- Code: Select all
..1 ..2 ..3
.2. .4. .5.
4.. 6.. 7..
..5 .2. ..8
.7. 3.8 2..
28. .16 375
.17 .3. .8.
5.. 8.. 1..
84. .61 537
Enjoy!
37 givens, no empty triplet
15 posts
• Page 1 of 1
37 givens, no empty triplet
by dobrichev » Thu Apr 16, 2015 6:28 pm
Enjoy!
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Re: 37 givens, no empty triplet
by Leren » Thu Apr 16, 2015 9:22 pm
- Code: Select all
*--------------------------------------------------------------*
| 679 569 1 | 579 789 2 | 4689 469 3 |
| 3679 2 3689 | 1 4 379 | 689 5 69 |
>| 4 359 389 | 6 89 359 | 7 12 T1-2 |<
|--------------------+--------------------+--------------------|
| 1369 369 5 | 479 2 479 | 469 B1469 8 |
| 169 7 469 | 3 5 8 | 2 B1469 1469 |
>| 2 8 49 | 49 1 6 | 3 7 5 |<
|--------------------+--------------------+--------------------|
| 69 1 7 | 2459 3 459 | 469 8 2469 |
>| 5 369 2369 | 8 79 479 | 1 2469 T469-2 |<
| 8 4 29 | 29 6 1 | 5 3 7 |
*--------------------------------------------------------------*
Would you believe my solver detected an Exocet : r4c8 r5c8 r3c9 r8c9 1469. Removing the non-base digit 2 from both target cells solves the puzzle in 1 move !
The problem is that the cross lines aren't much use. Proving digit 1 is obvious, digits 489 require a full digit expansion.
At least this shows that if you can determine which of the two 2's in Row 7 is True you can solve the puzzle in 1 move.
Leren
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Re: 37 givens, no empty triplet
by DonM » Fri Apr 17, 2015 12:04 am
Would you believe my solver detected an Exocet : r4c8 r5c8 r3c9 r8c9 1469. Removing the non-base digit 2 from both target cells solves the puzzle in 1 move !
The problem is that the cross lines aren't much use. Proving digit 1 is obvious, digits 489 require a full digit expansion.
At least this shows that if you can determine which of the two 2's in Row 7 is True you can solve the puzzle in 1 move.
Leren
I'm not following. There seems to be a conflict between the first and last sentences.
Edit: Well, on re-read, I guess I get it, though it gave the impression that the Exocet solved it in 1 move.
Last edited by DonM on Fri Apr 17, 2015 12:27 am, edited 1 time in total.
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Re: 37 givens, no empty triplet
by DonM » Fri Apr 17, 2015 12:37 am
Post deleted -solution had an error.
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Re: 37 givens, no empty triplet
by Leren » Fri Apr 17, 2015 9:24 am
DonM wrote : Well, on re-read, I guess I get it, though it gave the impression that the Exocet solved it in 1 move.
The Exocet did solve the puzzle in 1 move. However the point I was making was how the Exocet was detected. It required full digit expansions on 3 digits, so there is a lot of work going on underneath the "single move".
There are endless debates about how far you should go in proving that if a digit is in the Base cells it must occupy a Target cell. The wording of Champagne's original definition seems to allow for any method whatsoever, however the more work
involved in proving the Exocet, the less desirable it is. In fact I have an option to turn full digit expansions off but I was just playing around with the option on when the Exocet turned up (to my surprise).
I just thought it was a cool solution, I was "enjoying" the puzzle like dobrichev suggested. The alternative solutions I was getting involved a lot of boring chains.
Leren
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Re: 37 givens, no empty triplet
by JC Van Hay » Fri Apr 17, 2015 9:39 am
HP(12)r3c89
Analysis of the puzzle from the XWing(9R69) suggests the following solution as it implies +5r1c4, +7r1c1, ...
|
6r4c7=*[(4=6)r5c3 - 6r5c89=*(6-1)r4c8=(1-3)r4c1=3r4c2 - 3r8c2=(3-2)r8c3=2r9c3 -(2=94)r97c4] - (4=9)r6c3 - 9r6c4=9r9c4 -(9=7)r8c5 :=> -7r1c5; 8 Singles
Analysis of the puzzle from the XWing(9R69) suggests the following solution as it implies +5r1c4, +7r1c1, ...
