The New Sudoku Players' Forum

by ab » Wed May 03, 2006 3:54 pm

two more non-minimal 21s for which we already have 20s:

Code: Select all: ...|.7.|... ..9|...|5.. .58|...|39. ----------- ...|3.9|... 7..|.8.|..2 ...|6.7|... ----------- .35|...|96. ..6|...|8.. ...|.4.|... 1-4-4-2-1 ...|...|... .4.|...|.6. ..2|9.7|5.. ----------- ..7|.6.|2.. ...|538|... ..8|.4.|9.. ----------- ..9|2.6|8.. .6.|...|.5. ...|...|... 0-8-6-1-1

by **Ocean** » Fri May 05, 2006 1:31 pm

Here is a minimal 20. (We already have a non-minimal with equivalent pattern: #08 (ab))
This one is seems to be quite hard to solve (to me, at least).

Code: Select all: [M20 0-9-6-0-0] . . . | . . . | . . . . 1 . | . 2 . | . 3 . . . 4 | 5 . 6 | 7 . . -------+-------+------- . . 6 | . . . | 5 . . . 2 . | . . . | . 8 . . . 8 | . . . | 9 . . -------+-------+------- . . 5 | 4 . 7 | 6 . . . 8 . | . 9 . | . 1 . . . . | . . . | . . . 0-9-6-0 0-10-5-0 17-0-6-0 17-10-0-0 18-0-5-0 18-9-0-0

by **ronk** » Fri May 05, 2006 2:48 pm

Ocean wrote:[M20 0-9-6-0-0]
(...)
0-9-6-0 0-10-5-0 17-0-6-0 17-10-0-0 18-0-5-0 18-9-0-0 [/code]

The 'M20" is the only part I get. Where can I find a meaning for the other numbers?

by **Ocean** » Fri May 05, 2006 3:44 pm

ronk wrote:
Ocean wrote:[M20 0-9-6-0-0]
(...)
0-9-6-0 0-10-5-0 17-0-6-0 17-10-0-0 18-0-5-0 18-9-0-0-[/code]

The 'M20" is the only part I get. Where can I find a meaning for the other numbers?

"M20" is just my way of labelling a minimal puzzle with 20 clues.

[0-9-6-0-0] is the "pattern code" as JPF defined it earlier in this thread. The digits are decimal representations of the 'binary digits' that uniquely define the pattern.

0-9-6-0-0, 0-10-5-0-0, 17-0-6-0-0, 17-10-0-0-0, 18-0-5-0-0, 18-9-0-0-0 are pattern codes for the six equivalent symmetric patterns. See the list from gfroyle earlier in this thread. (I 'forgot' the last digit, which is always 0 for 20-clues with full symmetry.)

Code: Select all: Here is shown the 'defining' part of the pattern [0-9-6-0-0], together with one of its equivalents, [0-10-5-0-0] (swap row 2 and 3, row 7 and 8, column 2 and 3, column 7 and 8): [0-9-6-0-0] 0 0 0 | 0 0 . | . . . . 1 0 | 0 1 . | . . . . . 1 | 1 0 . | . . . -------+-------+------- . . . | 0 0 . | . . . . . . | . 0 . | . . . . . . | . . . | . . . -------+-------+------- . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . [0-10-5-0-0] 0 0 0 | 0 0 . | . . . . 1 0 | 1 0 . | . . . . . 1 | 0 1 . | . . . -------+-------+------- . . . | 0 0 . | . . . . . . | . 0 . | . . . . . . | . . . | . . . -------+-------+------- . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . .

The puzzle posted above might be a challenge to solve (have not figured out how yet). Pencilmarks after eliminations by three naked pairs, locked candidates, naked triples, hidden pairs, and two x-wings, and still no digit filled in:

Code: Select all: *------------------------------------------------------------------------* | 356789 567 2379 | 13789 47 13489 | 1248 456 145689 | | 56 1 79 | 789 2 489 | 48 3 56 | | 238 39 4 | 5 138 6 | 7 29 18 | |-----------------------+------------------------+-----------------------| | 139 47 6 | 12389 138 12389 | 5 47 123 | | 134579 2 1379 | 13679 4567 13459 | 134 8 13467 | | 13457 457 8 | 12367 4567 12345 | 9 467 123467 | |-----------------------+------------------------+-----------------------| | 123 39 5 | 4 138 7 | 6 29 38 | | 3467 8 237 | 236 9 235 | 234 1 3457 | | 134679 467 12379 | 12368 56 12358 | 2348 457 345789 | *------------------------------------------------------------------------*

by ab » Fri May 05, 2006 4:22 pm

Ocean wrote:The puzzle posted above might be a challenge to solve (have not figured out how yet).

