1. DB = Denis Berthier
2. RG = Richard Goodrich (the author of this post)
3. HLS2 = "Hidden Logic of Sudoku, Second Edition" (I own this book
4. PBCS = "Pattern-Based Constraint Satisfaction and Logic Puzzles" (Nov. 2012 ISBN 978-1-291-20339-4)
I downloaded PBCS as a PDF lately and had started a study of it, when I got back into trying to understand DB's Whip again. It think, I have made some significant progress. I picked the following puzzle from DB's PBCS:
Section 5.10.2. pages 130-133
I hope DB is still active on this forum? I think I found an error or two in his presentation of this puzzle. DB ad about 74 steps to his solution. I attempted to work through his example when I serendipitously found what I think is a much shorter solution!
- Code: Select all
...3..5...5..1..3...7..4..12.....4...6..9......1..6..28..7..2...9..8..5...5..9..7
.---------.---------.---------. .---------.---------.---------.
| . . . | 3 . . | 5 . . | | 9 1 4 | 3 7 8 | 5 2 6 |
| . 5 . | . 1 . | . 3 . | | 6 5 8 | 9 1 2 | 7 3 4 |
| . . 7 | . . 4 | . . 1 | | 3 2 7 | 5 6 4 | 9 8 1 |
:---------+---------+---------: :---------+---------+---------:
| 2 . . | . . . | 4 . . | | 2 8 9 | 1 3 7 | 4 6 5 |
| . 6 . | . 9 . | . . . | | 4 6 3 | 2 9 5 | 1 7 8 |
| . . 1 | . . 6 | . . 2 | | 5 7 1 | 8 4 6 | 3 9 2 |
:---------+---------+---------: :---------+---------+---------:
| 8 . . | 7 . . | 2 . . | | 8 4 6 | 7 5 3 | 2 1 9 |
| . 9 . | . 8 . | . 5 . | | 7 9 2 | 4 8 1 | 6 5 3 |
| . . 5 | . . 9 | . . 7 | | 1 3 5 | 6 2 9 | 8 4 7 |
'---------'---------'---------' '---------'---------'---------'
.--------------------.---------------------.---------------------.
| 1469 1248 24689 | 3 267 278 | 5 246789 4689 |
| 469 5 24689 | 2689 1 278 | 6789 3 4689 |
| 369 238 7 | 25689 256 4 | 689 2689 1 |
:--------------------+---------------------+---------------------:
| 2 378 389 | 158 357 13578 | 4 16789 35689 |
| 3457 6 348 | 12458 9 123578 | 1378 178 358 |
| 34579 3478 1 | 458 3457 6 | 3789 789 2 |
:--------------------+---------------------+---------------------:
| 8 134 346 | 7 3456 135 | 2 1469 3469 |
| 13467 9 2346 | 1246 8 123 | 136 5 346 |
| 1346 1234 5 | 1246 2346 9 | 1368 1468 7 |
'--------------------'---------------------'---------------------'
01 HS r8c1=7
02 chain n9: c1r123=r1c1-r1c7=r3c7-r3c3=r2c3-r2c7 =>
b3s2368-9, b1s467-9
03 BiC k9b3 k9b3c7 => c7r6-9
04 n6r4c89-n5c9r45-n5c1r56-n8b4s73 => r4c89-9
05 HS: r4c3=9,r1c1=9,r6c8=9,c9r7=9,r1c2=1,c1r9=1
06 BiC: k6b7c3 => c3r12-6
07 n1: c7r58-r7c86 => r5c6-1
08 n7: r5c87-r5c6=r2c6-r2c7 => r6c7-7
.-----------------.--------------------.-------------------.
| 9 1 248 | 3 267 278 | 5 24678 468 |
| 46 5 248 | 2689 1 278 | 6789 3 468 |
| 36 238 7 | 25689 256 4 | 689 268 1 |
:-----------------+--------------------+-------------------:
| 2 378 9 | 158 357 13578 | 4 1678 3568 |
| 345 6 348 | 12458 9 23578 | 1378 178 358 |
| 345 3478 1 | 458 3457 6 | 38 9 2 |
:-----------------+--------------------+-------------------:
| 8 34 346 | 7 3456 135 | 2 146 9 |
| 7 9 2346 | 1246 8 123 | 136 5 346 |
| 1 234 5 | 246 2346 9 | 368 468 7 |
'-----------------'--------------------'-------------------'
09 Chain n2: c3r12=r3c2-r3c9=r1c1 => r1c56-2
10 Whip n2: r3c52-r9c25 => r3c48-2
11 HSiC c8r1=2
12 n1: c4r48-c7r85 => c8r45-1
.-----------------.--------------------.-----------------.
| 9 1 48 | 3 67 78 | 5 2 468 |
| 46 5 248 | 2689 1 278 | 6789 3 468 |
| 36 238 7 | 5689 256 4 | 689 68 1 |
:-----------------+--------------------+-----------------:
| 2 378 9 | 158 357 13578 | 4 678 3568 |
| 345 6 348 | 12458 9 23578 | 1378 78 358 |
| 345 3478 1 | 458 3457 6 | 38 9 2 |
:-----------------+--------------------+-----------------:
| 8 34 346 | 7 3456 135 | 2 146 9 |
| 7 9 2346 | 1246 8 123 | 136 5 346 |
| 1 234 5 | 246 2346 9 | 368 468 7 |
'-----------------'--------------------'-----------------'
13: Set All Singles
.--------------.------------------.-------------.
| 9 1 48 | 3 67 78 | 5 2 468 |
| 6 5 248 | 9 1 28 | 7 3 48 |
| 3 28 7 | 568 256 4 | 9 68 1 |
:--------------+------------------+-------------:
| 2 78 9 | 158 357 13578 | 4 678 568 |
| 45 6 3 | 2458 9 2578 | 1 78 58 |
| 45 478 1 | 458 457 6 | 3 9 2 |
:--------------+------------------+-------------:
| 8 34 6 | 7 345 35 | 2 1 9 |
| 7 9 24 | 124 8 12 | 6 5 3 |
| 1 23 5 | 26 236 9 | 8 4 7 |
'--------------'------------------'-------------'
14 NPiB n45b4 => b4s8=4
15 NPiC n78c2r46 => c2r3-8
16 Set All Singles
.---------.---------.---------.
| 9 1 4 | 3 7 8 | 5 2 6 |
| 6 5 8 | 9 1 2 | 7 3 4 |
| 3 2 7 | 5 6 4 | 9 8 1 |
:---------+---------+---------:
| 2 8 9 | 1 3 7 | 4 6 5 |
| 4 6 3 | 2 9 5 | 1 7 8 |
| 5 7 1 | 8 4 6 | 3 9 2 |
:---------+---------+---------:
| 8 4 6 | 7 5 3 | 2 1 9 |
| 7 9 2 | 4 8 1 | 6 5 3 |
| 1 3 5 | 6 2 9 | 8 4 7 |
'---------'---------'---------'
I am hoping to find a DB fan on this forum. I have not been on this forum for a long time myself. I have been 'early' retired now for about 2 years and getting back to sudoku stuff.
The big breakthrough for me was in step 02 with the "chain n9" DB did not get the same result I did early on in his trace of his results. The first DB like Whip is in step 04, but I rewrote it in a more concise manner. Whips encompass chains and what he called 'lassos'. One of the 'big ideas' for 'Whips' is that DB's method makes whips appear as patterns vs a chain of inferences. I think I like it! I was hoping to find some others who would like to review my solution and perhaps show me theirs. Did any of you try using the 'whip' concept? I actually think it is very cool!
Any takers?