- Code: Select all
+-------------------+-----------------+------------------+
| 679 9(56) 1 | -7(5) 789 2 | 4689 469 3 |
| 3679 2 368 | 1 4 379 | 689 5 69 |
| 4 359 38 | 6 89 359 | 7 12 12 |
+-------------------+-----------------+------------------+
| 1369 39(6) 5 | (47) 2 479 | 469 1469 8 |
| 169 7 (46) | 3 5 8 | 2 1469 1469 |
| 2 8 (49) | (49) 1 6 | 3 7 5 |
+-------------------+-----------------+------------------+
| (69) 1 7 | 245 3 459 | 469 8 2469 |
| 5 39(6) 236 | 8 79 479 | 1 2469 2469 |
| 8 4 2(9) | 2(9) 6 1 | 5 3 7 |
+-------------------+-----------------+------------------+
- Code: Select all
+-----------------------+-------------------+------------------------+
| 679 69 1 | 5 9-7(8) 2 | 69(48) 469 3 |
| 3679 2 368 | 1 4 379 | 689 5 69 |
| 4 5 38 | 6 89 39 | 7 12 12 |
+-----------------------+-------------------+------------------------+
| 69(13) 69(3) 5 | 7 2 49 | 9(46) 49(16) 8 |
| 169 7 (46) | 3 5 8 | 2 149(6) 149(6) |
| 2 8 (49) | (49) 1 6 | 3 7 5 |
+-----------------------+-------------------+------------------------+
| 69 1 7 | (24) 3 5 | 69(4) 8 2469 |
| 5 69(3) 6(23) | 8 (79) 479 | 1 2469 2469 |
| 8 4 9(2) | (29) 6 1 | 5 3 7 |
+-----------------------+-------------------+------------------------+
|
6r4c7=*[(4=6)r5c3 - 6r5c89=*(6-1)r4c8=(1-3)r4c1=3r4c2 - 3r8c2=(3-2)r8c3=2r9c3 -(2=94)r97c4] - (4=9)r6c3 - 9r6c4=9r9c4 -(9=7)r8c5 :=> -7r1c5; 8 Singles
- Code: Select all
+------------------+-----------+-----------------------+
| 7 6(9) 1 | 5 8 2 | 46(9) 469 3 |
| 36(9) 2 36 | 1 4 7 | 8 5 69 |
| 4 5 8 | 6 9 3 | 7 12 12 |
+------------------+-----------+-----------------------+
| 136 369 5 | 7 2 49 | 46(9) 1469 8 |
| 16(9) 7 46 | 3 5 8 | 2 146(9) 146(9) |
| 2 8 49 | 49 1 6 | 3 7 5 |
+------------------+-----------+-----------------------+
| 6-9 1 7 | 24 3 5 | 46(9) 8 2469 |
| 5 369 236 | 8 7 49 | 1 2469 2469 |
| 8 4 29 | 29 6 1 | 5 3 7 |
+------------------+-----------+-----------------------+
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Re: 37 givens, no empty triplet
by blue » Fri Apr 17, 2015 11:23 am
A 2-stepper, if you don't count the X-Wing. Computer assisted.
