The New Sudoku Players' Forum

by **m_b_metcalf** » Tue Sep 12, 2023 7:40 am

Code: Select all: . . 1 . . 2 . . 3 . . . . 4 . . 8 . 9 . . 3 . . 5 . . . . 7 . . 6 . . 8 . 8 . . . . . 2 . 2 . . 4 . . 3 . . . . 5 . . 7 . . 1 . 2 . . 6 . . . . 7 . . 8 . . 9 . . Lots more symmetry, minimal, not easy ..1..2..3....4..8.9..3..5....7..6..8.8.....2.2..4..3....5..7..1.2..6....7..8..9..

by **marek stefanik** » Tue Sep 12, 2023 8:55 am

Central symmetry (123456789 → 987654321) => 5r5c5

Code: Select all: ,-------------------,--------------------,-------------------, | 4568 4567 1 | 5679 789 2 | 467 4679 3 | | 356 3567 236 | 15679 4 159 |b12-67 8 2679 | | 9 467 2468 | 3 7-18 d18 | 5 a1467 2467 | :-------------------+--------------------+-------------------: | 1345 13459 7 | 129 1239 6 | 14 1459 8 | | 1346 8 3469 | 179 5 139 | 1467 2 4679 | | 2 1569 69 | 4 1789 189 | 3 15679 5679 | :-------------------+--------------------+-------------------: | 3468 3469 5 |d29 3-29 7 |c2468 346 1 | | 1348 2 89-34| 159 6 13459 | 478 3457 457 | | 7 1346 346 | 8 123 1345 | 9 3456 2456 | '-------------------'--------------------'-------------------'

1r3c8 = (1–2)r2c7 = 2r7c7 – 2r7c4 = 9r7c4&1r3c6 – Loop => -67r2c7&34r8c3, -2r7c5&8r3c5, -1r3c5&9r7c5

Code: Select all: ,-------------------,-----------------,-------------------, | 4568 4567 1 | 569 89 2 | 467 4679 3 | | 356 3567 236 | 1569 4 159 | 12 8 2679 | | 9 #46 2468 | 3 7 18 | 5 1-46 246 | :-------------------+-----------------+-------------------: | 1345 13459 7 | 129 129 6 | 14 1459 8 | | 146 8 469 | 7 5 3 | 146 2 469 | | 2 1569 69 | 4 189 189 | 3 15679 5679 | :-------------------+-----------------+-------------------: | 468 9-46 5 | 29 3 7 | 2468 #46 1 | | 1348 2 89 | 159 6 1459 | 478 3457 457 | | 7 1346 346 | 8 12 145 | 9 3456 2456 | '-------------------'-----------------'-------------------'

gsp pair 46r3c2&r7c8 => -46r3c8, -46r7c2, stte

Marek

by **Cenoman** » Tue Sep 12, 2023 3:01 pm

A bit different (and much less elegant

):

Code: Select all: +------------------------+-------------------------+------------------------+ | c4568 4567 1 | 5679 b789 2 | 467 4679 3 | | 356 3567 236 | 15679 4 159 | f1267 8 2679 | | 9 467 2468 | 3 178 a18 | 5 g1467 2467 | +------------------------+-------------------------+------------------------+ | 1345 13459 7 | 129 1239 6 | 14 1459 8 | | 1346 8 3469 | 179 5 139 | 1467 2 4679 | | 2 1569 69 | 4 1789 189 | 3 15679 5679 | +------------------------+-------------------------+------------------------+ | d3468 3469 5 | 29 239 7 | e2468 346 1 | | 1348 2 3489 | 159 6 13459 | 478 3457 457 | | 7 1346 346 | 8 123 1345 | 9 3456 2456 | +------------------------+-------------------------+------------------------+

Central symmetry of the givens with digit permutation [1,9] [2,8] [3,7] [4,6] [5,5] => +5 r5c5
1. (1=8)r3c6 - r1c5 = r1c1 - r7c1 = (8-2)r7c7 = (2-1)r2c7 = (1)r3c8 loop => -18 r3c5, -67 r2c7, -8 r8c1, -46 r7c7 and (by sym.) -29 r7c5, -34 r8c3, -2r2c9, -46 r3c3; 4 placements

Code: Select all: +-----------------------+----------------------+-----------------------+ | 4568 4567 1 | 569 89 2 | 467 4679 3 | | 356 3567 i236 | 1569 4 159 |ih12 8 69-7 | | 9 46 28 | 3 7 18 | 5 146 246 | +-----------------------+----------------------+-----------------------+ | 1345 13459 7 | 129 129 6 | 4-1 1459 8 | | b146 8 469 | 7 5 3 | a146 2 469 | | 2 1569 6-9 | 4 189 189 | 3 15679 5679 | +-----------------------+----------------------+-----------------------+ | 468 469 5 | f29 3 7 | g28 46 1 | | c14-3 2 89 | 159 6 1459 | 478 3457 457 | | 7 d1346 i346 | 8 e12 145 | 9 3456 2456 | +-----------------------+----------------------+-----------------------+

