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ChPicard

Joined: 12 Mar 2008

Posts: 82

Location: Montreal, Canada

Items

Posted: Sat Jun 27, 2009 12:08 pm Post subject: Number of candidates removed

Hi What is the largest number of candidates removed when a cell is solved? What solving technic removes the largest number of candidates? Thank you

m_b_metcalf

Joined: 13 Mar 2006

Posts: 210

Location: Berlin

Items

Posted: Sat Jun 27, 2009 12:43 pm Post subject: Re: Number of candidates removed

ChPicard wrote:

What is the largest number of candidates removed when a cell is solved?
What solving technic removes the largest number of candidates?

Might it be 12? Given a puzzle with no 9s, then one can imagine arriving at:

Code:

1 2 3 4 5 6 7 8 x
x x x
x x x
x
x
x
x
x
x

When the single in r1c9 is solved, 12 other candidates, here marked by x, are eliminated. That said, a quick test on puzzles with no 9s gave a maximum of 8. Using standard puzzles gave 10.

Regards,

Mike Metcalf

wapati

Joined: 12 Jun 2007

Posts: 622

Location: Canada

Items

Posted: Sat Jun 27, 2009 1:34 pm Post subject: Re: Number of candidates removed

ChPicard wrote:

Hi

What solving technic removes the largest number of candidates?
Thank you

I would expect that a pure jellyfish would do that.
Any unfinned fish is pretty good in theory but in practice by the time you spot them most potential eliminations are gone.

An x-wing, the smallest fish, could do 14 under normal conditions.

Code:

/ . .|. . .|. . /
/ . .|. . .|. . /
/ . .|. . .|. . /
-----+-----+-----
X * *|* * *|* * X
/ . .|. . .|. . /
/ . .|. . .|. . /
-----+-----+-----
/ . .|. . .|. . /
/ . .|. . .|. . /
X * *|* * *|* * X

where X is the candidate in the vertical x-wing. Cells marked * are the eliminations. Cells marked / may not have X as a candidate.

Very unusual would be 18.

Code:

/ . /|. . .|. . .
/ . /|. . .|. . .
/ . /|. . .|. . .
-----+-----+-----
X * X|* * *|* * *
/ * /|. . .|. . .
/ * /|. . .|. . .
-----+-----+-----
/ * /|. . .|. . .
/ * /|. . .|. . .
X * X|* * *|* * *

gsf

Joined: 18 Aug 2005

Posts: 411

Location: NJ USA

Items

Posted: Sat Jun 27, 2009 4:51 pm Post subject: Re: Number of candidates removed

a variation on mbm's grid:

Code:

# 436 candidates

1 2 3 4 5 6 . . .
. . . . . . . . .
. . . . . . . . .

. . . . . . . . .
. . . . . . . . .
. . . . . . . . .

. . . . . . . . .
. . . . . . . . .
4 5 6 1 2 3 . 7 .

1 2 3 4 5 6 789 89 789
56789 46789 45789 23789 13789 12789 123456789 12345689 123456789
56789 46789 45789 23789 13789 12789 123456789 12345689 123456789
2356789 1346789 1245789 2356789 1346789 1245789 123456789 12345689 123456789
2356789 1346789 1245789 2356789 1346789 1245789 123456789 12345689 123456789
2356789 1346789 1245789 2356789 1346789 1245789 123456789 12345689 123456789
23789 13789 12789 56789 46789 45789 12345689 12345689 12345689
23789 13789 12789 56789 46789 45789 12345689 12345689 12345689
4 5 6 1 2 3 89 7 89

and placing a 9 in the top row yields:

Code:

# 381 candidates

1 2 3 4 5 6 7 8 9
. . . . . . . . .
. . . . . . . . .

. . . . . . . . .
. . . . . . . . .
. . . . . . . . .

. . . . . . . . .
. . . . . . . . .
4 5 6 1 2 3 9 7 8

1 2 3 4 5 6 7 8 9
56789 46789 45789 23789 13789 12789 123456 123456 123456
56789 46789 45789 23789 13789 12789 123456 123456 123456
2356789 1346789 1245789 2356789 1346789 1245789 1234568 1234569 1234567
2356789 1346789 1245789 2356789 1346789 1245789 1234568 1234569 1234567
2356789 1346789 1245789 2356789 1346789 1245789 1234568 1234569 1234567
23789 13789 12789 56789 46789 45789 123456 123456 123456
23789 13789 12789 56789 46789 45789 123456 123456 123456
4 5 6 1 2 3 9 7 8

55 candidates eliminated
but is it fair to count the forced placements after the 9 move as part of one move?