1) "Basics"
Singles: 1r4c2, 5r5c5
Hidden Pair: <12>r3c89 => -9r3c89
X-Wing: <9>r69\c34 => -9r2358c3, -9r147c4
2) Triple-Kraken network => -3r8c3
3) Basics
Singles: 3r8c2, 3r4c1, 1r5c1, 1r4c8, 2r3c8, 1r3c9
Hidden Pair: <38>r23c3 => -6r2c3
Line-box: 9r5c89 => -9r4c7
4) Dual-Kraken network => -9r9c4; stte
1) "Basics"
Singles: 1r4c2, 5r5c5
Hidden Pair: <12>r3c89 => -9r3c89
X-Wing: <9>r69\c34 => -9r2358c3, -9r147c4
2) Triple-Kraken network => -3r8c3
- Code: Select all
+---------------------+-------------------+--------------------+
| 679 (569) 1 | 7(5) 789 2 | 468(9) 469 3 |
| 3679 2 (368) | 1 4 379 | 68(9) 5 (69) |
| 4 359 (38) | 6 89 359 | 7 12 12 |
+---------------------+-------------------+--------------------+
| 1369 369 5 | 47 2 47(9) | 46(9) 1469 8 |
| 169 7 46 | 3 5 8 | 2 1469 1469 |
| 2 8 4(9) | 4(9) 1 6 | 3 7 5 |
+---------------------+-------------------+--------------------+
| 6(9) 1 7 | 4(25) 3 459 | 46(9) 8 2469 |
| 5 36(9) 6-3(2) | 8 79 479 | 1 2469 2469 |
| 8 4 (29) | 9(2) 6 1 | 5 3 7 |
+---------------------+-------------------+--------------------+
9r4c7 - r4c6 = r6c4 - r6c3 = 9r9c3 ---------
|| \
|| 9r9c3 --------------------------------
|| || \
|| 9r8c2 - 9r1c2 \
|| || || \
9r7c7 - 9r7c1 5r1c2 - r1c4 = (5-2)r7c4 = 2r9c4 - 2r9c3 = 2r8c3 - 3r8c3
|| || /
|| 6r1c2 - 6r2c3 = (NP: <38>r23c3) ----------------
|| /
9r12c7 - (9=6)r2c9 ---
3) Basics
Singles: 3r8c2, 3r4c1, 1r5c1, 1r4c8, 2r3c8, 1r3c9
Hidden Pair: <38>r23c3 => -6r2c3
Line-box: 9r5c89 => -9r4c7
4) Dual-Kraken network => -9r9c4; stte
- Code: Select all
+------------------+-------------------+-------------------+
| 679 569 1 | 57 789 2 | 468(9) 469 3 |
| (679) 2 38 | 1 4 39(7) | 68(9) 5 (69) |
| 4 59 38 | 6 89 359 | 7 2 1 |
+------------------+-------------------+-------------------+
| 3 69 5 | 47 2 4(79) | 46 1 8 |
| 1 7 46 | 3 5 8 | 2 469 469 |
| 2 8 49 | 4(9) 1 6 | 3 7 5 |
+------------------+-------------------+-------------------+
| 6(9) 1 7 | 245 3 459 | 46(9) 8 2469 |
| 5 3 26 | 8 (79) 49(7) | 1 469 2469 |
| 8 4 2(9) | 2-9 6 1 | 5 3 7 |
+------------------+-------------------+-------------------+
9r2c1 ---------------------------
|| \
6r2c1 - (6=9)r2c9 - r12c7 = 9r7c7 - 9r7c1 = r9c3 - 9r9c4
|| /
7r2c1 - 7r2c6 /
|| /
7r4c6 - 9r4c6 = 9r6c4 ----------------
|| /
7r8c6 - (7=9)r8c5 ------------------
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Re: 37 givens, no empty triplet
by bat999 » Fri Apr 17, 2015 3:52 pm
dobrichev wrote:Enjoy!
Singles: 1r4c2, 5r5c5
Hidden Pair: <12>r3c89 => -9r3c89
X-Wing: <9>r69\c34 => -9r2358c3, -9r147c4
I found those basics too, thought the X-wing was a killer, but no.
Had to use "a lot of boring chains" then finished off with Empty Rectangle(s).
Thanks dobrichev.
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Re: 37 givens, no empty triplet
by blue » Fri Apr 17, 2015 7:54 pm
I see I missed some easier 2-step solutions. (2 steps after the 9's X-Wing)
There are some where at least one of the steps, isn't as complicated as the two I used above.
The best ones, seemed to go like: (a complex network => -9r7c1 => +6r7c1), (kraken r1c2 => ??)
There are some where at least one of the steps, isn't as complicated as the two I used above.
The best ones, seemed to go like: (a complex network => -9r7c1 => +6r7c1), (kraken r1c2 => ??)
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Re: 37 givens, no empty triplet
by JC Van Hay » Sat Apr 18, 2015 6:57 am
blue wrote:I see I missed some easier 2-step solutions. (2 steps after the 9's X-Wing)
There are some where at least one of the steps, isn't as complicated as the two I used above.
The best ones, seemed to go like: (a complex network => -9r7c1 => +6r7c1), (kraken r1c2 => ??)
The analysis of the puzzle from the XWing(9R69) showed r6c3=9=r9c4 -> contradiction via Skyscraper(9C27)-(6=9)r7c1 while r6c4=9=r9c3 -> solution stte.
Not only the analysis implied +5r1c4, +7r1c1 but also +6r7c1. This last assignment effectively soften the network proving r6c4=9=r9c3.
