The New Sudoku Players' Forum

by **RichardGoodrich** » Mon Nov 11, 2013 2:29 am

OK, here are the 4 Berthier Grids I get from Denis Bethier's 4.1 Example for Whips on his URL:

http://denis.berthier.pagesperso-orange.fr/HLS/Whips.html

Code: Select all: _whips_4dot1 = '.16..5....7.4.9.....98....4.4.....29...54.....2..6.1.8..1....3.......6.5....8....'

The entries in square brackets [] are the givens. The solved squares will be in parenthesis ()

Code: Select all: RC=N => 2348 [1] [6] | 237 237 [5] | 23789 789 237 2358 [7] 2358 | [4] 123 [9] | 2358 1568 1236 235 35 [9] | [8] 1237 12367 | 2357 1567 [4] ------------------------+------------------------+------------------------ 135678 [4] 3578 | 137 137 1378 | 357 [2] [9] 136789 3689 378 | [5] [4] 12378 | 37 67 367 3579 [2] 357 | 379 [6] 37 | [1] 457 [8] ------------------------+------------------------+------------------------ 2456789 5689 [1] | 2679 2579 2467 | 24789 [3] 27 234789 389 23478 | 12379 12379 12347 | [6] 14789 [5] 2345679 3569 23457 | 123679 [8] 123467 | 2479 1479 127 RN=C => [2] 14579 14579 | 1 [6] [3] | 45789 178 78 589 13579 13579 | [4] 1378 89 | [2] 1378 [6] 568 1567 12567 | [9] 1278 68 | 5678 [4] [3] ------------------------+------------------------+------------------------ 1456 [8] 134567 | [2] 137 1 | 134567 136 [9] 16 6 123679 | [5] [4] 1289 | 136789 1236 12 [7] [2] 1346 | 8 138 [5] | 13468 [9] 14 ------------------------+------------------------+------------------------ [3] 145679 [8] | 167 125 1246 | 145679 127 12457 4568 13456 123456 | 1368 [9] [7] | 134568 1238 12458 4689 134679 12346 | 13678 123 1246 |1346789 [5] 12478 NC=R => 45 [1] [7] | 489 2348 34589 | [6] 2389 29 123789 [6] 289 | 1789 12378 35789 | 12379 [4] 1279 12345689 3589 245689 | 14689 12348 345689 | 12345 [7] 125 ---------------------------+---------------------------+--------------------------- 1789 [4] 89 | [2] [5] 789 | 79 689 [3] 234679 379 2469 | [5] 7 [1] | 234 236 [8] 4579 579 [1] | 79 [6] 379 | [8] 235 25 ---------------------------+---------------------------+--------------------------- 456789 [2] 45689 | 146789 13478 3456789 | 134579 135689 1579 124578 578 2458 | [3] [9] 45 | 127 128 [6] 56789 5789 [3] | 6789 78 [2] | 179 189 [4] BN=S => [2] 1467 14678 | 1 4678 [3] | [5] 146 [9] 589 12589 12589 | [4] [3] 9 | 1289 [7] [6] 568 13467 13467 | [9] 4578 568 | 12378 1245 12 ---------------------------+---------------------------+--------------------------- 14 [8] 1345679 | [2] 1379 145 | 134679 13456 457 1236 6 123679 | [5] [4] [8] | 123679 36 7 [7] [2] 146 | 8 18 56 | 14568 [9] [3] ---------------------------+---------------------------+--------------------------- [3] 14679 456789 | 14679 12789 1278 | 14679 12456 124578 45679 12345679 45679 | 369 2 1379 | 12345679 [8] 12457 589 1379 [2] | 1578 [6] [4] | 135789 15 1578

Here are the first batch of singleton solutions I get:

Code: Select all: s001 bns r1c1=n4, b1n4=s1, r1n4=c1, n4c1=r1 s002 bns r3c6=n6, b2n6=s9, r3n6=c6, n6c6=r3 s003 bns r5c6=n2, b5n2=s6, r5n2=c6, n2c6=r5 s004 bns r4c6=n8, b5n8=s3, r4n8=c6, n8c6=r4 s005 bns r6c4=n9, b5n9=s7, r6n9=c4, n9c4=r6 s006 bns r6c8=n4, b6n4=s8, r6n4=c8, n4c8=r6 s007 bns r4c7=n5, b6n5=s1, r4n5=c7, n5c7=r4 s008 bns r7c5=n5, b8n5=s2, r7n5=c5, n5c5=r7 s009 rnc r4c1=n6, r4n6=c1, n6c1=r4, b4n6=s1 s010 bns r5c1=n1, b4n1=s4, r5n1=c1, n1c1=r5 s011 rnc r5c2=n9, r5n9=c2, n9c2=r5, b4n9=s5 s012 rnc r5c3=n8, r5n8=c3, n8c3=r5, b4n8=s6 s013 ncr r8c5=n9, n9c5=r8, r8n9=c5, b8n9=s5

Which updates the four grids to this:

Code: Select all: RC=N => (4) [1] [6] | 237 237 [5] |23789 789 237 2358 [7] 235 | [4] 123 [9] | 238 1568 1236 235 35 [9] | [8] 1237 (6) | 237 157 [4] ------------------+------------------+------------------ (6) [4] 37 | 137 137 (8) | (5) [2] [9] (1) (9) (8) | [5] [4] (2) | 37 67 367 357 [2] 357 | (9) [6] 37 | [1] (4) [8] ------------------+------------------+------------------ 2789 68 [1] | 267 (5) 47 |24789 [3] 27 2378 38 2347 | 1237 (9) 1347 | [6] 178 [5] 23579 356 23457 |12367 [8] 1347 | 2479 179 127 RN=C => [2] 4579 4579 | (1) [6] [3] | 45789 78 78 589 13579 13579 | [4] 138 89 | [2] 178 [6] 58 157 1257 | [9] 128 (6) | 578 [4] [3] ------------------------+------------------------+------------------------ 45 [8] 345 | [2] (7) (1) | 345 (6) [9] (1) (6) 79 | [5] [4] 89 | 789 (3) (2) [7] [2] 136 | (8) 13 [5] | 136 [9] (4) ------------------------+------------------------+------------------------ [3] 1479 [8] | 67 (5) 24 | 14679 127 17 468 134 12346 | 36 [9] [7] | 13468 128 (5) 4689 13479 12346 | 367 123 24 |1346789 [5] 178 NC=R => (5) [1] [7] | 489 234 89 | [6] 2389 29 23789 [6] 289 | 1789 123 (5) |12379 [4] 1279 23689 389 24689 | 1489 1234 689 | 1235 [7] 125 ------------------+------------------+------------------ (1) [4] 89 | [2] [5] 789 | 79 (6) [3] 2369 39 269 | [5] (7) [1] | (4) 23 [8] (4) 79 [1] | 79 [6] (3) | [8] 25 25 ------------------+------------------+------------------ 6789 [2] 4689 |14789 134 6789 |13579 13589 1579 278 78 (5) | [3] [9] (4) | 127 128 [6] 79 (5) [3] | (6) (8) [2] | 179 19 [4] BN=S => [2] 467 4678 | (1) 4678 [3] | [5] 46 [9] 58 1258 1258 | [4] [3] (9) | 128 [7] [6] 568 13467 13467 | [9] 4578 568 | 12378 1245 12 ---------------------+---------------------+--------------------- (4) [8] 379 | [2] 379 (1) | 379 (6) (5) 12 (6) 129 | [5] [4] [8] | 129 (3) (7) [7] [2] 46 | (8) (1) 56 | 456 [9] [3] ---------------------+---------------------+--------------------- [3] 14679 456789| 14679 12789 1278 | 14679 12456 124578 4679 134679 4679 | 369 (2) 1379 | 134679 [8] (5) 589 1379 [2] | 1578 [6] [4] | 135789 15 1578

Now what I think will be interesting is what chains might I come up with these 4 grids to start with instead of
just the customary RCN grid. Of course there are some other simpler patterns that might POP-OUT first!

