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arkietech
Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA
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 Posted: Thu May 10, 2012 6:09 am Post subject: Collection 5/10/12 |
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| Code: |
*-----------*
|...|19.|...|
|.68|5..|...|
|5.1|...|98.|
|---+---+---|
|...|.3.|.7.|
|.8.|.4.|...|
|6.7|...|.5.|
|---+---+---|
|.2.|..9|...|
|35.|...|8.6|
|...|..1|3..|
*-----------*
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Play/Print online |
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Clement
Joined: 24 Apr 2006
Posts: 1111
Location: Dar es Salaam Tanzania
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| Posted: Thu May 10, 2012 11:27 am Post subject: Collection 5/10/12 |
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After the Basics | Code: |
+--------+-----------+------------+
| 7 34 2 | 1 9 8 | 56 36 45 |
| 9 6 8 | 5 27 347 | 1-7 23 1247 |
| 5 34 1 | 24 6 347 | 9 8 247 |
+--------+-----------+------------+
| 4 1 5 | 9 3 6 | 2 7 8 |
| 2 8 3 | 7 4 5 | 16 69 19 |
| 6 9 7 | 8 1 2 | 4 5 3 |
+--------+-----------+------------+
| 1 2 6 | 3 8 9 | 57 4 57 |
| 3 5 9 | 24 27 47 | 8 1 6 |
| 8 7 4 | 6 5 1 | 3 29 29 |
+--------+-----------+------------+
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XY-Chain as follows
(7=2)r2c5-(2=3)r2c8-(3=6)r1c8-(6=5)r1c7-(5=7)r1c7 => r2c7<>7 which solves it. |
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Clement
Joined: 24 Apr 2006
Posts: 1111
Location: Dar es Salaam Tanzania
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| Posted: Thu May 10, 2012 11:37 am Post subject: Collection 5/10/12 |
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Sorry: Correction in my above submission
The last cell is (5=7)r7c7. |
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aran
Joined: 19 Apr 2010
Posts: 70
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| Posted: Thu May 10, 2012 12:04 pm Post subject: |
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dailysudoku 10.5.12
| Code: |
ssts
*-----------------------------------------------------------*
| 7 34 2 | 1 9 8 | 56 36 45 |
| 9 6 8 | 5 27 347 | 17 23 1247 |
| 5 34 1 | 24 6 347 | 9 8 247 |
|-------------------+-------------------+-------------------|
| 4 1 5 | 9 3 6 | 2 7 8 |
| 2 8 3 | 7 4 5 | 16 69 19 |
| 6 9 7 | 8 1 2 | 4 5 3 |
|-------------------+-------------------+-------------------|
| 1 2 6 | 3 8 9 | 57 4 57 |
| 3 5 9 | 24 27 47 | 8 1 6 |
| 8 7 4 | 6 5 1 | 3 29 29 |
*-----------------------------------------------------------*
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24r2c9=17r2c79-7r3c9=7r3c6-7r2c6 : =>BUG-Lite : =>r2c9=(24-1) ste
Edit : bad logic here (as ronk points out : see later) : bivalues are necessary but not sufficient for BUG
Last edited by aran on Sat May 12, 2012 12:13 pm; edited 1 time in total |
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arkietech
Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA
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| Posted: Thu May 10, 2012 12:19 pm Post subject: |
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| Code: | *-----------------------------------------------------------*
| 7 34 2 | 1 9 8 | 56 36 45 |
| 9 6 8 | 5 *27 347 | 17 23 1247 |
| 5 34 1 |*24 6 *3-47 | 9 8 *247 |
|-------------------+-------------------+-------------------|
| 4 1 5 | 9 3 6 | 2 7 8 |
| 2 8 3 | 7 4 5 | 16 69 19 |
| 6 9 7 | 8 1 2 | 4 5 3 |
|-------------------+-------------------+-------------------|
| 1 2 6 | 3 8 9 | 57 4 57 |
| 3 5 9 |*24 *27 *47 | 8 1 6 |
| 8 7 4 | 6 5 1 | 3 29 29 |
*-----------------------------------------------------------*
dp(247)r38c46,r28c5,r3c469 => r3c6=3;stte
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is this a mug? |
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ronk
Joined: 07 May 2006
Posts: 398
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| Posted: Thu May 10, 2012 12:26 pm Post subject: |
