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daj95376
Joined: 23 Aug 2008
Posts: 3854
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 Posted: Sun Mar 20, 2011 5:47 pm Post subject: Puzzle 11/03/20: A Moderate |
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| Code: | +-----------------------+
| 4 . . | . . 7 | . 5 8 |
| . . 7 | 5 . . | . 9 1 |
| . 8 5 | . . . | 7 . . |
|-------+-------+-------|
| . 4 . | 7 . . | . 1 . |
| . . . | . 6 . | . . . |
| 7 . . | . . . | 2 . 5 |
|-------+-------+-------|
| . . 4 | . . 9 | . 8 . |
| 3 7 . | 4 . . | 1 6 9 |
| 9 6 . | . . 3 | . 2 . |
+-----------------------+
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Play this puzzle online at the Daily Sudoku site
Since my puzzles often have numerous solved cells after initial basics, I've decided to include something new. This puzzle shows all of the solved cells after basics, but not all of the eliminations. It'll get you to the "meat" of the puzzle quicker.
| givens + solved cells after initial basics wrote: | 4....7658..75..491.8594.732.4.7...16....64.737.6...245..46.938737.4..16996..73524
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Play this puzzle online at the Daily Sudoku site |
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tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
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| Posted: Mon Mar 21, 2011 3:01 pm Post subject: |
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Code after basics:
| Code: | *-----------------------------------------------------------*
| 4 1239 1239 | 123 123 7 | 6 5 8 |
| 26 23 7 | 5 238 268 | 4 9 1 |
| 16 8 5 | 9 4 16 | 7 3 2 |
|-------------------+-------------------+-------------------|
| 28 4 239 | 7 #2359 #25 | 89 1 6 |
| 1258 1259 129 | 12 6 4 | 89 7 3 |
| 7 139 6 | 138 1389 18 | 2 4 5 |
|-------------------+-------------------+-------------------|
| 125 125 4 | 6 12 9 | 3 8 7 |
| 3 7 28 | 4 #258 #258 | 1 6 9 |
| 9 6 18 | 18 7 3 | 5 2 4 |
*-----------------------------------------------------------* |
Hidden UR(25)r48c56, marked #, with x-wing overlay (5); r8c5<>2
However, if we examine the external sis: r5c4=2, r7c5=2; r4c5<>2 plus transport (2)r7c5-r7c12=(2)r8c3; r5c3<>2
Another "However", if we work with the internal sis: r4c5=39,r8c56=8
(39)r4c5=nq(1389)r4c5|r6c456-(1=2)r5c4
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(8)r8c56-(8=1)r9c4-(1=2)r5c4 which makes all three prior deletions plus r5c4=2
A skyscraper (3)r24c5 completes the puzzle.
Ted |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Mon Mar 21, 2011 10:44 pm Post subject: |
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Ted,
That's a nice use of that UR. However, I'm not comfortable with those two strong inferences in succession in your notation. How about this instead?
(2=1)r5c4 - (1=8)r9c4 - 25UR[(8)r8c56=(39)r4c5] - als(39=1)r6c456 - (1=2)r5c4; r5c4=2
Note that the same thing can be accomplished using the UR's external strong inferences:
(2=1)r5c4 - (1=8)r9c4 - als(8=2)r8c56 - 25UR[(2)r8c3=(2)r4c13] - (2)r5c123 =(2)r5c4; r5c4=2 |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Tue Mar 22, 2011 1:07 am Post subject: |
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| I needed an XYZ-Wing, X-Wing and three ERs. |
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tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
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| Posted: Tue Mar 22, 2011 2:53 am Post subject: |
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Asellus, I like your internal sis formulation very much, and I (now) see how you can use the internal strong inferences to achieve the same result.
I have struggle with the issue of incorporating a strong inference into a valid Eureka notation; this post is an example of that. How can you express that (39)r4c5 plus the digits in r6c456 form a naked quad the result in r5c4<>1?
Thanks for you help.............
Ted |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Tue Mar 22, 2011 5:55 am Post subject: |
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| Ted wrote: | | How can you express that (39)r4c5 plus the digits in r6c456 form a naked quad the result in r5c4<>1? |
Well, you could write:
25UR[(8)r8c56=nq(1389)r4c5|r6c456]
That statement is true and acceptable to me, but it goes a little bit too far in that it selects one specific use of the 39 bivalue in r4c5 rather than stating the most general nature of the internal strong inference of the UR. The alternative is to state it as I did above, considering it as a sequence of two ALS: the 39 bivalue and the 3-cell 1389 ALS. The 39 bivalue reduces the 1389 ALS to a LS that must contain 18. These are equivalent views of the same thing.
The fact that the 39 bivalue has other potential uses is clear if you focus on a naked quad in r4 instead of b5:
... - 25UR[(8)r8c56=(39)r4c5] - als[(39)=(2)r4c13]r2c137 - (2)r5c123=(2)r5c4; r5c4=2
Note: To be a real stickler, we should actually write
25UR[(8)r8c56=(39)r4c5] - als[(3|9)=1]r6c456
and
25UR[(8)r8c56=(39)r4c5] - als[(3|9)=(2)r4c13]r2c137
That is because (39) is true if either <3> or <9> is true and false only if both are false, whereas (3|9) is true only if both <3> and <9> are true and false in all other cases. (I have sometimes written this as {39} in the spirit of set notation.) You can think of it as a little branch in the AIC:
| Code: | als(3=2)
/ \
UR[...=(39)] ...