Let me know what you think?

by **RichardGoodrich** » Mon Nov 11, 2013 4:13 pm

Must be bug in code because it missed r2c1=n8h (the h on end is for hidden). Asserting that I get the following grids:

s14 r2c1=n8h (last h means hidden)

RC=N =>

Code: Select all: (4) [1] [6] | 237 237 [5] |23789 789 237 (8) [7] 235 | [4] 123 [9] | 23 156 1236 235 35 [9] | [8] 1237 1367 | 237 1567 [4] ------------------+------------------+------------------ (6) [4] 37 | (1) 37 (8) | (5) [2] [9] (1) (9) (8) | [5] [4] (2) | 37 67 367 357 [2] 357 | 379 [6] 37 | [1] (4) [8] ------------------+------------------+------------------ 279 68 [1] | 267 (5) 467 |24789 [3] 27 237 38 2347 | 237 (9) 1347 | [6] 178 [5] 23579 356 23457 | 2367 [8] 13467 | 2479 179 127

RN=C =>

Code: Select all: [2] 4579 4579 | (1) [6] [3] | 45789 78 78 589 3579 3579 | [4] 38 89 | [2] (1) [6] 568 157 12567 | [9] 128 68 | 5678 [4] [3] ------------------------+------------------------+------------------------ (4) [8] 35 | [2] (7) (1) | 35 (6) [9] (1) (6) 79 | [5] [4] 89 | 789 (3) (2) [7] [2] 1346 | (8) 13 [5] | 1346 [9] 14 ------------------------+------------------------+------------------------ [3] 1479 [8] | 67 (5) 246 | 14679 27 147 68 134 12346 | 36 [9] [7] | 13468 28 (5) 689 13479 12346 | 367 123 246 |1346789 [5] 1478

NC=R =>

Code: Select all: (5) [1] [7] | (4) 23 389 | [6] 2389 29 3789 [6] 289 | 1789 123 (5) |12379 [4] 1279 3689 389 24689 | 1689 1234 3689 | 1235 [7] 125 ------------------+------------------+------------------ (1) [4] 89 | [2] [5] 789 | 79 (6) [3] 369 39 269 | [5] (7) [1] | (4) 23 [8] (4) 79 [1] | 79 [6] 379 | [8] 235 25 ------------------+------------------+------------------ 6789 [2] 4689 |16789 134 36789 |13579 13589 1579 (2) 78 (5) | [3] [9] (4) | 17 18 [6] 679 (5) [3] | 679 (8) [2] | 179 19 [4]

BN=S =>

Code: Select all: [2] 67 678 | (1) 678 [3] | [5] (4) [9] 589 12589 12589 | [4] [3] 9 | 1289 [7] [6] 568 13467 13467 | [9] 4578 568 | 12378 1245 12 ---------------------+---------------------+--------------------- (4) [8] 379 | [2] 379 (1) | 379 (6) (5) (1) (6) 279 | [5] [4] [8] | 279 (3) 7 [7] [2] 46 | (8) (1) 56 | 456 [9] [3] ---------------------+---------------------+--------------------- [3] 14679 456789| 14679 12789 1278 | 14679 12456 124578 4679 134679 4679 | 369 (2) 1379 | 134679 [8] (5) 589 1379 [2] | 1578 [6] [4] | 135789 15 1578

Now here is where the utility of the four grids start paying off:
In the RN=C grid we see: r1n89=c78 which when translated to
the RC=N grid shows this: r1c78 = n89

Clearly that is a hidden pair leading to the following eliminations and produces
the following in my trace:

01 HPiR r1c78=n89 (HPiR = Hidden Pair in Row)
02 ------------------>
03 s15 r1c7-n2
04 s16 r1c7-n3
05 s17 r1c7-n7
06 s18 r1c8-n7
07 ----------------<

My trace just above notes a condition as shown on line 01. Then using the dashed
lines of line 02 and line 07 brackets the grid operations on lines 03-06 which are
eliminations where the '-' is used instead of '<>' because I can enter r1c7-n2
for example (and it likes - vs <>) and the 4 grids are updated.