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| aran wrote: | | Code: |
ssts
*-----------------------------------------------------------*
| 7 34 2 | 1 9 8 | 56 36 45 |
| 9 6 8 | 5 27 347 | 17 23 1247 |
| 5 34 1 | 24 6 347 | 9 8 247 |
|-------------------+-------------------+-------------------|
| 4 1 5 | 9 3 6 | 2 7 8 |
| 2 8 3 | 7 4 5 | 16 69 19 |
| 6 9 7 | 8 1 2 | 4 5 3 |
|-------------------+-------------------+-------------------|
| 1 2 6 | 3 8 9 | 57 4 57 |
| 3 5 9 | 24 27 47 | 8 1 6 |
| 8 7 4 | 6 5 1 | 3 29 29 |
*-----------------------------------------------------------*
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24r2c9=17r2c79-7r3c9=7r3c6-7r2c6 : =>BUG-Lite |
Sure it is ... NOT! |
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JC Van Hay
Joined: 13 Jun 2010
Posts: 494
Location: Charleroi, Belgium
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| Posted: Thu May 10, 2012 12:58 pm Post subject: |
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| 3r3c6=3r2c6-(3=2)r2c8-(2=7)r2c5 :=> -7r3c6 |
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tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
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| Posted: Thu May 10, 2012 1:40 pm Post subject: |
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Another variation is:
(2=7)r2c5-(7=1)r2c7-(1=6=9)r5c78-(9=2)r9c8; r2c8<>2
Ted |
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aran
Joined: 19 Apr 2010
Posts: 70
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| Posted: Thu May 10, 2012 4:30 pm Post subject: |
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| ronk wrote: | | aran wrote: | | Code: |
ssts
*-----------------------------------------------------------*
| 7 34 2 | 1 9 8 | 56 36 45 |
| 9 6 8 | 5 27 347 | 17 23 1247 |
| 5 34 1 | 24 6 347 | 9 8 247 |
|-------------------+-------------------+-------------------|
| 4 1 5 | 9 3 6 | 2 7 8 |
| 2 8 3 | 7 4 5 | 16 69 19 |
| 6 9 7 | 8 1 2 | 4 5 3 |
|-------------------+-------------------+-------------------|
| 1 2 6 | 3 8 9 | 57 4 57 |
| 3 5 9 | 24 27 47 | 8 1 6 |
| 8 7 4 | 6 5 1 | 3 29 29 |
*-----------------------------------------------------------*
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24r2c9=17r2c79-7r3c9=7r3c6-7r2c6 : =>BUG-Lite |
Sure it is ... NOT! |
NOT...so quick
To put it more clearly, and verbally :
not 24 r2c9 reduces r2c9 to a bivalue, and assigns 17r2c79 which reduces r3c9 to a bivalue, which assigns 7 to r3c6 which reduces r2c5 to a bivalue.
At this point all is bivalue=>starting premiss is false.
Hence r2c9=24 =><1> r2c9
Edit : bad logic here, bivalues alone do not guarantee BUG (see earlier and later).
Last edited by aran on Sat May 12, 2012 12:16 pm; edited 1 time in total |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Thu May 10, 2012 4:35 pm Post subject: |
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| Code: | *-----------------------------------------------------------*
| 7 34 2 | 1 9 8 | 56 36 45 |
| 9 6 8 | 5 27 347 | 17 23 1247 |
| 5 34 1 | 24 6 347 | 9 8 247 |
|-------------------+-------------------+-------------------|
| 4 1 5 | 9 3 6 | 2 7 8 |
| 2 8 3 | 7 4 5 | 16 69 19 |
| 6 9 7 | 8 1 2 | 4 5 3 |
|-------------------+-------------------+-------------------|
| 1 2 6 | 3 8 9 | 57 4 57 |
| 3 5 9 | 24 27 47 | 8 1 6 |
| 8 7 4 | 6 5 1 | 3 29 29 |
*-----------------------------------------------------------* |
A chain-free solution. M-Wing (27) in r2c5 and r3c9; r2c7<>7.
XY-Wing (342), pivot r2c6; r2c5<>2. |
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ronk
Joined: 07 May 2006
Posts: 398
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| Posted: Thu May 10, 2012 10:44 pm Post subject: |
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| aran wrote: | | ronk wrote: |
Sure it is ... NOT! |
NOT...so quick
To put it more clearly, and verbally :
not 24 r2c9 reduces r2c9 to a bivalue, and assigns 17r2c79 which reduces r3c9 to a bivalue, which assigns 7 to r3c6 which reduces r2c5 to a bivalue.
