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David Bryant
Joined: 29 Jul 2005
Posts: 559
Location: Denver, Colorado
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 Posted: Fri Jul 28, 2006 1:58 am Post subject: Nightmare, July 27 |
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This is a very interesting puzzle. Here's the initial setup. Oh -- you can find the original puzzle on Ruud's "Nightmare" web site.
| Code: | *-----------*
|...|3.6|59.|
|...|.5.|..4|
|..6|..9|..3|
|---+---+---|
|3..|.1.|9.5|
|7..|..4|.2.|
|..1|5..|..7|
|---+---+---|
|.4.|2..|1..|
|9.7|...|...|
|.2.|.65|...|
*-----------* |
I was able to solve this one with two relatively short double-implication chains plus a "non-unique rectangle." Or, without assuming uniquity, I got there via a third DIC.
Interestingly, when I ran this Nightmare through Ruud's "SudoCue" program, it produced the following series of unusual moves.
Finned Jellyfish (on "8"s)
Connected pair (aka multicoloring) on "8"
6 candidates (for "8") eliminated by "template check" (aka Nishio)
XY-Wing
Plus two forcing chains
I had a hard time locating the "finned jellyfish" even after I knew that it was there. And I never did figure out how to eliminate 6 candidates using Nishio -- I could only find 5.
Anyway, if anybody else has worked through this puzzle, I'd be interested in seeing how you did it. I'll post my own (relatively simple) solution in another day or two. dcb
Last edited by David Bryant on Sun Jul 30, 2006 8:58 pm; edited 1 time in total |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Fri Jul 28, 2006 9:27 pm Post subject: Hiddden pairs? |
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Another interesting thing about this puzzle:
There are two hidden pairs which you can find from the initial clues without making lists of candidates. Can you see them? (Hints below.)
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The pairs are <39> and <24>.
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They are in Box 1 and Box 4. Much easier to find, I think, from the solved cells than from the candidate lists (pencil marks).
Keith |
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Myth Jellies
Joined: 27 Jun 2006
Posts: 64
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| Posted: Sat Jul 29, 2006 7:26 am Post subject: |
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Here is mine. Catching a jellyfish is kinda cool. | Code: | *-----------------------------------------------------------*
| 18a 178a 4 | 3 *78A 6 | 5 9 2 |
| 2 39 39 | 178 5 178 | 678 68b 4 |
| 5 *78A 6 | 4 2 9 | 78a 1 3 |
|-------------------+-------------------+-------------------|
| 3 68 2 | 678 1 78 | 9 4 5 |
| 7 5689 589 | 689 389 4 | 368 2 1 |
| 4 -689 1 | 5 -389 2 | 368 *68B 7 |
|-------------------+-------------------+-------------------|
| 6 4 358 | 2 789 378 | 1 357 89 |
| 9 1358 7 | 18 4 138 | 2 35 6 |
| 18 2 38 | 1789 6 5 | 4 37 89 |
*-----------------------------------------------------------* |
Grouped multicoloring on the 8's.
8A=8a-8b=8B => any cell which sees all the 8A's in a group and 8B's in a group cannot be an 8. r6c25 <> 8. Locked 8's in r6 => r5c7 <> 8 | Code: | *-----------------------------------------------------------*
|*18 -178 *4 | 3 *78 6 | 5 9 *2 |
| 2 39 39 | 178 5 178 | 678 68 4 |
| 5 78 6 | 4 2 9 | 78 1 3 |
|-------------------+-------------------+-------------------|
| 3 68 2 | 678 1 78 | 9 4 5 |
|*7 -5689 *589 |-689 *389 4 | 36 2 *1 |
| 4 69 1 | 5 39 2 | 368 68 7 |
|-------------------+-------------------+-------------------|
|*6 4 *358 | 2 *789 -378 | 1 357 *89 |
| 9 1358 7 | 18 4 138 | 2 35 6 |
|*18 2 *38 |-1789 *6 5 | 4 37 *89 |
*-----------------------------------------------------------*
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r1579c1359 jellyfish on 8s => r1c2, r5c2, r5c4, r7c6, & r9c4 <> 8 | Code: | *-----------------------------------------------------------*
| 18 17 4 | 3 78 6 | 5 9 2 |
| 2 39 39 | 178 5 178 | 678 68 4 |
| 5 78 6 | 4 2 9 | 78 1 3 |
|-------------------+-------------------+-------------------|
| 3 68 2 | 678 1 78 | 9 4 5 |
| 7 569 589 |*69 -389 4 |*36 2 1 |
| 4 69 1 | 5 *39 2 |-368 68 7 |
|-------------------+-------------------+-------------------|
| 6 4 358 | 2 789 37 | 1 357 89 |
| 9 1358 7 | 18 4 138 | 2 35 6 |
| 18 2 38 | 179 6 5 | 4 37 89 |
*-----------------------------------------------------------* |
XY-Wing: 36-69-93 in r5c7, r5c4, r6c5 => r5c5 & r6c7 <> 3
Basic moves take you to...
| Code: | *--------------------------------------------------*
| 18 17 4 | 3 78 6 | 5 9 2 |
| 2 3 9 | 178 5 178 |*678 *68 4 |
| 5 78 6 | 4 2 9 | 78 1 3 |
|----------------+----------------+----------------|
| 3 68 2 | 678 1 78 | 9 4 5 |
| 7 56 58 | 69 89 4 | 3 2 1 |
| 4 9 1 | 5 3 2 |*68 *68 7 |
|----------------+----------------+----------------|
| 6 4 358 | 2 789 37 | 1 357 89 |
| 9 158 7 | 18 4 138 | 2 35 6 |
| 18 2 38 | 179 6 5 | 4 37 89 |
*--------------------------------------------------*
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68-UR in r26c78 sets r2c7 = 7. More basic stuff, then...