\ /
als(9=2) |
Taken strictly, the way I wrote it above with "(39)" as part of the strong inference within the ALS does not work since "(39)" in such a case is ALWAYS true and the logic breaks down! |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Tue Mar 22, 2011 2:27 pm Post subject: |
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The current discussion on notation is deeper than I ever plan to utilize. As for me, just a little rearranging of Ted's original posting makes me happy.
| update on what Ted wrote: | | Code: | *-----------------------------------------------------------*
| 4 1239 1239 | 123 123 7 | 6 5 8 |
| 26 23 7 | 5 238 268 | 4 9 1 |
| 16 8 5 | 9 4 16 | 7 3 2 |
|-------------------+-------------------+-------------------|
| 28 4 239 | 7 #2359 #25 | 89 1 6 |
| 1258 1259 129 | 12 6 4 | 89 7 3 |
| 7 139 6 | 138 1389 18 | 2 4 5 |
|-------------------+-------------------+-------------------|
| 125 125 4 | 6 12 9 | 3 8 7 |
| 3 7 28 | 4 #258 #258 | 1 6 9 |
| 9 6 18 | 18 7 3 | 5 2 4 |
*-----------------------------------------------------------*
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Hidden UR(25)r48c56, marked #, with x-wing overlay (5); r8c5<>2
If we examine the external sis: r5c4=2, r7c5=2; r4c5<>2 plus transport (2)r7c5-r7c12=(2)r8c3; r5c3<>2
If we work with the internal sis: r4c5=3|9,r8c56=8
| Code: | (3|9)r4c5-(3|9=189|138)r6c456-(1)r5c4
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(8)r8c56-(8=1)r9c4-(1)r5c4
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A skyscraper (3)r24c5 completes the puzzle.
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The first expression can be split into:
| Code: | (3)r4c5-(3=189)r6c456-(1)r5c4
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(9)r4c5-(9=138)r6c456-(1)r5c4
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... if desired.
Otherwise, I might use:
| Code: | (1=389)r6c456 - UR[(39)r4c56 = (8)r8c56] - (8=1)r9c4 => r5c4<>1
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Tue Mar 22, 2011 6:26 pm Post subject: |
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Danny,
I agree that your last way of writing it:
"(1=389)r6c456 - UR[(39)r4c56 = (8)r8c56"
is very good and easy to grasp.
I have to object to "(3|9)r4c5". "3 and 9" is always false within a single cell since the cell can only have one true value. (It has the same problem as my grouped (39) used in the internal ALS inference: the (39) group within the ALS can never be false since an ALS can only have one false candidate digit.) Changing it back to "(39)r4c5" works fine.
Note that when you write something like "1=389" the 389 is being treated as a set and not as a group. Writing "[1=(389)]" for the ALS, where the notation is explicit for a group, would not be valid. There is no agreed explicit notation for a set that I am aware of. For me, "(3|8|9)" would work, though it's cumbersome. I prefer "{389}" though it would likely not be understood by others. |
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ronk
Joined: 07 May 2006
Posts: 398
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| Posted: Tue Mar 22, 2011 6:35 pm Post subject: |
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| Asellus wrote: | | I have to object to "(3|9)r4c5". "3 and 9" is always false within a single cell since the cell can only have one true value. |
Huh? The '|' symbol means "and" to you? I've always taken it to mean "or" ... except for its common misuse in a list (or set) of cells. |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Tue Mar 22, 2011 6:48 pm Post subject: |
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| Yes, in Eureka notation "|" has always meant "and" to me. But then, I generally avoid using it other than in those concatenated cell addresses. If "|" is "or" then I see no difference between "(39)" and "(3|9)", unless you mean to say that "|" is an exclusive or. |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Tue Mar 22, 2011 9:56 pm Post subject: |
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| Asellus wrote: | | Yes, in Eureka notation "|" has always meant "and" to me. But then, I generally avoid using it other than in those concatenated cell addresses. If "|" is "or" then I see no difference between "(39)" and "(3|9)", unless you mean to say that "|" is an exclusive or. |
To my knowledge, almost everyone uses:
| Code: | | ... for OR -and-
& ... for AND
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This corresponds to the bit-wise operators in C/C++, for example.
Yes, (39) and (3|9) are often used interchangeably, with the former being more common. I'm guilty of this as well. Other times, (39) actually means (3&9), but the latter form is almost never used. I think most people use (39) without clarification and leave it up to the reader to understand the context. In my UR statement above, the "- (39)" means "-(3) & -(9)" ... or equivalently ... "- (3|9)". The reader gets to choose the context that's most comfortable for him/her.
I only recall seeing "&" used in some of Myth Jellies nightmarish logical statements embedded in chains. Brrrrr!!!
I admit that I sometimes/often don't use the set operators "{}" when it's appropriate. Chalk it up to being in a hurry and assuming that most won't care about the distinction anyway. More often, I use the following symbols to imply level of embedded operations: { [ ( ) ] }. |
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