At this point all is bivalue=>starting premiss is false. |
"All is bivalue" is a necessary but insufficient condition for a BUG or BUG-Lite. If it were sufficient, how would one correctly select the two candidates to be eliminated in a BUG+1 grid? |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Fri May 11, 2012 6:56 am Post subject: |
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Working from aran's grid, I found five candidates whose absence would lead to all bivalue (unsolved) cells. The remaining candidates would form stable cycles for their respective values. I'm pretty sure this qualifies as a sufficient, if not necessary, scenario for a BUG. Thus, at least one of the five candidates must be true.
| Code: | *-----------------------------------------------------------*
| 7 34 2 | 1 9 8 | 56 36 45 |
| 9 6 8 | 5 27 34+7 | 1-7 23 14+27 |
| 5 34 1 | 24 6 37+4 | 9 8 27+4 |
|-------------------+-------------------+-------------------|
| 4 1 5 | 9 3 6 | 2 7 8 |
| 2 8 3 | 7 4 5 | 16 69 19 |
| 6 9 7 | 8 1 2 | 4 5 3 |
|-------------------+-------------------+-------------------|
| 1 2 6 | 3 8 9 | 57 4 57 |
| 3 5 9 | 24 27 47 | 8 1 6 |
| 8 7 4 | 6 5 1 | 3 29 29 |
*-----------------------------------------------------------*
r2c69=7 => r2c7<>7
r3c69=4, r3c4=2, r2c5=7 => r2c7<>7
r2c 9=2, r2c5=7 => r2c7<>7
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Fri May 11, 2012 6:31 pm Post subject: |
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Although I wasn't able to follow aran's solution, I did notice that it was very close to an AIC that I could understand.
| Code: | (24)r2c9 = (17)r2c79 - (7)r3c9 = r3c6 - (7=4)r9c6 - r2c6 = (4)r2c9 => r2c9<>17
*-----------------------------------------------------------*
| 7 34 2 | 1 9 8 | 56 36 45 |
| 9 6 8 | 5 27 347 | 17 23 1247 |
| 5 34 1 | 24 6 347 | 9 8 247 |
|-------------------+-------------------+-------------------|
| 4 1 5 | 9 3 6 | 2 7 8 |
| 2 8 3 | 7 4 5 | 16 69 19 |
| 6 9 7 | 8 1 2 | 4 5 3 |
|-------------------+-------------------+-------------------|
| 1 2 6 | 3 8 9 | 57 4 57 |
| 3 5 9 | 24 27 47 | 8 1 6 |
| 8 7 4 | 6 5 1 | 3 29 29 |
*-----------------------------------------------------------*
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Fri May 11, 2012 10:14 pm Post subject: |
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| daj95376 wrote: | Working from aran's grid, I found five candidates whose absence would lead to all bivalue (unsolved) cells. The remaining candidates would form stable cycles for their respective values. I'm pretty sure this qualifies as a sufficient, if not necessary, scenario for a BUG. Thus, at least one of the five candidates must be true.
| Code: | *-----------------------------------------------------------*
| 7 34 2 | 1 9 8 | 56 36 45 |
| 9 6 8 | 5 27 34+7 | 1-7 23 14+27 |
| 5 34 1 | 24 6 37+4 | 9 8 27+4 |
|-------------------+-------------------+-------------------|
| 4 1 5 | 9 3 6 | 2 7 8 |
| 2 8 3 | 7 4 5 | 16 69 19 |
| 6 9 7 | 8 1 2 | 4 5 3 |
|-------------------+-------------------+-------------------|
| 1 2 6 | 3 8 9 | 57 4 57 |
| 3 5 9 | 24 27 47 | 8 1 6 |
| 8 7 4 | 6 5 1 | 3 29 29 |
*-----------------------------------------------------------*
r2c69=7 => r2c7<7> r2c7<7> r2c7<>7
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I do not see any reason for aran's starting hypothesis that r2c9<>24. Is it just a guess? If so, singles only lead to an invalid solution. Uniqueness has nothing to do with it.
Danny is correct, though I do not know what this means: | Quote: | | The remaining candidates would form stable cycles for their respective values. |
ronk's point is that a BUG contains only bivalue unsolved cells, and each unsolved candidate occurs only twice in each row, column, or block.