So how did you find it then??

by **Ocean** » Fri May 05, 2006 4:39 pm

ab wrote:
Ocean wrote:The puzzle posted above might be a challenge to solve (have not figured out how yet).

So how did you find it then??

I mean, I haven't figured out how to solve it by logic. Solving it by brute force is no problem.

by **Havard** » Fri May 05, 2006 5:24 pm

Ocean wrote:
ab wrote:
Ocean wrote:The puzzle posted above might be a challenge to solve (have not figured out how yet).

So how did you find it then??

I mean, I haven't figured out how to solve it by logic. Solving it by brute force is no problem.

is that a challenge?

Code: Select all: Swordfish in columns: 2 5 8 356789 567X 2379 | 13789 47 13489 | 1248 456X 145689 56 1 79 | 789 2 489 | 48 3 56 238 39 4 | 5 138 6 | 7 29 18 ---------------------+----------------------+--------------------- 139 47 6 | 12389 138 12389 | 5 47 123 134579 2 1379 | 13679 4567X 13459 | 134 8 13467 13457 457X 8 | 12367 4567X 12345- | 9 467 123467 ---------------------+----------------------+--------------------- 123 39 5 | 4 138 7 | 6 29 38 3467 8 237 | 236 9 235 | 234 1 3457 134679 467 12379 | 12368 56X 12358 | 2348 457X 345789 5 5X . | . . . | . 5X 5 5 . . | . . . | . . 5 . . . | 5 . . | . . . ---------+----------+--------- . . . | . . . | 5 . . 5 . . | . 5X 5 | . . . 5 5X . | . 5X 5- | . . . ---------+----------+--------- . . 5 | . . . | . . . . . . | . . 5 | . . 5 . . . | . 5X 5 | . 5X 5 Swordfish in columns: 2 5 8 356789 567X 2379 | 13789 47 13489 | 1248 456X 145689 56 1 79 | 789 2 489 | 48 3 56 238 39 4 | 5 138 6 | 7 29 18 ---------------------+----------------------+--------------------- 139 47 6 | 12389 138 12389 | 5 47 123 134579 2 1379 | 13679 4567X 13459 | 134 8 13467 13457 457 8 | 12367- 4567X 1234 | 9 467X 123467 ---------------------+----------------------+--------------------- 123 39 5 | 4 138 7 | 6 29 38 3467 8 237 | 236 9 235 | 234 1 3457 134679 467X 12379 | 12368 56X 12358 | 2348 457 345789 6 6X . | . . . | . 6X 6 6 . . | . . . | . . 6 . . . | . . 6 | . . . ---------+----------+--------- . . 6 | . . . | . . . . . . | 6 6X . | . . 6 . . . | 6- 6X . | . 6X 6 ---------+----------+--------- . . . | . . . | 6 . . 6 . . | 6 . . | . . . 6 6X . | 6 6X . | . . . Jellyfish in columns: 3 4 6 7 356789 567 2379 | 13789X 47 13489X | 1248X 456 145689- 56 1 79 | 789 2 489 | 48 3 56 238 39 4 | 5 138 6 | 7 29 18 ------------------------+-------------------------+------------------------ 139 47 6 | 12389X 138- 12389X | 5 47 123 134579- 2 1379X | 13679X- 4567 13459X- | 134X 8 13467- 13457 457 8 | 1237X 4567 1234X | 9 467 123467 ------------------------+-------------------------+------------------------ 123 39 5 | 4 138 7 | 6 29 38 3467 8 237 | 236 9 235 | 234 1 3457 134679- 467 12379X | 12368X 56 12358X | 2348 457 345789 . . . | 1X . 1X | 1X . 1- . 1 . | . . . | . . . . . . | . 1 . | . . 1 ------------+-------------+------------ 1 . . | 1X 1- 1X | . . 1 1- . 1X | 1X- . 1X- | 1X . 1- 1 . . | 1X . 1X | . . 1 ------------+-------------+------------ 1 . . | . 1 . | . . . . . . | . . . | . 1 . 1- . 1X | 1X . 