| Code: | *--------------------------------------------------*
| 8 1 4 | 3 7 6 | 5 9 2 |
| 2 3 9 |*18 5 *18 | 7 6 4 |
| 5 7 6 | 4 2 9 | 8 1 3 |
|----------------+----------------+----------------|
| 3 68 2 | 67 1 78 | 9 4 5 |
| 7 56 58 | 69 89 4 | 3 2 1 |
| 4 9 1 | 5 3 2 | 6 8 7 |
|----------------+----------------+----------------|
| 6 4 35 | 2 89 37 | 1 357 89 |
| 9 58 7 |*18 4 *138 | 2 35 6 |
| 1 2 38 | 79 6 5 | 4 37 89 |
*--------------------------------------------------*
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18-UR in r28c46 sets r8c6 = 3 & cracks it |
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David Bryant
Joined: 29 Jul 2005
Posts: 559
Location: Denver, Colorado
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| Posted: Sat Jul 29, 2006 4:31 pm Post subject: Using DICs to solve this one |
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Thanks for the explanation, MJ. Your method makes more sense (to me) than the one that "SudoCue" comes up with. Here's how I went about it -- double-implication chains are among my favorite tools. 
Right at the outset it appears that the key to solving this puzzle lies in the placement of the digit "9".
| Code: | . . . . . . . . .
. 9? 9? . . . . . .
. . . . . . . . .
. . . . . . . . .
. 9? 9? 9? 9? . . . .
. 9? . . 9? . . . .
. . . . 9? . . . 9?
. . . . . . . . .
. . . 9? . . . . 9? |
We can see immediately that placing a "9" at r9c9 will determine the placement of all the rest of the "9"s:
r9c9 = 9 ==> r7c5 = 9 ==> r5c4 = 9 ==> r6c2 = 9 ==> r2c3 = 9
After making all the more or less obvious moves I arrived at this position. Oh -- this is exactly the same spot where MJ started the multicoloring on the digit "8".
| Code: | 18* 178 4 3 78 6 5 9 2
2 39 39 178 5 178 678 68 4
5 78 6 4 2 9 78 1 3
3 68 2 678 1 78 9 4 5
7 5689 589 689 389 4 368 2 1
4 689 1 5 389 2 368 68 7
6 4 358 2 789 378 1 357 89
9 1358 7 18 4 138 2 35 6
18 2 38* 1789 6 5 4 37 89 |
I spotted two different double-implication chains here, both tying into the network of "9"s.
A. r9c3 = 3 ==> r2c3 = 9
B. r9c3 = 8 ==> r9c9 = 9 ==> ... r2c3 = 9 (see discussion above)
A. r1c1 = 1 ==> r9c1 = 8 ==> r9c9 = 9
B. r1c1 = 1 ==> {7, 8} pair in column 2 ==> r4c2 = 6 ==> {7, 8} pair in row 4
{7, 8} in row 4 ==> {3, 9} pair in column 5 ==> r7c5 <> 9 ==> r9c4 = 9
So placing a "1" in r1c1 forces a contradiction -- we can set r1c1 = 8, and r3c3 = 9. This forces a long series of simple moves, ending here. (This position is substantially similar to the last position MJ posted above, except that mine hasn't yet resolved row 6, and I also have more possible "8"s floating around.)
| Code: | 8 1 4 3 7 6 5 9 2
2 3 9 18 5 18 7 6 4
5 7 6 4 2 9 8 1 3
3 68 2 678 1 78 9 4 5
7 5689 58 689 389 4 36 2 1
4 69 1 5 39 2 36 8 7
6 4 35 2 89 37 1 357 89
9 58 7 18 4 138 2 35 6
1 2 38 789 6 5 4 37 89 |
Now the "UR" in r28c46 is enough to solve the puzzle (via r8c6 = 3). Or, if we'd rather not depend on uniquity, we can use one more double implication chain.
A. r7c6 = 3 ==> r7c3 = 5 ==> r5c3 = 8 ==> r4c2 = 6
B. r7c6 = 7 ==> r4c6 = 8 ==> r4c2 = 6
And r4c2 = 6 is also enough to solve the rest of the puzzle. dcb |
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Chuck B
Joined: 24 Jun 2006
Posts: 24
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| Posted: Sat Jul 29, 2006 7:22 pm Post subject: |
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After reaching MJ's first position I found that hypothesizing r1c1=1 forces a contradiction:
?r1c1=1 -> r4c2=6 -> ( r4c46={78}, r5c4=6 ) -> r56c5={39}
?r1c1=1 -> r9c1=8 -> r9c9=9 -> r7c5=9 ?! (i.e., two 9's in c5)
So the puzzle is valid only if r1c1 = 8.
Setting r1c1=8 and following the bread crumbs eventually leads here: | Code: | *-----------------------------------------------------------*
| 8 1 4 | 3 7 6 | 5 9 2 |
| 2 39 39 |*18 5 *18 | 7 6 4 |
| 5 7 6 | 4 2 9 | 8 1 3 |
|-------------------+-------------------+-------------------|
| 3 *68 2 |*678 1 *78 | 9 4 5 |
| 7 5689 589 | 689 389 4 | 36 2 1 |
| 4 69 1 | 5 39 2 | 36 8 7 |
|-------------------+-------------------+-------------------|
| 6 4 358 | 2 89 378 | 1 357 89 |
| 9 *358 7 |*18 4 *138 | 2 35 6 |
| 1 2 38 | 789 6 5 | 4 37 89 |
*-----------------------------------------------------------* |
A swordfish in 8 (rows 2, 4 & 8), followed eventually by a pair of XY wings, cracks it.
Nice one, David - thanks for posting it!
- cb |
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