hobiwan

Joined: 11 Feb 2008

Posts: 83

Items

Posted: Sat Jun 27, 2009 6:16 pm Post subject:

Some real life examples from my database (only one example per technique):

18 eliminations:

Code:

.------------------------.--------------------------------.-------------------.
| 8 356 569 | 2 1 356 | 3569 4 7 |
| 3567 4 256 | 3567 8 9 | 1 236 236 |
| 135679 123567 12569 | 3567 4 3567 | 35689 23689 236 |
:------------------------+--------------------------------+-------------------:
| 1346 1236 1246 | 467 9 8 | 367 12367 5 |
| 1456 9 124568 | 4567 3 24567 | 678 12678 126 |
| 356 23568 7 | 56 256 1 | 4 2368 9 |
:------------------------+--------------------------------+-------------------:
| 145679 15678 145689 | 1345-6-789 25-6-7 2345-6-7 | 3679 13679 136 |
| 1-6-79 1-6-78 3 | 1-6-789 *67 *67 | 2 5 4 |
| 2 1567 14569 | 1345-6-79 5-6-7 345-6-7 | 3679 13679 8 |
'------------------------'--------------------------------'-------------------'

Locked Pair: 6,7 in r8c56 => r7c456,r8c124,r9c456<>6, r7c456,r8c124,r9c456<>7

Code:

.--------------------.------------------------.--------------------------------.
| 4 89 189 | 5 1268 689 | 3 7 12689 |
| 3 2 15789 | 179 168 6789 | 5689 1568 4 |
| 157 6 15789 | 123479 1238 34789 | 2589 1258 12589 |
:--------------------+------------------------+--------------------------------:
| 8 59 45679 | 179 16 2 | 4-5-6-7 3 1-5-6-7 |
| 2 1 3-5-6-79 | 8 4 3-5-6-79 | *567 *56 *567 |
| 567 35 34567 | 137 136 3567 | 24-5-6-78 9 12-5-6-78 |
:--------------------+------------------------+--------------------------------:
| 56 7 23568 | 234 9 348 | 1 24568 23568 |
| 9 4 238 | 6 5 1 | 278 28 2378 |
| 156 358 123568 | 234 7 348 | 245689 24568 235689 |
'--------------------'------------------------'--------------------------------'

Locked Triple: 5,6,7 in r5c789 => r4c79,r5c36,r6c79<>5, r4c79,r5c36,r6c79<>6, r4c79,r5c36,r6c79<>7

17 eliminations:

Code:

from the "Pure Jellyfish Collection":
.------------------------.--------------------------.------------------------.
| 345678-9 *4589 *359 | 568-9 2678-9 2568-9 | *279 *1479 123478-9 |
| 345678-9 *4589 *359 | 568-9 1 2568-9 | *279 *479 23478-9 |
| 789 1 2 | 3 789 4 | 5 6 789 |
:------------------------+--------------------------+------------------------:
| 1458-9 *4589 *159 | 14678-9 23 23 | *679 *179 1567-9 |
| 1459 2 7 | 1469 469 169 | 3 8 1569 |
| 189 3 6 | 1789 5 189 | 4 2 179 |
:------------------------+--------------------------+------------------------:
| 1235-9 *59 *1359 | 14568-9 3468-9 13568-9 | *2679 *479 2467-9 |
| 39 6 8 | 2 349 7 | 1 5 49 |
| 1259 7 4 | 1569 69 1569 | 8 3 269 |
'------------------------'--------------------------'------------------------'

Jellyfish: 9 c2378 r1247 => r1c14569,r2c1469,r4c149,r7c14569<>9

Code:

.--------------------------------.-------------------------.--------------------.
| -1346-7-89 -1346-7-8 6-7-89 | 246-7 146-78 124-7 | 158 157 1578 |
| 2 B1678 B678 | A67 15-6-78 15-7 | 3 4 9 |
| 5 B1478 B78 | A47 3 9 | 2 6 178 |
:--------------------------------+-------------------------+--------------------:
| 1678 9 25678 | 2346-7 467 2347 | 156 1257 12357 |
| 367 23567 4 | 1 67 237 | 9 8 2357 |
| 1367 -12367 267 | 5 9 8 | 16 1237 4 |
:--------------------------------+-------------------------+--------------------:
| 479 457 1 | 8 2 3457 | 45 359 6 |
| 4689 24568 25689 | 349 145 1345 | 7 12359 1238 |
| 4789 24578 3 | 4-79 1457 6 | 1458 1259 1258 |
'--------------------------------'-------------------------'--------------------'

Almost Locked Set XZ-Rule: A=r23c4 {467}, B=r2c23,r3c23 {14678}, X=4,6, Z=6 => r2c5<>6, r1c123456,r2c56,r49c4<>7, r1c12,r6c2<>1, r1c123<>8