For example, R2:
| Code: | | | 9 6 8 | 5 27 347 | 17 23 1247 | |
<7> and <2> occur twice in bivalue cells. The only way for R2 to be a BUG is
| Code: | | | 9 6 8 | 5 27 34 | 17 23 14 | |
This condition needs to be checked in R23, C9, and B23, which leads to Danny's grid.
Keith |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Fri May 11, 2012 11:18 pm Post subject: |
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| keith wrote: | ... though I do not know what this means:
| Danny wrote: | | The remaining candidates would form stable cycles for their respective values. |
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Keith, stable cycles is just another way of saying that, for each value, the candidates occur twice in every box/column/row containing them ... and ... that they form cyclic/interlinking relationships.
This last part may be considered redundant to some people, but I include it because it solidifies the concept that you can't choose True/False candidates by considering them one value at a time.
Note: more than one cycle may exist for a value, but there's only one cycle for each value in this grid.
| Code: | cycle a-b-c-d-a cycle a-b-c-d-e-f-g-h-a
+-----------------------------------+ +-----------------------------------+
| . . . | 1 . . | . . . | | . . 2 | . . . | . . . |
| . . . | . . . | a1 . b1 | | . . . | . a2 . | . b2 ~2 |
| . . 1 | . . . | . . . | | . . . | f2 . . | . . e2 |
|-----------+-----------+-----------| |-----------+-----------+-----------|
| . 1 . | . . . | . . . | | . . . | . . . | 2 . . |
| . . . | . . . | d1 . c1 | | 2 . . | . . . | . . . |
| . . . | . 1 . | . . . | | . . . | . . 2 | . . . |
|-----------+-----------+-----------| |-----------+-----------+-----------|
| 1 . . | . . . | . . . | | . 2 . | . . . | . . . |
| . . . | . . . | . 1 . | | . . . | g2 h2 . | . . . |
| . . . | . . 1 | . . . | | . . . | . . . | . c2 d2 |
+-----------------------------------+ +-----------------------------------+
cycle a-b-c-d-e-f-a cycle a-b-c-d-e-f-g-h-a
+-----------------------------------+ +-----------------------------------+
| . a3 . | . . . | . b3 . | | . a4 . | . . . | . . b4 |
| . . . | . . d3 | . c3 . | | . . . | . . d4 | . . c4 |
| . f3 . | . . e3 | . . . | | . h4 . | g4 . ~4 | . . ~4 |
|-----------+-----------+-----------| |-----------+-----------+-----------|
| . . . | . 3 . | . . . | | 4 . . | . . . | . . . |
| . . 3 | . . . | . . . | | . . . | . 4 . | . . . |
| . . . | . . . | . . 3 | | . . . | . . . | 4 . . |
|-----------+-----------+-----------| |-----------+-----------+-----------|
| . . . | 3 . . | . . . | | . . . | . . . | . 4 . |
| 3 . . | . . . | . . . | | . . . | f4 . e4 | . . . |
| . . . | . . . | 3 . . | | . . 4 | . . . | . . . |
+-----------------------------------+ +-----------------------------------+
cycle a-b-c-d-a cycle a-b-c-d-a
+-----------------------------------+ +-----------------------------------+
| . . . | . . . | a5 . b5 | | . . . | . . . | a6 b6 . |
| . . . | 5 . . | . . . | | . 6 . | . . . | . . . |
| 5 . . | . . . | . . . | | . . . | . 6 . | . . . |
|-----------+-----------+-----------| |-----------+-----------+-----------|
| . . 5 | . . . | . . . | | . . . | . . 6 | . . . |
| . . . | . . 5 | . . . | | . . . | . . . | d6 c6 . |
| . . . | . . . | . 5 . | | 6 . . | . . . | . . . |
|-----------+-----------+-----------| |-----------+-----------+-----------|
| . . . | . . . | d5 . c5 | | . . 6 | . . . | . . . |
| . 5 . | . . . | . . . | | . . . | . . . | . . 6 |
| . . . | . 5 . | . . . | | . . . | 6 . . | . . . |
+-----------------------------------+ +-----------------------------------+
cycle a-b-c-d-e-f-g-h-a solved ... no candidates
+-----------------------------------+ +-----------------------------------+
| 7 . . | . . . | . . . | | . . . | . . 8 | . . . |
| . . . | . a7 ~7 | b7 . ~7 | | . . 8 | . . . | . . . |
| . . . | . . f7 | . . e7 | | . . . | . . . | . 8 . |
|-----------+-----------+-----------| |-----------+-----------+-----------|
| . . . | . . . | . 7 . | | . . . | . . . | . . 8 |
| . . . | 7 . . | . . . | | . 8 . | . . . | . . . |
| . . 7 | . . . | . . . | | . . . | 8 . . | . . . |
|-----------+-----------+-----------| |-----------+-----------+-----------|
| . . . | . . . | c7 . d7 | | . . . | . 8 . | . . . |
