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Myth Jellies
Joined: 27 Jun 2006
Posts: 64
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 Posted: Wed Jun 04, 2008 5:02 pm Post subject: Mega-uniqueness |
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Most of the seventeen-clue puzzles are fairly simple to solve. Here is one of the "intransigent 17's" that is a bit more difficult.
| Code: | . 7 . | . . . | 4 . 8
2 . . | . 9 . | . . .
. . . | . 3 . | 6 . .
-----------+-----------+-----------
. 6 . | 7 . . | 5 . .
. . . | . . . | . 9 2
. . 1 | . . . | . . .
-----------+-----------+-----------
9 . . | . . . | . 1 .
. . . | 8 . . | . . .
3 . . | . . . | . . . |
It turns out that aside from the basics, one can solve this puzzle using only uniqueness deductions, but you will need to use a permeable MUG pattern (one that I presented in the permeable MUG tutorial above) in your arsenal of uniqueness tricks. Even after that I had to get pretty clever. See if you can find a basics + uniqueness only pathway to the solution. (Thanks to Eleven for finding this MUG example)
edited to add link
Last edited by Myth Jellies on Thu Jun 05, 2008 6:21 pm; edited 1 time in total |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Wed Jun 04, 2008 10:45 pm Post subject: |
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harder indeed, SE 7.2 with 9 forcing chains
| Code: | .---------------------.---------------------.---------------------.
| 156 7 9 | 1256 256 256 | 4 3 8 |
| 2 34 346 | 46 9 8 | 7 5 1 |
|-145 18 45-8 | 145 3 7 | 6 2 9 |
:---------------------+---------------------+---------------------:
| 8 6 2 | 7 1 9 | 5 4 3 |
| 457 345 3457 | 56 8 456 | 1 9 2 |
| 45 9 1 | 3 -245 245 | 8 67 67 |
:---------------------+---------------------+---------------------:
| 9 28 4567(8) | 256 (2)4567 2456 | 3 1 4567 |
|(1)4567 12 4567 | 8 (2)4567 3 | 9 67 4567 |
| 3 45 4567 | 9 4567 1 | 2 8 4567 |
'---------------------'---------------------'---------------------' |
the grid above actually has a UR type 1 on {6,7} in r68c89 which removes 6 and 7 from r8c9, that aside...
i am just going to take a guess from what I know about MUGs so far, that the candidates {4,5,6,7} have something to do with the MUG pattern.
with my knowledge about BUGs, I would assume that the extra candidate must be placed in the cells that have them. or can be assumed to occupy them in a way to eliminate other candidates they see??
for example since the 2's in r78c5 ( according to BUG ) must go in either... you could eliminate the 2 in r6c5
 just taking an educated stab |
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Myth Jellies
Joined: 27 Jun 2006
Posts: 64
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| Posted: Wed Jun 04, 2008 11:29 pm Post subject: |
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Norm, you have the right digits, but one too many cells. 7.2; the cool part is that we are going to avoid all of those forcing chains  . Once you find the correct MUG deduction, there is still quite a bit of work to do.
Last edited by Myth Jellies on Wed Jun 04, 2008 11:44 pm; edited 1 time in total |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Wed Jun 04, 2008 11:37 pm Post subject: |
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so just the three columns?? 3,5,9... the concept is that if only 4,5,6,7 were in those cells, that the puzzle would have more than one solution??
so can I assume that the number of solutions wouldn't be worth figuring out since there are many extra candidates? |
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Myth Jellies
Joined: 27 Jun 2006
Posts: 64
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| Posted: Wed Jun 04, 2008 11:53 pm Post subject: |
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Yes, the MUG
| Code: |
abcd . . | abcd . . | abcd . .
abcd . . | abcd . . | abcd . .
abcd . . | abcd . . | abcd . .
-----------+------------+------------
. . . | . . . | . . .
. . . | . . . | . . .
. . . | . . . | . . .
-----------+------------+------------
. . . | . . . | . . .
. . . | . . . | . . .
. . . | . . . | . . . |
is a pattern that will always result in zero or multiple solutions. Just how many doesn't matter so long as it can never be one solution. Thus that pattern has to be avoided just like a UR. |
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ravel
Joined: 21 Apr 2006
Posts: 536
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| Posted: Thu Jun 05, 2008 10:26 am Post subject: |
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Nice pattern (but not very common, i suppose).