For example, like these 3 krakens using 8, 7, 7 constraints respectively [instead of 2 krakens using 11 and 7 constraints respectively if one first wants to prove +6r7c1]
- Code: Select all
+-------------------+-----------------+------------------+
| 679 9(56) 1 | -7(5) 789 2 | 4689 469 3 |
| 3679 2 368 | 1 4 379 | 689 5 69 |
| 4 359 38 | 6 89 359 | 7 12 12 |
+-------------------+-----------------+------------------+
| 1369 39(6) 5 | (47) 2 479 | 469 1469 8 |
| 169 7 (46) | 3 5 8 | 2 1469 1469 |
| 2 8 (49) | (49) 1 6 | 3 7 5 |
+-------------------+-----------------+------------------+
| (69) 1 7 | 245 3 459 | 469 8 2469 |
| 5 39(6) 236 | 8 79 479 | 1 2469 2469 |
| 8 4 2(9) | 2(9) 6 1 | 5 3 7 |
+-------------------+-----------------+------------------+
- Code: Select all
+---------------------+-----------------+--------------------+
| 67(9) 6(9) 1 | 5 789 2 | 468(9) 469 3 |
| 367(9) 2 36(8) | 1 4 379 | 6(89) 5 69 |
| 4 5 (38) | 6 89 (39) | 7 12 12 |
+---------------------+-----------------+--------------------+
| 1369 369 5 | 7 2 4(9) | 46(9) 1469 8 |
| 169 7 46 | 3 5 8 | 2 1469 1469 |
| 2 8 49 | 4(9) 1 6 | 3 7 5 |
+---------------------+-----------------+--------------------+
| 6-9 1 7 | 24 3 5 | 46(9) 8 2469 |
| 5 369 236 | 8 79 479 | 1 2469 2469 |
| 8 4 2(9) | 2(9) 6 1 | 5 3 7 |
+---------------------+-----------------+--------------------+
- Code: Select all
+-------------------+-----------------+------------------+
| 79 (569) 1 | (57) 789 2 | 4689 469 3 |
| 379 2 38(6) | 1 4 379 | 689 5 69 |
| 4 359 38 | 6 89 359 | 7 12 12 |
+-------------------+-----------------+------------------+
| 139 369 5 | (47) 2 479 | 469 1469 8 |
| 19 7 (46) | 3 5 8 | 2 1469 1469 |
| 2 8 9(4) | -4(9) 1 6 | 3 7 5 |
+-------------------+-----------------+------------------+
| 6 1 7 | 245 3 459 | 49 8 249 |
| 5 3(9) 23 | 8 79 479 | 1 2469 2469 |
| 8 4 2(9) | 2(9) 6 1 | 5 3 7 |
+-------------------+-----------------+------------------+
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Re: 37 givens, no empty triplet
by daj95376 » Sat Apr 18, 2015 4:53 pm
My solver returned several steps (including chains) that weren't outlandish. In debug mode, I was able to find two SINs to crack the puzzle after the X-Wing. However, the first SIN relied heavily on remembering secondary eliminations on <9> in order to derive -3r8c3. I didn't check the alternate SINs found. Finally, I ran my multi-value template analyzer. After the X-Wing, there were three, 4-value template combinations that cracked the puzzle with subsequent Basics. The second combination is the most interesting because it so closely matches JC's latest post on r6c4=9=r9c3. Maybe someone who uses Xsudo can determine why this 4-value combination produces the listed results.
_
<3679>: Show
<3789>: Show
<4679>: Show
_
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Re: 37 givens, no empty triplet
by JC Van Hay » Sat Apr 18, 2015 5:46 pm
Oops ... mixing of solutions in my last post : there, the third step is of application only if +6r7c1 is first proved. But, because of the first step the AIC between the square brackets is only necessary.