2. (1)r5c7 = r5c1 - (*1)r8c1 = r9c2 - (1=2)r9c5 - r7c4 = r7c7 - (2)r2c7 = (1r2c7 & 23r29c3) => -1 r4c7, -3 r8c1* and (by sym.) -9 r6c3, -7 r2c9; ste

by **P.O.** » Tue Sep 12, 2023 6:05 pm

Code: Select all: 4568 4567 1 5679 5789 2 467 4679 3 356 3567 236 15679 4 159 1267 8 2679 9 467 2468 3 178 18 5 1467 2467 1345 13459 7 1259 12359 6 14 1459 8 13456 8 3469 1579 13579 1359 1467 2 45679 2 1569 69 4 15789 1589 3 15679 5679 3468 3469 5 29 239 7 2468 346 1 1348 2 3489 159 6 13459 478 3457 457 7 1346 346 8 1235 1345 9 3456 2456 n2r2c3 OR n2r3c3 => r5c5 <> 1 n4r7c12 OR n4r7c78 => r3c9 <> 2 ste.

n2r2c3 context:

Hidden Text: Show

Code: Select all: ((2 0) (2 3 1) (2 3 6)) n2r2c3 ((2 1 3) (3 9 3) (2 4 6 7)) n2r3c9 ((2 1 1) (7 7 9) (2 4 6 8)) n2r7c7 ((2 1 1) (7 7 9) (2 4 6 8)) n2r7c7 ((3 2 21) (7 5 8) (2 3 9)) n3r7c5 ((8 2 10) (8 7 9) (4 7 8)) n8r8c7 ((8 2 10) (7 1 7) (3 4 6 8)) n8r7c1 ((9 2 9) (7 4 8) (2 9)) n9r7c4 ((2 2 3) (9 5 8) (1 2 3 5)) n2r9c5 ((2 2 1) (4 4 5) (1 2 5 9)) n2r4c4 ((3 2 21) (7 5 8) (2 3 9)) n3r7c5 ((3 3 3) (5 6 5) (1 3 5 9)) n3r5c6 ((8 2 10) (7 1 7) (3 4 6 8)) n8r7c1 ((8 3 1) (3 3 1) (2 4 6 8)) n8r3c3 ((8 3 1) (1 5 2) (5 7 8 9)) n8r1c5 ((9 2 9) (7 4 8) (2 9)) n9r7c4 ((9 3 1) (8 3 7) (3 4 8 9)) n9r8c3 ((9 3 1) (8 3 7) (3 4 8 9)) n9r8c3 ((6 4 9) (6 3 4) (6 9)) n6r6c3 ((8 3 1) (1 5 2) (5 7 8 9)) n8r1c5 ((7 4 21) (3 5 2) (1 7 8)) n7r3c5 ((1 4 9) (3 6 2) (1 8)) n1r3c6 ((8 4 1) (6 6 5) (1 5 8 9)) n8r6c6 ((7 4 21) (3 5 2) (1 7 8)) n7r3c5 ((7 5 3) (5 4 5) (1 5 7 9)) n7r5c4 ((1 4 9) (3 6 2) (1 8)) n1r3c6 ((1 5 1) (2 7 3) (1 2 6 7)) n1r2c7 ((1 5 1) (2 7 3) (1 2 6 7)) n1r2c7 ((4 6 9) (4 7 6) (1 4)) n4r4c7

Code: Select all: 456 456 1 56 8 2 7 469 3 356 3567 2 56 4 59 1 8 69 9 46 8 3 7 1 5 46 2 135 1359 7 2 159 6 4 159 8 15 8 4 7 159 3 6 2 59 2 159 6 4 159 8 3 1579 579 8 46 5 9 3 7 2 46 1 14 2 9 15 6 45 8 3457 457 7 146 3 8 2 45 9 456 456 1r5c5 => r3c2 <> 4,6 r5c5=1 - r5c1{n1 n5} - r5c9{n5 n9} - r2c9{n9 n6} - r3c8{n6 n4} r5c5=1 - r5c1{n1 n5} - r5c9{n5 n9} - r2c9{n9 n6} - c1n6{r2 r1} => r5c5 <> 1

n2r3c3 context:

Hidden Text: Show

Code: Select all: ((2 0) (3 3 1) (2 4 6 8)) n2r3c3 ((8 1 10) (8 3 7) (3 4 8 9)) n8r8c3 ((8 1 10) (1 1 1) (4 5 6 8)) n8r1c1 ((8 1 10) (8 3 7) (3 4 8 9)) n8r8c3 ((9 2 10) (7 2 7) (3 4 6 9)) n9r7c2 ((8 2 1) (7 7 9) (2 4 6 8)) n8r7c7 ((8 1 10) (1 1 1) (4 5 6 8)) n8r1c1 ((4 2 2 11) ((1 2 1) (4 5 6 7)) ((3 2 1) (4 6 7))) n4r13c2 ((9 2 10) (7 2 7) (3 4 6 9)) n9r7c2 ((3 3 21) (7 5 8) (2 3 9)) n3r7c5 ((2 3 9) (7 4 8) (2 9)) n2r7c4 ((8 2 1) (7 7 9) (2 4 6 8)) n8r7c7 ((2 3 10) (9 9 9) (2 4 5 6)) n2r9c9 ((2 3 10) (2 7 3) (1 2 6 7)) n2r2c7 ((2 3 10) (9 9 9) (2 4 5 6)) n2r9c9 ((6 4 2 11) ((7 8 9) (3 4 6)) ((9 8 9) (3 4 5 6))) n6r79c8 ((2 3 10) (2 7 3) (1 2 6 7)) n2r2c7 ((1 4 10) (3 8 3) (1 4 6 7)) n1r3c8 ((3 3 21) (7 5 8) (2 3 9)) n3r7c5 ((3 4 3) (5 6 5) (1 3 5 9)) n3r5c6 ((2 3 9) (7 4 8) (2 9)) n2r7c4 ((2 4 1) (4 5 5) (1 2 3 5 9)) n2r4c5 ((1 4 10) (3 8 3) (1 4 6 7)) n1r3c8 ((7 5 21) (3 5 2) (1 7 8)) n7r3c5 ((8 5 9) (3 6 2) (1 8)) n8r3c6 ((7 5 21) (3 5 2) (1 7 8)) n7r3c5 ((7 6 3) (5 4 5) (1 5 7 9)) n7r5c4 ((8 5 9) (3 6 2) (1 8)) n8r3c6 ((8 6 1) (6 5 5) (1 5 7 8 9)) n8r6c5

Code: Select all: 8 4567 1 569 59 2 467 479 3 356 3567 36 1569 4 159 2 8 679 9 46 2 3 7 8 5 1 46 1345 135 7 159 2 6 14 459 8 1456 8 469 7 159 3 146 2 4569 2 156 69 4 8 159 3 579 5679 46 9 5 2 3 7 8 46 1 134 2 8 159 6 1459 47 3457 457 7 136 346 8 15 145 9 3456 2 1r5c5 => r2c1 <> 3,5,6 r5c5=1 - r9c5{n1 n5} - r1c5{n5 n9} - b3n9{r1c8 r2c9} - r5n9{c9 c3} - r6c3{n9 n6} - r2c3{n6 n3} r5c5=1 - r6n1{c6 c2} - r9n1{c2 c6} - c6n4{r9 r8} - r8c7{n4 n7} - r8c9{n47 n5} - r5n5{c9 c1} r5c5=1 - r9c5{n1 n5} - r1c5{n5 n9} - b3n9{r1c8 r2c9} - r5n9{c9 c3} - c3n4{r5 r9} - r7c1{n4 n6} => r5c5 <> 1

Code: Select all: ((4 0 1 0) ((7 1 7) (3 4 6 8)) ((7 2 7) (3 4 6 9))) n4r7c12 4568 4567 1 5679 5789 2 467 4679 3 356 3567 236 15679 4 159 1267 8 2679 9 467 2468 3 178 18 5 1467 2467 1345 13459 7 1259 12359 6 14 1459 8 13456 8 3469 1579 13579 1359 1467 2 45679 2 1569 69 4 15789 1589 3 15679 5679 3468 3469 5 29 239 7 268 36 1 138 2 389 159 6 13459 478 3457 457 7 136 36 8 1235 1345 9 3456 2456 2r3c9 => r6c3 <> 6,9 r3c9=2 - c7n2{r2 r7} - 39r7c45 - r7c8{n3 n6} - r3n6{c8 c23} - c1n6{r12 r5} r3c9=2 - c7n2{r2 r7} - r7c4{n2 n9} - b7n9{r7c2 r8c3} => r3c9 <> 2

Code: Select all: ((4 0 1 0) ((7 7 9) (2 4 6 8)) ((7 8 9) (3 4 6))) n4r7c78 4568 4567 1 5679 5789 2 467 4679 3 356 3567 236 15679 4 159 1267 8 2679 9 467 2468 3 178 18 5 1467 2467 1345 13459 7 1259 12359 6 14 1459 8 13456 8 3469 1579 13579 1359 1467 2 45679 2 1569 69 4 15789 1589 3 15679 5679 368 369 5 29 239 7 2468 346 1 1348 2 3489 159 6 13459 78 357 57 7 1346 346 8 1235 1345 9 356 256 2r3c9 => r3c6 <> 1,8 r3c9=2 - c7n2{r2 r7} - r7n4{c7 c8} - b3n4{r13c8 r2c7} - r4c7{n4 n1} - b3n1{r2c7 r3c8} r3c9=2 - c7n2{r2 r7} - r7n8{c7 c1} - r1n8{c1 c5} => r3c9 <> 2

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