16 eliminations:

Code:

.-----------------------.---------------------------.--------------------------.
| 145 1578 6 | 3 1278 478 | 9 178 127-8 |
| 3 2 1489 | 456 156789 5678 | 1468 1678 167-8 |
| 19 178 1489 | *246 1-26789 678 | *12468 5 3 |
:-----------------------+---------------------------+--------------------------:
| 16 136 12 | 8 2567 9 | 1356 1367 4 |
| 46 9 5 | 1 67 *34-6-7 | *3-68 2 *678 |
| 7 1368 1248 | *24-5-6 256 356 | 1356 136 9 |
:-----------------------+---------------------------+--------------------------:
| 8 4 19 | 7 3 2 | 16 169 5 |
| *-12-5-69 156 7 | 56 4 568 | *-123-8 *-13-89 12-8 |
| *256 56 3 | 9 568 1 | 7 4 *28 |
'-----------------------'---------------------------'--------------------------'

Continuous Nice Loop 9= r8c1 =2= r9c1 -2- r9c9 -8- r5c9 =8= r5c7 =3= r5c6 =4= r6c4 =2= r3c4 -2- r3c7 =2= r8c7 =3= r8c8 =9= r8c1 =2 => r8c178<>1, r3c5<>2, r6c4,r8c1<>5, r5c67,r6c4,r8c1<>6, r5c6<>7, r128c9,r8c78<>8

15 eliminations:

Code:

.---------------.-----------------------------.-------------.
| 3 9 468 | -1-245-6 *126 -1-25-68 | 7 12 128 |
| 12 128 48 | -1-247 -1-2379 -1-23789 | 6 5 128 |
| 5 1268 7 | *126 *126 -1-2-68 | 3 4 9 |
:---------------+-----------------------------+-------------:
| 27 4 9 | 3 8 127 | 5 127 6 |
| 6 27 1 | 27 5 4 | 9 8 3 |
| 8 5 3 | 1267 12679 12679 | 4 127 12 |
:---------------+-----------------------------+-------------:
| 9 67 56 | 8 267 2567 | 1 3 4 |
| 17 137 2 | 9 4 137 | 8 6 5 |
| 4 1368 568 | 156 136 1356 | 2 9 7 |
'---------------'-----------------------------'-------------'

Naked Triple: 1,2,6 in r13c5,r3c4 => r1c46,r2c456,r3c6<>1, r1c46,r2c456,r3c6<>2, r1c46,r3c6<>6

14 eliminations:

Code:

.---------------------------.-----------------.-----------.
| 9 8 124 | 14 12 6 | 3 7 5 |
| 3 7 6 | 8 5 29 | 1 4 29 |
| 124 145 1245 | 7 1239 2349 | 8 6 29 |
:---------------------------+-----------------+-----------:
| 5 6 9 | 3 4 7 | 2 1 8 |
| 148 14 148 | 69 269 29 | 5 3 7 |
| 7 2 3 | 5 8 1 | 4 9 6 |
:---------------------------+-----------------+-----------:
| -1-46 -13-49 *14 | 2 1369 5 | 7 8 134 |
| -12-468 -13-4 -12-478 | 146 1367 34 | 9 5 134 |
| *14 -13-459 -1-457 | 149 1379 8 | 6 2 134 |
'---------------------------'-----------------'-----------'

Naked Pair: 1,4 in r7c3,r9c1 => r7c12,r8c123,r9c23<>1, r7c12,r8c123,r9c23<>4

Code:

.---------------.--------------------.----------------------------.
| 27 3 5 | 89 4 6789 | 268 1 2-6-8 |
| 6 9 8 | 1 3 2 | 4 7 5 |
| 27 4 1 | 58 678 5678 | 3 268 9 |
:---------------+--------------------+----------------------------:
| 3 6 27 | 289 178 1789 | 789 5 4 |
| 458 58 27 | 23489 78 34789 | 6789 689 1 |
| 48 1 9 | 6 5 478 | 278 28 3 |
:---------------+--------------------+----------------------------:
| 1589 58 36 | 7 2 134568 | 15-6-89 34-6-89 68 |
| 158 *27 4 | 358 9 13568 | 125-6-8 23-6-8 *2678 |
| 1589 *27 36 | 3458 168 134568 | 125-6-89 234-6-89 *2678 |
'---------------'--------------------'----------------------------'

Uniqueness Test 3: 2/7 in r8c29,r9c29 => r1c9,r7c78,r8c78,r9c78<>6, r1c9,r7c78,r8c78,r9c78<>8

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