1X | . . . Almost Locked Sets XY rule: 356789 567 2379 | 13789 47 13489 | 1248 456 45689 56 1 79 | 789 2 489 | 48 3 56 238 39 4 | 5 138#a 6 | 7 29 18#b ---------------------+----------------------+--------------------- 139 47 6 | 12389 38#a 12389 | 5 47 123 34579 2 1379 | 3679 4567 3459 | 134 8 3467 13457 457 8 | 1237 4567 1234 | 9 467 123467 ---------------------+----------------------+--------------------- 123 39 5 | 4 138-3 7 | 6 29 38#c 3467 8 237 | 236 9 235 | 234 1 3457 34679 467 12379 | 12368 56 12358 | 2348 457 345789 Swordfish in rows: 4 6 7 356789 567 2379 | 13789 47 13489 | 1248 456 45689 56 1 79 | 789 2 489 | 48 3 56 238 39 4 | 5 138 6 | 7 29 18 ------------------------+-------------------------+------------------------ 139X 47 6 | 12389X 38X 12389X | 5 47 123X 34579 2 1379 | 3679 4567 3459 | 134 8 3467 13457X 457 8 | 1237X 4567 1234X | 9 467 123467X ------------------------+-------------------------+------------------------ 123X 39X 5 | 4 18 7 | 6 29 38X 3467- 8 237 | 236 9 235 | 234 1 3457 34679- 467 12379 | 12368 56 12358 | 2348 457 345789 3 . 3 | 3 . 3 | . . . . . . | . . . | . 3 . 3 3 . | . 3 . | . . . ---------+----------+--------- 3X . . | 3X 3X 3X | . . 3X 3 . 3 | 3 . 3 | 3 . 3 3X . . | 3X . 3X | . . 3X ---------+----------+--------- 3X 3X . | . . . | . . 3X 3- . 3 | 3 . 3 | 3 . 3 3- . 3 | 3 . 3 | 3 . 3 Almost Locked Sets XZ rule 356789 567 2379 | 13789 47 13489 | 1248#a 456 45689-8 56 1 79 | 789 2 489 | 48#a 3 56 238 39 4 | 5 138 6 | 7 29 18#a ------------------------+-------------------------+--------------------------- 139 47 6 | 12389 38 12389 | 5 47 123 34579 2 1379 | 3679 4567 3459 | 134-4 8 3467 13457 457 8 | 1237 4567 1234 | 9 467 123467 ------------------------+-------------------------+--------------------------- 123 39 5 | 4 18 7 | 6 29 38#b 467 8 237 | 236 9 235 | 234#b 1 3457-3 4679 467 12379 | 12368 56 12358 | 2348#b 457 345789-38 Almost Locked Sets XY rule: 356789 567 2379 | 13789-9 47#c 13489-9 | 1248 456#a 4569#a 56 1 79 | 789#c 2 489#c | 48#b 3 56#a 238 39 4 | 5 138 6 | 7 29 18 ------------------------+-------------------------+------------------------ 139 47 6 | 12389 38 12389 | 5 47 123 34579 2 1379 | 3679 4567 3459 | 13 8 3467 13457 457 8 | 1237 4567 1234 | 9 467 123467 ------------------------+-------------------------+------------------------ 123 39 5 | 4 18 7 | 6 29 38 467 8 237 | 236 9 235 | 234 1 457 4679 467 123 | 1238 56 1238 | 238 457 4579 XY-wing: 8 56 9 | 13 7 13 | 2 456 456 56 1 7 | 9 2 4 | 8 3 56 2 3 4 | 5 8 6 | 7 9 1 ------------------+-------------------+------------------ 19 47 6 | 18# 3 189 | 5 47 2 4579 2 3 | 67 456 59 | 1 8 467 1457 457 8 | 127-2 456 12# | 9 467 3 ------------------+-------------------+------------------ 3 9 5 | 4 1 7 | 6 2 8 67 8 2 | 36 9 35 | 4 1 57 467 467 1 | 28# 56 28-2 | 3 57 9 XY-wing: 8 56 9 | 13 7 13 | 2 456 456 56# 1 7 | 9 2 4 | 8 3 56-5 2 3 4 | 5 8 6 | 7 9 1 ---------------+----------------+--------------- 19 47 6 | 8 3 19 | 5 47 2 4579 2 3 | 67 456 59 | 1 8 467 1457 457 8 | 17 456 2 | 9 467 3 ---------------+----------------+--------------- 3 9 5 | 4 1 7 | 6 2 8 67# 8 2 | 36 9 35 | 4 1 57# 467 467 1 | 2 56 8 | 3 57 9 X-Wing in columns: 2 8 8 6 9 | 13 7 13 | 2 45 45 5 1 7 | 9 2 4 | 8 3 6 2 3 4 | 5 8 6 | 7 9 1 ---------------+----------------+--------------- 19 47X 6 | 8 3 19 | 5 47X 2 479 2 3 | 67 56 59 | 1 8 47 17 5 8 | 17 4 2 | 9 6 3 ---------------+----------------+--------------- 3 9 5 | 4 1 7 | 6 2 8 67 8 2 | 36 9 35 | 4 1 57 467- 47X 1 | 2 56 8 | 3 57X 9 . . . | . 7 . | . . . . . 7 | . . . | . . . . . . | . . . | 7 . . ---------+----------+--------- . 7X . | . . . | . 7X . 7 . . | 7 . . | . . 7 7 . . | 7 . . | . . . ---------+----------+--------- . . . | . . 7 | . . . 7 . . | . . . | . . 7 7- 7X . | . . . | . 7X . Almost Locked Sets XY rule: 8 6 9 | 13#c 7 13#d | 2 45 45 5 1 7 | 9 2 4 | 8 3 6 2 3 4 | 5 8 6 | 7 9 1 ---------------+----------------+--------------- 19 47 6 | 8 3 19#g | 5 47 2 479 2 3 | 67 56 59#f | 1 8 47 17-7 5 8 | 17#h 4 2 | 9 6 3 ---------------+----------------+--------------- 3 9 5 | 4 1 7 | 6 2 8 67#a 8 2 | 36#b 9 35#e | 4 1 57 46 47 1 | 2 56 8 | 3 57 9

