Jeff wrote:I am quite surprised you were able to find so many simple nice loops in this grid; perhaps after a few ALSs. I haven't completely solved this one yet. Would you like to open a new thread and post your full solution for us?
Jeff, I feel uneasy that you do not see many nice loops, so I'll appreciate it if you and the other Nice Guys can check my interpretation. I am sure about the implications, but maybe they are not all nice loops according to your definition.
Maybe I have to go back to school on this .
There are 10 simple loops (longest 6 links), 7 ALSs and 1 unique rectangle (type 1).
The rest is very basic (singles, locked candidates and 1 naked pair). I think the trick to solving this puzzle lies in finding the right ALSs.
If anyone who reads this is still working on this puzzle or wants to try it first, he should stop reading now.
- Code: Select all
*-----------*
|1.8|4..|5..|
|...|..7|..2|
|...|...|...|
|---+---+---|
|.2.|.9.|..7|
|.6.|.5.|.89|
|9..|.1.|.4.|
|---+---+---|
|...|...|...|
|5..|6..|...|
|..4|..3|9.8|
*-----------*
1* 379 8* 4* 236 269 5* 3679 36
346 3459 3569 13589 368 7* 13468 1369 2*
23467 34579 235679 123589 2368 125689 134678 13679 1346
348 2* 135 38 9* 468 136 1356 7*
347 6* 137 237 5* 24 123 8* 9*
9* 3578 357 2378 1* 268 236 4* 356
23678 13789 123679 125789 2478 124589 123467 123567 13456
5* 13789 12379 6* 2478 12489 12347 1237 134
267 17 4* 1257 27 3* 9* 12567 8*
locked candidates 1: square-1 row-3 digit=2
locked candidates 2: square-1 col-2 digit=4
locked candidates 2: square-2 col-5 digit=3
locked candidates 2: square-2 col-5 digit=6
locked candidates 1: square-4 col-3 digit=1
locked candidates 1: square-5 col-6 digit=4
locked candidates 1: square-5 col-4 digit=7
locked candidates 1: square-6 col-7 digit=2
[r6c6]=6=[r4c6]=4=[r4c1]=8=[r6c2]-8-[r6c6] => [r6c6]<>8
1* 379 8* 4* 236 29 5* 3679 36
36 3459 3569 1589 368 7* 13468 1369 2*
2367 34579 235679 1589 368 1589 134678 13679 1346
348 2* 135 38 9* 468 136 1356 7*
347 6* 137 237 5* 24 123 8* 9*
9* 3578 357 2378 1* 268 236 4* 356
23678 13789 23679 12589 2478 12589 13467 123567 13456
5* 13789 2379 6* 2478 1289 1347 1237 134
267 17 4* 125 27 3* 9* 12567 8*
[r7c4]-8-[r6c4]=8=[r6c2]-8-[r4c1]=8=[r7c1]-8-[r7c4] => [r7c4]<>8
1* 379 8* 4* 236 29 5* 3679 36
36 3459 3569 1589 368 7* 13468 1369 2*
2367 34579 235679 1589 368 1589 134678 13679 1346
348 2* 135 38 9* 468 136 1356 7*
347 6* 137 237 5* 24 123 8* 9*
9* 3578 357 2378 1* 26 236 4* 356
23678 13789 23679 12589 2478 12589 13467 123567 13456
5* 13789 2379 6* 2478 1289 1347 1237 134
267 17 4* 125 27 3* 9* 12567 8*
als A=2368@{r1c5,r2c5,r3c5} B=12589@{r2c4,r3c4,r7c4,r9c4} rc=8 c=2
eliminate 2@r7c5 2@r8c5 2@r9c5
als C=2478@{r7c5,r8c5,r9c5} B=12589@{r2c4,r3c4,r7c4,r9c4} rc=2 c=8
eliminate 8@r2c5 8@r3c5
1* 379 8* 4* 236 29 5* 3679 36
36 3459 3569 1589 368 7* 13468 1369 2*
2367 34579 235679 1589 368 1589 134678 13679 1346