Would I have found the hidden pair 89 in the RC=N grid - maybe but it was
glaring in the RN=C grid. Now the grids are:

RC=N =>

Code: Select all: (4) [1] [6] | 237 237 [5] | 89 89 237 (8) [7] 235 | [4] 123 [9] | 23 156 1236 235 35 [9] | [8] 1237 1367 | 237 1567 [4] ------------------+------------------+------------------ (6) [4] 37 | (1) 37 (8) | (5) [2] [9] (1) (9) (8) | [5] [4] (2) | 37 67 367 357 [2] 357 | 379 [6] 37 | [1] (4) [8] ------------------+------------------+------------------ 279 68 [1] | 267 (5) 467 |24789 [3] 27 237 38 2347 | 237 (9) 1347 | [6] 178 [5] 23579 356 23457 | 2367 [8] 13467 | 2479 179 127

RN=C =>

Code: Select all: [2] 459 459 | (1) [6] [3] | 459 78 78 589 3579 3579 | [4] 38 89 | [2] (1) [6] 568 157 12567 | [9] 128 68 | 5678 [4] [3] ------------------------+------------------------+------------------------ (4) [8] 35 | [2] (7) (1) | 35 (6) [9] (1) (6) 79 | [5] [4] 89 | 789 (3) (2) [7] [2] 1346 | (8) 13 [5] | 1346 [9] 14 ------------------------+------------------------+------------------------ [3] 1479 [8] | 67 (5) 246 | 14679 27 147 68 134 12346 | 36 [9] [7] | 13468 28 (5) 689 13479 12346 | 367 123 246 |1346789 [5] 1478

NC=R =>

Code: Select all: (5) [1] [7] | (4) 23 389 | [6] 2389 29 3789 [6] 289 | 1789 123 (5) | 2379 [4] 1279 3689 389 24689 | 1689 1234 3689 | 235 [7] 125 ------------------+------------------+------------------ (1) [4] 89 | [2] [5] 789 | 79 (6) [3] 369 39 269 | [5] (7) [1] | (4) 23 [8] (4) 79 [1] | 79 [6] 379 | [8] 235 25 ------------------+------------------+------------------ 6789 [2] 4689 |16789 134 36789 | 3579 3589 1579 (2) 78 (5) | [3] [9] (4) | 17 18 [6] 679 (5) [3] | 679 (8) [2] | 179 19 [4]

BN=S =>

Code: Select all: [2] 67 678 | (1) 678 [3] | [5] (4) [9] 589 12589 12589 | [4] [3] 9 | 1289 [7] [6] 568 3467 3467 | [9] 4578 568 | 378 1245 12 ---------------------+---------------------+--------------------- (4) [8] 379 | [2] 379 (1) | 379 (6) (5) (1) (6) 279 | [5] [4] [8] | 279 (3) 7 [7] [2] 46 | (8) (1) 56 | 456 [9] [3] ---------------------+---------------------+--------------------- [3] 14679 456789| 14679 12789 1278 | 14679 12456 124578 4679 134679 4679 | 369 (2) 1379 | 134679 [8] (5) 589 1379 [2] | 1578 [6] [4] | 135789 15 1578

The New Sudoku Players' Forum

Denis Berhtier Whip 4dot1 in BigSudoku Python Code

Denis Berhtier Whip 4dot1 in BigSudoku Python Code

Re: Denis Berhtier Whip 4dot1 in BigSudoku Python Code