## A Denis Berthier Puzzle using some of his "Whips"

Post puzzles for others to solve here.

### A Denis Berthier Puzzle using some of his "Whips"

Here are some useful abbreviations I will use in the remainder of this post.

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=702 chain n9: c1r123=r1c1-r1c7=r3c7-r3c3=r2c3-r2c7 =>             b3s2368-9, b1s467-903 BiC k9b3 k9b3c7 => c7r6-904 n6r4c89-n5c9r45-n5c1r56-n8b4s73 => r4c89-905 HS: r4c3=9,r1c1=9,r6c8=9,c9r7=9,r1c2=1,c1r9=106 BiC: k6b7c3 => c3r12-607 n1: c7r58-r7c86 => r5c6-108 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 => r1c56-210 Whip  n2: r3c52-r9c25 => r3c48-211 HSiC  c8r1=212 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=415 NPiC n78c2r46 => c2r3-816 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?
GrandPaBig
RichardGoodrich

Posts: 40
Joined: 12 December 2012
Location: Cash, Texas USA

### Denis Berthier methods

Anyone using Denis Berthier methods such as whips?
GrandPaBig
RichardGoodrich

Posts: 40
Joined: 12 December 2012
Location: Cash, Texas USA

### Re: A Denis Berthier Puzzle using some of his "Whips"

Type whips into the search box, click on the search button and you'll get your answer.

Leren
Leren

Posts: 3324
Joined: 03 June 2012

### Re: A Denis Berthier Puzzle using some of his "Whips"

BTW, step 02 in my trace has errors where r1 should have been r6 and the whole "chain" / "whip" or whatever you call it does NOT really logically work (e.g. it does NOT prove all cases). It just happens to work on this puzzle which makes it much shorter than Denis Berthier's solution. However, since no one seems much interested, I will simply continue on my own blog.
GrandPaBig
RichardGoodrich

Posts: 40
Joined: 12 December 2012
Location: Cash, Texas USA