3 8 | 126 7 4 7 69 4 | 12 5 2-1 | 69 3 8

(1)r5c8 - r5c4 = r9c4 - (1)r9c6
(2)r5c8 - (2=1)r6c7 - r2c7 = r2c6 - (1)r9c6
(9)r5c8 - (9=1)r3c8 - r2c7 = r2c6 - (1)r9c6; stte

Phil

Website · by **denis_berthier** » Sun May 08, 2022 6:27 am

.

Code: Select all: Resolution state after Singles and whips[1]: +----------------+----------------+----------------+ ! 1 68 68 ! 5 9 3 ! 7 4 2 ! ! 29 3 5 ! 4 7 12 ! 19 8 6 ! ! 29 4 7 ! 8 12 6 ! 3 19 5 ! +----------------+----------------+----------------+ ! 3 128 1289 ! 6 128 7 ! 4 5 19 ! ! 6 7 129 ! 12 4 5 ! 8 129 3 ! ! 4 5 128 ! 3 128 9 ! 12 6 7 ! +----------------+----------------+----------------+ ! 8 129 3 ! 7 6 4 ! 5 129 19 ! ! 5 126 126 ! 9 3 8 ! 126 7 4 ! ! 7 69 4 ! 12 5 12 ! 69 3 8 ! +----------------+----------------+----------------+ 69 candidates

Two trivial steps using the simplest-first strategy:

Code: Select all: whip[2]: r3n1{c8 c5} - b5n1{r4c5 .} ==> r5c8≠1 biv-chain[3]: r2c7{n9 n1} - r6c7{n1 n2} - r5c8{n2 n9} ==> r3c8≠9 stte

Or a more complicated 1-step solution:

Code: Select all: z-chain[5]: c7n9{r2 r9} - c9n9{r7 r4} - b6n1{r4c9 r5c8} - c4n1{r5 r9} - c6n1{r9 .} ==> r2c7≠1 with z-candidates = n1r6c7 n1r2c6 stte

or:

Code: Select all: z-chain[5]: r3c8{n1 n9} - b6n9{r5c8 r4c9} - r7c9{n9 n1} - c8n1{r7 r5} - b5n1{r5c4 .} ==> r3c5≠1 with z-candidates = n1r3c8 n1r6c5 n1r4c5 stte

After seeing Cenoman's solution, I tried solving with only oddagons. I find 3 of them

Code: Select all: oddagon[7]: r2n1{c6 c7},b3n1{r2c7 r3c8},c8n1{r3 r5},r5n1{c8 c4},c4n1{r5 r9},r9n1{c4 c6},c6n1{r9 r2} ==> r5c8≠1 with z-candidates = n1r7c8 n1r5c3 oddagon[7]: c5n1{r3 r6},r6n1{c5 c7},b6n1{r6c7 r4c9},c9n1{r4 r7},r7n1{c9 c8},c8n1{r7 r3},r3n1{c8 c5} ==> r4c2≠1 with z-candidates = n1r4c5 n1r6c3 n1r7c2 whip[1]: c2n1{r8 .} ==> r8c3≠1 oddagon[7]: r7c8{n1 n2},c8n2{r7 r5},r5c8{n2 n9},b6n9{r5c8 r4c9},c9n9{r4 r7},r7c9{n9 n1},r7n1{c9 c8} ==> r7c2≠9, r7c8≠1 with z-candidates = n9r7c8 n1r7c2 stte

17clue symmetric