- Code: Select all
+------------------+-----------------+------------------+
| 79 (69) 1 | 5 789 2 | 4689 469 3 |
| 379 2 38(6) | 1 4 379 | 689 5 69 |
| 4 5 38 | 6 89 39 | 7 12 12 |
+------------------+-----------------+------------------+
| 139 369 5 | 7 2 49 | 469 1469 8 |
| 19 7 (46) | 3 5 8 | 2 1469 1469 |
| 2 8 -9(4) | -4(9) 1 6 | 3 7 5 |
+------------------+-----------------+------------------+
| 6 1 7 | 24 3 5 | 49 8 249 |
| 5 3(9) 23 | 8 79 479 | 1 2469 2469 |
| 8 4 2(9) | 2(9) 6 1 | 5 3 7 |
+------------------+-----------------+------------------+
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Re: 37 givens, no empty triplet
by blue » Tue Apr 21, 2015 6:22 pm
daj95376 wrote:After the X-Wing, there were three, 4-value template combinations that cracked the puzzle with subsequent Basics. The second combination is the most interesting because it so closely matches JC's latest post on r6c4=9=r9c3. Maybe someone who uses Xsudo can determine why this 4-value combination produces the listed results.
These combinations eliminate the "other two" 9's in b7, and solve the X-Wing.
Than as JC says, that cracks the puzzle.
- Code: Select all
+-----------------------+-------------------+------------------+
| 6(79) 56(9) 1 | 57 789 2 | 4689 469 3 |
| 6(379) 2 68(3) | 1 4 9(37) | 689 5 69 |
| 4 35(9) 38 | 6 89 359 | 7 12 12 |
+-----------------------+-------------------+------------------+
| 1369 369 5 | 47 2 4(79) | 469 1469 8 |
| 169 7 46 | 3 5 8 | 2 1469 1469 |
| 2 8 49 | 4(9) 1 6 | 3 7 5 |
+-----------------------+-------------------+------------------+
| 69 1 7 | 245 3 459 | 469 8 2469 |
| 5 6-9(3) 26(3) | 8 (79) 49(7) | 1 2469 2469 |
| 8 4 2(9) | 2(9) 6 1 | 5 3 7 |
+-----------------------+-------------------+------------------+
8 Truths = {3R28 9R9 7C6 8N5 7B1 9B15}
11 Links = {79r8 3c3 9c24 12n1 8n2 24n6 9b7}
1 Elimination --> r8c2<>9
- Code: Select all
+--------------------+-------------------+-----------------------+
| 679 569 1 | 57 789 2 | 4689 469 3 |
| 367(9) 2 36(8) | 1 4 (379) | 6(89) 5 6(9) |
| 4 359 (38) | 6 89 59(3) | 7 12 12 |
+--------------------+-------------------+-----------------------+
| 1369 369 5 | 47 2 4(79) | 469 1469 8 |
| 16(9) 7 46 | 3 5 8 | 2 146(9) 146(9) |
| 2 8 49 | 4(9) 1 6 | 3 7 5 |
+--------------------+-------------------+-----------------------+
| 6-9 1 7 | 245 3 459 | 46(9) 8 246(9) |
| 5 369 236 | 8 (79) 49(7) | 1 246(9) 246(9) |
| 8 4 2(9) | 2(9) 6 1 | 5 3 7 |
+--------------------+-------------------+-----------------------+
10 Truths = {8R2 9R259 37C6 3N3 8N5 9B59}
13 Links = {3r3 7r8 9r78 8c3 9c1489 24n6 2n7 9b7}
1 Elimination --> r7c1<>9
They are built using "truths" that are either for "house digits" <3789>, or for cells with (only) candidates from <3789>.
Each one has (also) a represention as network-based elimination.
If you're interested, I'll work up a diagram for each.
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Re: 37 givens, no empty triplet
by daj95376 » Tue Apr 21, 2015 7:50 pm
blue wrote:Each one has (also) a represention as network-based elimination.
If you're interested, I'll work up a diagram for each.
Thanks for checking using Xsudo. It's nice to know that its approach performs eliminations in [b7].
I expanded my template solver's output and learned:
*) Every template for <3>, <7>, and <8> can be found in some acceptable combination for <378>. No casualties!
*) When the acceptable <378> combinations are combined with <9>, less than half of the <9> templates were acceptable.
This explains why only eliminations in <9>, or eliminations other than <3789> occur.
- Code: Select all
Value: 1 2 3 4 5 6 7 8 9
Templates: 3 3 4 10 2 20 3 2 44
_ _ _ __ _ __ _ _ __
Used: 4 3 2 16
Specific: Show
_
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Re: 37 givens, no empty triplet
by pjb » Tue Apr 21, 2015 11:49 pm
A further observation, using extended coloring, placing r9c3=9 leads to resolution of all cells.
Phil
Phil
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15 posts
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