348 2* 135 38 9* 468 136 1356 7*
347 6* 137 237 5* 24 123 8* 9*
9* 3578 357 2378 1* 26 236 4* 356
23678 13789 23679 1259 2478 12589 13467 123567 13456
5* 13789 2379 6* 2478 1289 1347 1237 134
267 17 4* 125 27 3* 9* 12567 8*
naked single: 7@r9c5, 1@r9c2
hidden single: 2@r1c5 in col-5
naked single: 9@r1c6
hidden single: 9@r7c4 in square-8
locked candidates 2: square-2 col-4 digit=1
locked candidates 2: square-3 row-1 digit=6
locked candidates 2: square-8 col-5 digit=8
naked pair: 36 in row-2
unique rectangle 1: r2c5-r3c5-r2c1-r3c1 eliminate 3@r3c1 6@r3c1
1* 37 8* 4* 2* 9* 5* 367 36
36 459 59 158 36 7* 148 19 2*
2367 34579 235679 158 36 58 13478 1379 134
348 2* 135 38 9* 468 136 1356 7*
347 6* 137 237 5* 24 123 8* 9*
9* 3578 357 2378 1* 26 236 4* 356
23678 378 2367 9* 48 125 13467 123567 13456
5* 3789 2379 6* 48 12 1347 1237 134
26 1* 4* 25 7* 3* 9* 256 8*
als A=2367@{r1c2,r2c1,r3c1} B=26@{r9c1} rc=26
eliminate 3@r3c2 7@r3c2 3@r3c3 7@r3c3 6@r7c1
als A=367@{r1c2,r2c1} B=267@{r3c1,r9c1} rc=67
eliminate 3@r3c2 7@r3c2 3@r3c3 7@r3c3 2@r7c1
als A=34579@{r1c2,r2c2,r2c3,r3c2} B=2367@{r2c1,r3c1,r9c1} rc=37
eliminate 5@r3c3 7@r3c3 9@r3c3 2@r7c1 6@r7c1
1* 37 8* 4* 2* 9* 5* 367 36
36 459 59 158 36 7* 148 19 2*
27 34579 235679 158 36 58 13478 1379 134
348 2* 135 38 9* 468 136 1356 7*
347 6* 137 237 5* 24 123 8* 9*
9* 3578 357 2378 1* 26 236 4* 356
23678 378 2367 9* 48 125 13467 123567 13456
5* 3789 2379 6* 48 12 1347 1237 134
26 1* 4* 25 7* 3* 9* 256 8*
[r4c8]-1-[r2c8]-9-[r2c3]-5-[r4c3]=5=[r4c8] => [r4c8]<>1
1* 37 8* 4* 2* 9* 5* 367 36
36 459 59 158 36 7* 148 19 2*
27 459 26 158 36 58 13478 1379 134
348 2* 135 38 9* 468 136 1356 7*
347 6* 137 237 5* 24 123 8* 9*
9* 3578 357 2378 1* 26 236 4* 356
378 378 2367 9* 48 125 13467 123567 13456
5* 3789 2379 6* 48 12 1347 1237 134
26 1* 4* 25 7* 3* 9* 256 8*
locked candidates 1: square-6 col-7 digit=1
[r6c9]-6-[r6c6]=6=[r4c6]=8=[r3c6]=5=[r7c6]-5-[r7c9]=5=[r6c9] => [r6c9]<>6
1* 37 8* 4* 2* 9* 5* 367 36
36 459 59 158 36 7* 48 19 2*
27 459 26 158 36 58 3478 1379 134
348 2* 135 38 9* 468 136 356 7*
347 6* 137 237 5* 24 123 8* 9*
9* 3578 357 2378 1* 26 236 4* 356
378 378 2367 9* 48 125 3467 123567 13456
5* 3789 2379 6* 48 12 347 1237 134
26 1* 4* 25 7* 3* 9* 256 8*
als A=356@{r4c8,r6c9} B=3468@{r4c1,r4c4,r4c6} rc=6 c=3
eliminate 3@r4c7
1* 37 8* 4* 2* 9* 5* 367 36
36 459 59 158 36 7* 48 19 2*
27 459 26 158 36 58 3478 1379 134
348 2* 135 38 9* 468 136 356 7*
347 6* 137 237 5* 24 123 8* 9*
9* 3578 357 2378 1* 26 236 4* 35
378 378 2367 9* 48 125 3467 123567 13456
5* 3789 2379 6* 48 12 347 1237 134
26 1* 4* 25 7* 3* 9* 256 8*
[r6c2]=8=[r4c1]-8-[r4c6]=8=[r3c6]=5=[r7c6]-5-[r7c9]=5=[r6c9]-5-[r6c2] => [r6c2]<>5
1* 37 8* 4* 2* 9* 5* 367 36
36 459 59 158 36 7* 48 19 2*
27 459 26 158 36 58 3478 1379 134
348 2* 135 38 9* 468 16 356 7*
347 6* 137 237 5* 24 123 8* 9*
9* 3578 357 2378 1* 26 236 4* 35
378 378 2367 9* 48 125 3467 123567 13456
5* 3789 2379 6* 48 12 347 1237 134