Havard

by **ronk** » Fri May 05, 2006 5:57 pm

Havard wrote:
Code: Select all
Almost Locked Sets XY rule: 8 6 9 | 13#c 7 13#d | 2 45 45 5 1 7 | 9 2 4 | 8 3 6 2 3 4 | 5 8 6 | 7 9 1 ---------------+----------------+--------------- 19 47 6 | 8 3 19#g | 5 47 2 479 2 3 | 67 56 59#f | 1 8 47 17-7 5 8 | 17#h 4 2 | 9 6 3 ---------------+----------------+--------------- 3 9 5 | 4 1 7 | 6 2 8 67#a 8 2 | 36#b 9 35#e | 4 1 57 46 47 1 | 2 56 8 | 3 57 9

For two reasons, I take issue with your use of the term "Almost Locked Sets XY rule".

bennys' defined the ALS xy-rule as involving exactly three sets
for this exclsion, you are illustrating an xy-chain

by **Havard** » Fri May 05, 2006 6:33 pm

ronk wrote:
Havard wrote:
Code: Select all
Almost Locked Sets XY rule: 8 6 9 | 13#c 7 13#d | 2 45 45 5 1 7 | 9 2 4 | 8 3 6 2 3 4 | 5 8 6 | 7 9 1 ---------------+----------------+--------------- 19 47 6 | 8 3 19#g | 5 47 2 479 2 3 | 67 56 59#f | 1 8 47 17-7 5 8 | 17#h 4 2 | 9 6 3 ---------------+----------------+--------------- 3 9 5 | 4 1 7 | 6 2 8 67#a 8 2 | 36#b 9 35#e | 4 1 57 46 47 1 | 2 56 8 | 3 57 9

For two reasons, I take issue with your use of the term "Almost Locked Sets XY rule".
bennys' defined the ALS xy-rule as involving exactly three sets
for this exclsion, you are illustrating an xy-chain

What about "ALS-Chain" ?

Havard

by **ronk** » Fri May 05, 2006 7:11 pm

Havard wrote:What about "ALS-Chain" ?

Much better than "ALS XY rule" and even correct, I suppose, but not as precise as "xy-chain".

Should we then also refer to an xy-wing as an ALS chain? I certainly hope not.

by **tarek** » Fri May 05, 2006 7:15 pm

an alternative solution:

Code: Select all: 20 Givens & 61 Left *--------------------------------------------------------------------------* | 356789 567 2379 | 13789 47 13489 |*1248 456 145689 | | 56 1 79 | 789 2 489 | 48 3 56 | | 238 39 4 | 5 138 6 | 7 29 18 | |------------------------+------------------------+------------------------| | 139 47 6 |#12389 138 12389 | 5 47 123 | | 134579 2 *1379 |*13679 4567 -13459 |*134 8 13467 | | 13457 457 8 |#12367 4567 12345 | 9 467 123467 | |------------------------+------------------------+------------------------| | 123 39 5 | 4 138 7 | 6 29 38 | | 3467 8 237 | 236 9 235 | 234 1 3457 | | 134679 467 *12379 |*12368 56 12358 | 2348 457 345789 | *--------------------------------------------------------------------------* Eliminating 1 From r5c6 (Finned Swordfish in Columns 347) *--------------------------------------------------------------------------* | 356789 *567 2379 | 13789 47 13489 | 1248 *456 145689 | | 56 1 79 | 789 2 489 | 48 3 56 | | 238 39 4 | 5 138 6 | 7 29 18 | |------------------------+------------------------+------------------------| | 139 47 6 | 12389 138 12389 | 5 47 123 | | 134579 2 1379 | 13679 #4567 3459 | 134 8 13467 | | 13457 *457 8 | 12367 *4567 -12345 | 9 467 123467 | |------------------------+------------------------+------------------------| | 123 39 5 | 4 138 7 | 6 29 38 | | 3467 8 237 | 236 9 235 | 234 1 3457 | | 134679 467 12379 | 12368 *56 12358 | 2348 *457 345789 | *--------------------------------------------------------------------------* Eliminating 5 From r6c6 (Finned Swordfish in Columns 258) *--------------------------------------------------------------------------* | 356789 567 2379 | 13789 47 13489 | 1248 456 145689 | |*56 1 79 | 789 2 489 | 48 3 *56 | | 238 39 4 | 5 138 6 | 7 29 18 | |------------------------+------------------------+------------------------| | 139 47 6 | 12389 138 12389 | 5 47 123 | | 134579 2 1379 |*13679 #4567 3459 | 134 8 *13467 | | 13457 457 8 |-12367 4567 1234 | 9 467 123467 | |------------------------+------------------------+------------------------| | 123 39 5 | 4 138 7 | 6 29 38 | |*3467 8 237 |*236 9 235 | 234 1 3457 | | 134679 467 12379 | 12368 56 12358 | 2348 457 345789 | *--------------------------------------------------------------------------* Eliminating 6 From r6c4 (Finned Swordfish in rows 258) *--------------------------------------------------------------------------* | 356789 567 2379 | 13789 47 13489 | 1248 456 145689 | | 56 1 79 | 789 2 489 |*48 3 56 | | 238 39 4 | 5 138 6 | 7 29 18 | |------------------------+------------------------+------------------------| | 139 47 6 | 12389 138 12389 | 5 47 123 | | 134579 2 1379 | 13679 4567 3459 | 134 8 13467 | | 13457 457 8 | 1237 4567 1234 | 9 467 123467 | |------------------------+------------------------+------------------------| | 123 %39 5 | 4 138 7 | 6 %29 -38 | | 3467 8 237 | 236 9 235 |*234 1 3457 | | 134679 467 12379 | 12368 56 12358 |*2348 457 345789 | *--------------------------------------------------------------------------* Eliminating 3 from r7c9(ALS-XZ A=2348 in r2c7, r8c7, r9c7 B=239 in r7c2, r7c8 x=2 z=3) *--------------------------------------------------------------------------* | 356789 567 2379 | 13789 47 13489 | 248 456 4569 | | 56 1 79 | 789 2 489 | 48 3 56 | | 238 39 4 | 5 38 6 | 7 29 1 | |------------------------+------------------------+------------------------| | 139 47 6 | 12389 38 12389 | 5 47 23 | | 34579 2 379 | 3679 4567 3459 | 1 8 3467 | | 13457 457 8 | 1237 4567 1234 | 9 467 23467 | |------------------------+------------------------+------------------------| | 23 39 5 | 4 1 7 | 6 29 8 | | 3467 8 237 | 236 9 235 | 234 1 3457 | | 34679 467 1 | 2368 56 2358 | 234 457 34579 | *--------------------------------------------------------------------------* Eliminating 3 From r8c9 (Column 7 & Box 9 Box-line interaction) Eliminating 3 From r9c9 (Column 7 & Box 9 Box-line interaction) *--------------------------------------------------------------------------* | 356789 567 2379 | 13789 47 13489 | 248 456 4569 | | 56 1 79 | 789 2 489 | 48 3 56 | | 238 39 4 | 5 38 6 | 7 29 1 | |------------------------+------------------------+------------------------| | 139 47 6 | 12389 38 12389 | 5 47 23 | | 34579 2 379 | 3679 4567 3459 | 1 8 3467 | | 13457 457 8 | 1237 4567 1234 | 9 467 23467 | |------------------------+------------------------+------------------------| | 23 39 5 | 4 1 7 | 6 29 8 | | 3467 8 237 | 236 9 235 | 234 1 457 | | 34679 467 1 | 2368 56 2358 | 234 457 4579 | *--------------------------------------------------------------------------* Eliminating 