| . . . | . h7 g7 | . . . | | . . . | . . . | 8 . . |
| . 7 . | . . . | . . . | | 8 . . | . . . | . . . |
+-----------------------------------+ +-----------------------------------+
cycle a-b-c-d-a
+-----------------------------------+
| . . . | . 9 . | . . . |
| 9 . . | . . . | . . . |
| . . . | . . . | 9 . . |
|-----------+-----------+-----------|
| . . . | 9 . . | . . . |
| . . . | . . . | . a9 b9 |
| . 9 . | . . . | . . . |
|-----------+-----------+-----------|
| . . . | . . 9 | . . . |
| . . 9 | . . . | . . . |
| . . . | . . . | . d9 c9 |
+-----------------------------------+
|
Regards, Danny
[Edit: corrected cycle for "4". Thanks ronk!]
Last edited by daj95376 on Sat May 12, 2012 1:46 pm; edited 1 time in total |
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aran
Joined: 19 Apr 2010
Posts: 70
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| Posted: Fri May 11, 2012 11:36 pm Post subject: |
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All who found fault...are indeed correct.
As Ronk quite rightly observes, bivalues are necessary but not sufficient for BUG.
To satisfy oneself of that : take any solved puzzle, then convert r1c12 into a pair. There is now a grid consisting of bivalues.
I fell into a trap of my own making.
Apologies for that. |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Fri May 11, 2012 11:37 pm Post subject: |
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Danny,
Thank you. That's a concept I use all the time. I didn't know it had a name.
In my words, if there's a cycle, move on to another digit. There are no single-digit eliminations (coloring, skyscrapers, ...)
Keith |
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aran
Joined: 19 Apr 2010
Posts: 70
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| Posted: Sat May 12, 2012 12:24 pm Post subject: |
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| keith wrote: | Is it just a guess?
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There's a minefield behind a question like that ! |
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ronk
Joined: 07 May 2006
Posts: 398
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| Posted: Sat May 12, 2012 1:16 pm Post subject: |
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| daj95376 wrote: | stable cycles is just another way of saying that, for each value, the candidates occur twice in every box/column/row containing them ... and ... that they form cyclic/interlinking relationships | Code: | cycle a-b-c-d-e-f-a cycle a-b-c-d-e-f-a
+-----------------------------------+ +-----------------------------------+
| . a3 . | . . . | . b3 . | | . a4 . | . . . | . . b4 |
| . . . | . . d3 | . c3 . | | . . . | . . d4 | . . c4 |
| . f3 . | . . e3 | . . . | | . f4 . | e4 . ~4 | . . ~4 |
|-----------+-----------+-----------| |-----------+-----------+-----------|
| . . . | . 3 . | . . . | | 4 . . | . . . | . . . |
| . . 3 | . . . | . . . | | . . . | . 4 . | . . . |
| . . . | . . . | . . 3 | | . . . | . . . | 4 . . |
|-----------+-----------+-----------| |-----------+-----------+-----------|
| . . . | 3 . . | . . . | | . . . | . . . | . 4 . |
| 3 . . | . . . | . . . | | . . . | 4 . 4 | . . . |
| . . . | . . . | 3 . . | | . . 4 | . . . | . . . |
+-----------------------------------+ +----------------------------------- |
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Unfortunately, as in your digit <4> grid, one can have a "stable cycle" without including two candidates in every row, column and box. |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Sat May 12, 2012 1:50 pm Post subject: |
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| ronk wrote: | | Unfortunately, as in your digit <4> grid, one can have a "stable cycle" without including two candidates in every row, column and box. |
Thanks Ron. Yes, I missed the candidates in [b8] for <4>. I should have realized that something was wrong when I used two cells on a diagonal. I've updated my original post. You are correct that you can have a stable cycle without having two candidates in every box/column/row, but I'm pretty sure all that means is that you missed a Single somewhere. |
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