26 1* 4* 25 7* 3* 9* 256 8*
locked candidates 2: square-1 col-2 digit=5
naked single: 9@r2c3, 1@r2c8
hidden single: 1@r3c4 in square-2, 9@r3c8 in square-3,
hidden single: 9@r8c2 in square-7, 8@r8c5 in row-8
naked single: 4@r7c5
[r7c9]-3-[r3c9]-4-[r3c2]-5-[r3c6]=5=[r7c6]=1=[r7c9] => [r7c9]<>3
1* 37 8* 4* 2* 9* 5* 367 36
36 45 9* 58 36 7* 48 1* 2*
27 45 26 1* 36 58 3478 9* 34
348 2* 135 38 9* 468 16 356 7*
347 6* 137 237 5* 24 123 8* 9*
9* 378 357 2378 1* 26 236 4* 35
378 378 2367 9* 4* 125 367 23567 1356
5* 9* 237 6* 8* 12 347 237 134
26 1* 4* 25 7* 3* 9* 256 8*
[r1c9]-3-[r3c9]-4-[r3c2]-5-[r3c6]=5=[r7c6]=1=[r7c9]=6=[r1c9] => [r1c9]<>3
1* 37 8* 4* 2* 9* 5* 367 36
36 45 9* 58 36 7* 48 1* 2*
27 45 26 1* 36 58 3478 9* 34
348 2* 135 38 9* 468 16 356 7*
347 6* 137 237 5* 24 123 8* 9*
9* 378 357 2378 1* 26 236 4* 35
378 378 2367 9* 4* 125 367 23567 156
5* 9* 237 6* 8* 12 347 237 134
26 1* 4* 25 7* 3* 9* 256 8*
naked single: 6@r1c9
-[r2c4]-8-[r2c7]=8=[r3c7]=7=[r3c1]=2=[r9c1]-2-[r9c4]-5-[r2c4]-
=> [r3c7]<>3,[r3c7]<>4,[r9c8]<>2
1* 37 8* 4* 2* 9* 5* 37 6*
36 45 9* 58 36 7* 48 1* 2*
27 45 26 1* 36 58 3478 9* 34
348 2* 135 38 9* 468 16 356 7*
347 6* 137 237 5* 24 123 8* 9*
9* 378 357 2378 1* 26 236 4* 35
378 378 2367 9* 4* 125 367 23567 15
5* 9* 237 6* 8* 12 347 237 134
26 1* 4* 25 7* 3* 9* 256 8*
[r6c9]-3-[r3c9]-4-[r3c2]-5-[r3c6]=5=[r7c6]-5-[r7c9]=5=[r6c9] => [r6c9]<>3
1* 37 8* 4* 2* 9* 5* 37 6*
36 45 9* 58 36 7* 48 1* 2*
27 45 26 1* 36 58 78 9* 34
348 2* 135 38 9* 468 16 356 7*
347 6* 137 237 5* 24 123 8* 9*
9* 378 357 2378 1* 26 236 4* 35
378 378 2367 9* 4* 125 367 23567 15
5* 9* 237 6* 8* 12 347 237 134
26 1* 4* 25 7* 3* 9* 56 8*
naked single: 5@r6c9, naked single: 1@r7c9
hidden single: 5@r4c3 in square-4, 1@r5c3 in square-4
hidden single: 1@r4c7 in square-6, 1@r8c6 in square-8
als A=236@{r4c8,r5c7} B=256@{r9c4,r9c8} rc=6 c=2
eliminate 2@r5c4
1* 37 8* 4* 2* 9* 5* 37 6*
36 45 9* 58 36 7* 48 1* 2*
27 45 26 1* 36 58 78 9* 34
348 2* 5* 38 9* 468 1* 36 7*
347 6* 1* 237 5* 24 23 8* 9*
9* 378 37 2378 1* 26 236 4* 5*
378 378 2367 9* 4* 25 367 23567 1*
5* 9* 237 6* 8* 1* 347 237 34
26 1* 4* 25 7* 3* 9* 56 8*
[r4c8]-3-[r1c8]-7-[r3c7]-8-[r3c6]=8=[r4c6]=6=[r4c8] => [r4c8]<>3
1* 37 8* 4* 2* 9* 5* 37 6*
36 45 9* 58 36 7* 48 1* 2*
27 45 26 1* 36 58 78 9* 34
348 2* 5* 38 9* 468 1* 36 7*
347 6* 1* 37 5* 24 23 8* 9*
9* 378 37 2378 1* 26 236 4* 5*
378 378 2367 9* 4* 25 367 23567 1*
5* 9* 237 6* 8* 1* 347 237 34
26 1* 4* 25 7* 3* 9* 56 8*
naked single: 6@r4c8, 5@r9c8, 2@r9c4, 5@r7c6, 8@r3c6, 5@r2c4
naked single: 4@r2c2, 8@r2c7, 5@r3c2, 7@r3c7, 3@r1c8, 7@r1c2
naked single: 2@r3c1, 6@r3c3, 3@r2c1, 6@r2c5, 3@r3c5, 4@r3c9
naked single: 4@r4c6, 8@r4c1, 3@r4c4, 7@r5c4, 4@r5c1, 2@r5c6
naked single: 3@r5c7, 3@r6c2, 7@r6c3, 8@r6c4, 6@r6c6, 2@r6c7
naked single: 7@r7c1, 8@r7c2, 6@r7c7, 2@r7c8, 3@r7c3, 2@r8c3
naked single: 4@r8c7, 7@r8c8, 3@r8c9, 6@r9c1,
Thanks in anticipation, flip