3 From r8c1 (Row 7 & Box 7 Box-line interaction) Eliminating 3 From r8c3 (Row 7 & Box 7 Box-line interaction) Eliminating 3 From r9c1 (Row 7 & Box 7 Box-line interaction) *--------------------------------------------------------------------------* | 356789 567 2379 | 13789 47 13489 | 248 456 4569 | | 56 1 79 | 789 2 489 | 48 3 56 | | 238 39 4 | 5 38 6 | 7 29 1 | |------------------------+------------------------+------------------------| | 139 47 6 | 12389 38 12389 | 5 47 23 | | 34579 2 379 | 3679 4567 3459 | 1 8 3467 | | 13457 457 8 | 1237 4567 1234 | 9 467 23467 | |------------------------+------------------------+------------------------| | 23 39 5 | 4 1 7 | 6 29 8 | | 467 8 27 | 236 9 235 | 234 1 457 | | 4679 467 1 | 2368 56 2358 | 234 457 4579 | *--------------------------------------------------------------------------* r9c4 Must only have 238 as valid Candidates (238 is a Hidden Triple in Row 9) r9c6 Must only have 238 as valid Candidates (238 is a Hidden Triple in Row 9) r9c7 Must only have 23 as valid Candidates (238 is a Hidden Triple in Row 9) *--------------------------------------------------------------------------* | 356789 567 2379 | 13789 47 13489 | 248 456 4569 | | 56 1 *79 | 789 2 489 | 48 3 56 | | 238 -39 4 | 5 38 6 | 7 29 1 | |------------------------+------------------------+------------------------| | 139 47 6 | 12389 38 12389 | 5 47 23 | | 34579 2 379 | 3679 4567 3459 | 1 8 3467 | | 13457 457 8 | 1237 4567 1234 | 9 467 23467 | |------------------------+------------------------+------------------------| |%23 %39 5 | 4 1 7 | 6 29 8 | | 467 8 *27 | 236 9 235 | 234 1 457 | | 4679 467 1 | 238 56 238 | 23 457 4579 | *--------------------------------------------------------------------------* Eliminating 9 from r3c2(ALS-XZ A=279 in r2c3, r8c3 B=239 in r7c2, r7c1 x=2 z=9) *--------------------------------------------------------* | 8 56 9 | 13 7 13 | 2 456 456 | | 56 1 7 | 9 2 4 | 8 3 56 | | 2 3 4 | 5 8 6 | 7 9 1 | |------------------+------------------+------------------| | 19 47 6 |*18 3 189 | 5 47 2 | | 4579 2 3 | 67 456 59 | 1 8 467 | | 1457 457 8 |-127 456 *12 | 9 467 3 | |------------------+------------------+------------------| | 3 9 5 | 4 1 7 | 6 2 8 | | 67 8 2 | 36 9 35 | 4 1 57 | | 467 467 1 |*28 56 -28 | 3 57 9 | *--------------------------------------------------------* Eliminating 2 From r9c6 (8 & 1 in r4c4 form an XY wing with 2 in r9c4 & r6c6) Eliminating 2 From r6c4 (8 & 1 in r4c4 form an XY wing with 2 in r9c4 & r6c6) *--------------------------------------------------------* | 8 56 9 | 13 7 13 | 2 456 456 | |*56 1 7 | 9 2 4 | 8 3 -56 | | 2 3 4 | 5 8 6 | 7 9 1 | |------------------+------------------+------------------| | 19 47 6 | 8 3 19 | 5 47 2 | | 4579 2 3 | 67 456 59 | 1 8 467 | | 1457 457 8 | 17 456 2 | 9 467 3 | |------------------+------------------+------------------| | 3 9 5 | 4 1 7 | 6 2 8 | |*67 8 2 | 36 9 35 | 4 1 *57 | | 467 467 1 | 2 56 8 | 3 57 9 | *--------------------------------------------------------* Eliminating 5 From r2c9 (7 & 6 in r8c1 form an XY wing with 5 in r8c9 & r2c1) *-----------------------------------------------* | 8 6 9 | 13 7 13 | 2 45 45 | | 5 1 7 | 9 2 4 | 8 3 6 | | 2 3 4 | 5 8 6 | 7 9 1 | |---------------+---------------+---------------| | 19 *47 6 | 8 3 19 | 5 *47 2 | | 479 2 3 | 67 56 59 | 1 8 47 | | 17 5 8 | 17 4 2 | 9 6 3 | |---------------+---------------+---------------| | 3 9 5 | 4 1 7 | 6 2 8 | | 67 8 2 | 36 9 35 | 4 1 57 | |-467 *47 1 | 2 56 8 | 3 *57 9 | *-----------------------------------------------* Eliminating 7 From r9c1 ( XWing in Columns 28) *-----------------------------------------------* | 8 6 9 |%13 7 13 | 2 45 45 | | 5 1 7 | 9 2 4 | 8 3 6 | | 2 3 4 | 5 8 6 | 7 9 1 | |---------------+---------------+---------------| | 19 47 6 | 8 3 19 | 5 47 2 | | 479 2 3 | 67 56 59 | 1 8 47 | |*17 5 8 |-17 4 2 | 9 6 3 | |---------------+---------------+---------------| | 3 9 5 | 4 1 7 | 6 2 8 | |*67 8 2 |%36 9 35 | 4 1 57 | | 46 47 1 | 2 56 8 | 3 57 9 | *-----------------------------------------------* Eliminating 1 from r6c4(ALS-XZ A=167 in r8c1, r6c1 B=136 in r8c4, r1c4 x=6 z=1) *-----------------------------* | 8 6 9 | 1 7 3 | 2 4 5 | | 5 1 7 | 9 2 4 | 8 3 6 | | 2 3 4 | 5 8 6 | 7 9 1 | |---------+---------+---------| | 9 4 6 | 8 3 1 | 5 7 2 | | 7 2 3 | 6 5 9 | 1 8 4 | | 1 5 8 | 7 4 2 | 9 6 3 | |---------+---------+---------| | 3 9 5 | 4 1 7 | 6 2 8 | | 6 8 2 | 3 9 5 | 4 1 7 | | 4 7 1 | 2 6 8 | 3 5 9 | *-----------------------------* Non single moves: 12

