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daj95376
Joined: 23 Aug 2008
Posts: 3854
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 Posted: Wed Jun 17, 2009 4:29 pm Post subject: Set XY_03 Puzzle *** -- Chastized |
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I recently joined the Eureka! forum just so I could add a UR solution to a puzzle where the initial solution was questioned as being an AUR. The UR Deduction thread was started by David P. Bird and he used an AICWENS, but he called it an AIC.
AICWENS: AIC with embedded network/structure (my definition)
Anyway, I was promptly chastized in that forum for using a UR solution approach that David felt was equivalent to a poke in the eye with a sharp stick. Okay, he's allowed his opinion. Besides, how often would I or anyone else run into a UR pattern where his deduction approach could be applied.
Well, ~!#$% if I didn't run into it on the very first XY_03 puzzle I was reviewing to post next. Darn!!!!!!!!!!!!!!!!!!!
Here's my puzzle with David's UR deduction approach -- instead of the W-Wing I'd originally considered.
| Code: | +-----------------------+
| . . 7 | 6 8 . | 3 2 . |
| . 4 . | . . 2 | 9 6 . |
| 1 . . | . 3 . | 7 . 8 |
|-------+-------+-------|
| 3 . . | 8 . . | . . . |
| 2 . 4 | . 9 . | . . . |
| . 7 . | . . 3 | . 9 . |
|-------+-------+-------|
| 4 8 9 | . . . | 5 . . |
| 7 3 . | . . 9 | . 8 . |
| . . 6 | . . . | . . . |
+-----------------------+
c9b3 Locked Candidate 1 <> 1 [r467c9]
c6b2 Locked Candidate 1 <> 4 [r4c6]
c68 X-Wing <> 5 [r5c49]
c5b8 Locked Candidate 1 <> 6 [r4c5]
c8b8 Empty Rectangle <> 1 [r4c5]
c4b9 Empty Rectangle <> 4 [r6c7]
XY-Wing [r4c8]/[r4c5]+[r6c7] <> 2 [r4c7],[r6c45]
XY-Wing [r9c5]/[r4c5]+[r7c4] <> 2 [r6c4],[r78c5] extraneous
r6 b5 Locked Candidate 1 <> 4 [r6c9]
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| Code: | UR{ (1=45)r6c45 - (45)r8c45 } = (4)r9c5 - (4=1)r9c7 => [r6c7]<>1
+-----------------------------------------------------+
| 9 5 7 | 6 8 14 | 3 2 14 |
| 8 4 3 | 15 7 2 | 9 6 15 |
| 1 6 2 | 9 3 45 | 7 45 8 |
|-----------------+-----------------+-----------------|
| 3 9 5 | 8 2 16 | 146 14 7 |
| 2 1 4 | 7 9 56 | 8 35 36 |
| 6 7 8 | *145 *145 3 | 2-1 9 25 |
|-----------------+-----------------+-----------------|
| 4 8 9 | 12 16 7 | 5 13 236 |
| 7 3 1 | *245 *456 9 | 246 8 246 |
| 5 2 6 | 3 14 8 | 14 7 9 |
+-----------------------------------------------------+
# 34 eliminations remain
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-or-
| Code: | W-Wing: 1/4 in r1c6,r4c8 connected by 4 in r3c68 => r4c6<>1
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ttt
Joined: 06 Dec 2008
Posts: 42
Location: vietnam
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| Posted: Wed Jun 17, 2009 6:21 pm Post subject: Re: Set XY_03 Puzzle *** -- Chastized |
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| daj95376 wrote: | | Besides, how often would I or anyone else run into a UR pattern where his deduction approach could be applied. |
| Code: | *--------------------------------------------------*
| 9 5 7 | 6 8 14 | 3 2 14 |
| 8 4 3 | 15 7 2 | 9 6 15 |
| 1 6 2 | 9 3 45 | 7 45 8 |
|----------------+----------------+----------------|
| 3 9 5 | 8 2 16 | 146 14 7 |
| 2 1 4 | 7 9 56 | 8 35 36 |
| 6 7 8 | 145* 145* 3 | 12 9 25 |
|----------------+----------------+----------------|
| 4 8 9 | 12 16 7 | 5 13 236 |
| 7 3 1 | 245* 456* 9 | 246 8 246 |
| 5 2 6 | 3 14 8 | 14 7 9 |
*--------------------------------------------------* |
Hi Danny,
On my experience, the applying AURs based on viewing candidates – internal, external (on box, row, column) or both, that relates to other bivalue cells, bilocations or strong sets. On Eureka, you used internal and David used external (16)r3c8 & internal (2)r4c9 that could be written as AIC.
For example on your puzzle above: AUR(45)r45c68, we have some cases:
1- At least one of [(5)r5c6, (4)r9c5] must be true: (5)r5c6=(4)r9c5-(4)r6c5=(4)r6c4 => r6c4<>5
2- At least one of [(5)r6c9, (4)r8c79] must be true: (5)r6c9=(4)r8c79-(4=1)r9c7-(1=2)r6c7 => r6c9<>2
…..
If we use all internal candidate [(1)r6c45, (2)r8c4, (6)r8c5] then we must be presented as net (AAIC).
BTW, good news: Player's Forum just recovered... 
ttt |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Wed Jun 17, 2009 6:44 pm Post subject: |
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just to add some other strong inferences on the UR {45}
and to add to what ttt already said...
these are strong inferences:
a... according to the UR45 either the xy-wing[(12)r7c4, (16)r7c5, (26)r8c45] is true or the 1's in r6c45 are true. which also leads to Danny's conclusion.
........interestingly this is the same as... if the 1's in r6c45 are not true, the remaining type 3 eliminates the 1 in r9c5
UR45[{xy-wing(12)r7c4, (16)r7c5, (26)r8c45} = (1)r6c45]...
b... according to the UR 45, either the 1's in r6c45 are true or if not, then by virtue of the remaining type 4, the 4 in r9c5 must be true, again, leads to Danny's conclusion.
UR45[(1)r6c45 = (4)r9c5]... |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Wed Jun 17, 2009 6:53 pm Post subject: |
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| Quote: | If we use all internal candidate [(1)r6c45, (2)r8c4, (6)r8c5] then we must be presented as net (AAIC).
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in this case, you can use all of the internal candidates as I have shown with the xy-wing approach.
but i agree that there are cases where that is impossible without a net |
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