Thanks for your new MUG thread, Myth, now i have a good one to point to for deadly patterns. |
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Steve R
Joined: 24 Oct 2005
Posts: 289
Location: Birmingham, England
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| Posted: Thu Jun 05, 2008 7:55 pm Post subject: |
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I think this is the same solution as Norm’s. After basics:
| Code: | +---------------------------------------------------+
| 156 7 9 | 1256 256 256 | 4 3 8 |
| 2 34 346 | 46 9 8 | 7 5 1 |
| 145 18 458 | 145 3 7 | 6 2 9 |
--------------------------------------------------
| 8 6 2 | 7 1 9 | 5 4 3 |
| 457 345 3457 | 56 8 456 | 1 9 2 |
| 45 9 1 | 3 245 245 | 8 67 67 |
--------------------------------------------------
| 9 28 4567+8 | 256 4567+2 2456 | 3 1 4567+ |
| 14567 12 4567+ | 8 4567+2 3 | 9 67 4567+ |
| 3 45 4567+ | 9 4567+ 1 | 2 8 4567+ |
+---------------------------------------------------+ |
The MUG marked + means that r78c5 contain 2 or r7c3 contains 8. In the latter case the (28) in r7c2 forces the 2 of box 8 into r8c5. Whichever applies 2 may be eliminated from r7c46. This brings us to
| Code: | +---------------------------------------------------+
| 1 7 9 | 2 56 56 | 4 3 8 |
| 2 3 6 | 4 9 8 | 7 5 1 |
| 45 8 45 | 1 3 7 | 6 2 9 |
--------------------------------------------------
| 8 6 2 | 7 1 9 | 5 4 3 |
| 7 45 3 | 56+ 8 56+4 | 1 9 2 |
| 45 9 1 | 3 45 2 | 8 6 7 |
--------------------------------------------------
| 9 2 8 | 56+ 7 56+4 | 3 1 456 |
| 6 1 45 | 8 2 3 | 9 7 45 |
| 3 45 7 | 9 456 1 | 2 8 456 |
+---------------------------------------------------+ |
Now the UR marked + means that r5c6 or r7c6 contains 4. If the latter, 4 is eliminated from r9c5 directly; if the former, the conjugates in column 2 force the same elimination. And the puzzle is solved.
A fine MUG, indeed!
Steve |
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Myth Jellies
Joined: 27 Jun 2006
Posts: 64
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| Posted: Fri Jun 06, 2008 5:45 am Post subject: |
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Steve. That will work.
It figures  . Essentially a skyscraper/finned fish finishes it off. My paper got a bit messy so I missed that and went for the following nut-job moves.
| Code: |
*--------------------------------------------------*
| 1 7 9 | 2 56 56 | 4 3 8 |
| 2 3 6 | 4 9 8 | 7 5 1 |
| 45 8 45 | 1 3 7 | 6 2 9 |
|----------------+----------------+----------------|
| 8 6 2 | 7 1 9 | 5 4 3 |
| 7 45 3 | 56 8 46+5 | 1 9 2 |
| 45 9 1 | 3 45 2 | 8 6 7 |
|----------------+----------------+----------------|
| 9 2 8 | 56 7 45+6 | 3 1 46+5 |
| 6 1 45 | 8 2 3 | 9 7 45 |
| 3 45 7 | 9 46+5 1 | 2 8 56+4 |
*--------------------------------------------------*
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BUG+5! BUG avoidance options in r5c6, r7c69, and r9c5 directly inhibit r7c6 = 5, The remaining BUG avoidance option, a 4 in r9c9 also inhibits the 5 in r7c6 due to the bilocated 4's in row 7. Hence r7c6 <> 5.
| Code: |
*--------------------------------------------------*
| 1 7 9 | 2 56 56 | 4 3 8 |
| 2 3 6 | 4 9 8 | 7 5 1 |
|*45 8 *45 | 1 3 7 | 6 2 9 |
|----------------+----------------+----------------|
| 8 6 2 | 7 1 9 | 5 4 3 |
| 7 *45 3 |*56 8 *46+5 | 1 9 2 |
|*45 9 1 | 3 45 2 | 8 6 7 |
|----------------+----------------+----------------|
| 9 2 8 |*56 7 *46 | 3 1 *45+6 |
| 6 1 *45 | 8 2 3 | 9 7 *45 |
| 3 *45 7 | 9 *45+6 1 | 2 8 456 |
*--------------------------------------------------*
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Still not seeing the easy patterns in the fours. Starred cells denote a big BUG-Lite+3. Two of the BUG avoidance digits inhibit the 6 in r7c4 directly, and the final option in r5c6 inhibits it via the 56-cell in r5c4. Hence r7c4 <> 6.
And then of course from here...
| Code: |
*--------------------------------------------------*
| 1 7 9 | 2 56 56 | 4 3 8 |
| 2 3 6 | 4 9 8 | 7 5 1 |
| 45 8 45 | 1 3 7 | 6 2 9 |
|----------------+----------------+----------------|
| 8 6 2 | 7 1 9 | 5 4 3 |
| 7 45 3 | 6 8 45 | 1 9 2 |
| 45 9 1 | 3 45 2 | 8 6 7 |
|----------------+----------------+----------------|
| 9 2 8 | 5 7 46 | 3 1 46 |
| 6 1 45 | 8 2 3 | 9 7 45 |
| 3 45 7 | 9 46 1 | 2 8 56+4 |
*--------------------------------------------------*
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...just to be consistent, it's got to be a BUG+1.
At least the MUG was still useful, which was the whole point. What my endgame lacked in grace and simplicity, I'd like to think it made up for in sheer bloody-mindedness |
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