tarek

by **ronk** » Fri May 05, 2006 8:42 pm

Havard wrote:
Code: Select all
Jellyfish in columns: 3 4 6 7 (...) . . . | 1X . 1X | 1X . 1- . 1 . | . . . | . . . . . . | . 1 . | . . 1 ------------+-------------+------------ 1 . . | 1X 1- 1X | . . 1 1- . 1X | 1X- . 1X- | 1X . 1- 1 . . | 1X . 1X | . . 1 ------------+-------------+------------ 1 . . | . 1 . | . . . . . . | . . . | . 1 . 1- . 1X | 1X . 1X | . . . Swordfish in rows: 4 6 7 (...) 3 . 3 | 3 . 3 | . . . . . . | . . . | . 3 . 3 3 . | . 3 . | . . . ---------+----------+--------- 3X . . | 3X 3X 3X | . . 3X 3 . 3 | 3 . 3 | 3 . 3 3X . . | 3X . 3X | . . 3X ---------+----------+--------- 3X 3X . | . . . | . . 3X 3- . 3 | 3 . 3 | 3 . 3 3- . 3 | 3 . 3 | 3 . 3

I don't see a "fish" in either one of those. Would you please give a logical explanation of why those eliminations are valid? If those are examples of your pet "frankenfish", I've stated before I don't understand that creature. Maybe an English explanation will do the trick.

Havard wrote:
Code: Select all
Almost Locked Sets XZ rule 356789 567 2379 | 13789 47 13489 | 1248#a 456 45689-8 56 1 79 | 789 2 489 | 48#a 3 56 238 39 4 | 5 138 6 | 7 29 18#a ------------------------+-------------------------+--------------------------- 139 47 6 | 12389 38 12389 | 5 47 123 34579 2 1379 | 3679 4567 3459 | 134-4 8 3467 13457 457 8 | 1237 4567 1234 | 9 467 123467 ------------------------+-------------------------+--------------------------- 123 39 5 | 4 18 7 | 6 29 38#b 467 8 237 | 236 9 235 | 234#b 1 3457-3 4679 467 12379 | 12368 56 12358 | 2348#b 457 345789-38

I see you found a very nice application of the doubly-linked ALS xz-rule. (I added it as an example here.) Good work!

by ab » Fri May 05, 2006 10:58 pm

Ocean wrote:I mean, I haven't figured out how to solve it by logic. Solving it by brute force is no problem.

That wasn't my question. I have a program I can use to solve it by brute force. My question was how did you generate the puzzle?

by **Havard** » Fri May 05, 2006 11:02 pm

ronk wrote:
Havard wrote:
Code: Select all
Jellyfish in columns: 3 4 6 7 (...) . . . | 1X . 1X | 1X . 1- . 1 . | . . . | . . . . . . | . 1 . | . . 1 ------------+-------------+------------ 1 . . | 1X 1- 1X | . . 1 1- . 1X | 1X- . 1X- | 1X . 1- 1 . . | 1X . 1X | . . 1 ------------+-------------+------------ 1 . . | . 1 . | . . . . . . | . . . | . 1 . 1- . 1X | 1X . 1X | . . . Swordfish in rows: 4 6 7 (...) 3 . 3 | 3 . 3 | . . . . . . | . . . | . 3 . 3 3 . | . 3 . | . . . ---------+----------+--------- 3X . . | 3X 3X 3X | . . 3X 3 . 3 | 3 . 3 | 3 . 3 3X . . | 3X . 3X | . . 3X ---------+----------+--------- 3X 3X . | . . . | . . 3X 3- . 3 | 3 . 3 | 3 . 3 3- . 3 | 3 . 3 | 3 . 3

I don't see a "fish" in either one of those. Would you please give a logical explanation of why those eliminations are valid? If those are examples of your pet "frankenfish", I've stated before I don't understand that creature. Maybe an English explanation will do the trick.

I'll try...

Lets first look at the cannibalistic eliminations, which is the most interesting... Basically it says that that part of the Jellyfish can not be true... Let's try it...

Code: Select all: . . . | FX . 1X | 1X . 1- . 1 . | . . . | . . . . . . | . 1 . | . . 1 ------------+-------------+------------ 1 . . | FX 1- FX | . . 1 1- . FX | TX- . FX- | FX . 1- 1 . . | FX . FX | . . 1 ------------+-------------+------------ 1 . . | . 1 . | . . . . . . | . . . | . 1 . 1- . 1X | FX . 1X | . . .

And we see this leads to a contradiction, so the elimination is valid!

next lets look at the elimination in r4c5. For it to be proven wrong, all the candidates in the box must be false:

Code: Select all: . . . | 1X . 1X | 1X . 1- . 1 . | . . . | . . . . . . | . 1 . | . . 1 ------------+-------------+------------ 1 . . | FX 1- FX | . . 1 1- . 1X | FX- . FX- | 1X . 1- 1 . . | FX . FX | . . 1 ------------+-------------+------------ 1 . . | . 1 . | . . . . . . | . . . | . 1 . 1- . 1X | 1X . 1X | . . .

Which creates an X-wing in columns 4 and 6, so that r9c3 and r1c7 also are false, which again creates a contradiction in row5, hence that elimination is valid too.

Next, for the row5 eliminations, we need this scenario for those eliminations not to be true:

Code: Select all: . . . | FX . FX | TX . 1- . 1 . | . . . | . . . . . . | . 1 . | . . 1 ------------+-------------+------------ 1 . . | 1X 1- 1X | . . 1 1- . FX | FX- . FX- | FX . 1- 1 . . | 1X . 1X | . . 1 ------------+-------------+------------ 1 . . | . 1 . | . . . . . . | . . . | . 1 . 1- . TX | FX . FX | . . .

Which you can see leads to no possible place for 1's in both column 4 and 6, hence those eliminations are valid too.

Because of the symmetrical structure of the puzzle, it should now be enough to show just one of the eliminations for either r9c1 or r1c9.
For the elimination in r9c1 not to be true you would have to have:

Code: Select all: . . . | FX . FX | TX . 1- . 1 . | . . . | . . . . . . | . 1 . | . . 1 ------------+-------------+------------ 1 . . | 1X 1- 1X | . . 1 1- . TX | FX- . FX- | FX . 1- 1 . . | 1X . 1X | . . 1 ------------+-------------+------------ 1 . . | . 1 . | . . . . . . | . . . | . 1 . 1- . FX | FX . FX | . . .

Which again is a contradiction... Hence those eliminations is proven as well...

phew... Now for the swordfish:

Code: Select all: 3 . 3 | 3 . 3 | . . . . . . | . . . | . 3 . 3 3 . | . 3 . | . . . ---------+----------+--------- 3X . . | 3X 3X 3X | . . 3X 3 . 3 | 3 . 3 | 3 . 3 3X . . | 3X . 3X | . . 3X ---------+----------+--------- 3X 3X . | . . . | . . 3X 3- . 3 | 3 . 3 | 3 . 3 3- . 3 | 3 . 3 | 3 . 3

For those eliminations to NOT be true, we have to have this scenario:

Code: Select all: 3 . 3 | 3 . 3 | . . . . . . | . . . | . 3 . 3 3 . | . 3 . | . . . ---------+----------+--------- FX . . | 3X 3X 3X | . . FX 3 . 3 | 3 . 3 | 3 . 3 FX . . | 3X . 3X | . . FX ---------+----------+--------- FX FX . | . . . | . . TX 3- . 3 | 3 . 3 | 3 . 3 3- . 3 | 3 . 3 | 3 . 3

Which again is a contradiction, and the elimination can be done!

ronk wrote:
Havard wrote:
Code: Select all
Almost Locked Sets XZ rule 356789 567 2379 | 13789 47 13489 | 1248#a 456 45689-8 56 1 79 | 789 2 489 | 48#a 3 56 238 39 4 | 5 138 6 | 7 29 18#a ------------------------+-------------------------+--------------------------- 139 47 6 | 12389 38 12389 | 5 47 123 34579 2 1379 | 3679 4567 3459 | 134-4 8 3467 13457 457 8 | 1237 4567 1234 | 9 467 123467 ------------------------+-------------------------+--------------------------- 123 39 5 | 4 18 7 | 6 29 38#b 467 8 237 | 236 9 235 | 234#b 1 3457-3 4679 467 12379 | 12368 56 12358 | 2348#b 457 345789-38

I see you found a very nice application of the doubly-linked ALS xz-rule. (I added it as an example here.) Good work!

Thanks!

Havard

by **ronk** » Fri May 05, 2006 11:34 pm

Havard wrote:And we see this leads to a contradiction, so the elimination is valid!

Sorry, I should have thought to tell you I don't consider "elimiination by contradiction" to be "logic". T&E can do as well.

[edit 2: already quoted, so restored to original]

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