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daj95376
Joined: 23 Aug 2008
Posts: 3854
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 Posted: Sat Oct 31, 2009 6:06 pm Post subject: Puzzle NR_079 |
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| Code: | NR puzzles can be solved using these techniques:
Basics: Naked/Hidden Single, Naked Pair/Triple, Locked Candidates 1/2
Basics+: Naked Quad, Hidden Pair/Triple/Quad
VH: BUG+1, UR Type 1, X-Wing, XY-Wing
VH+: 2-String Kite, Empty Rectangle, Remote Pair, Skyscraper,
XYZ-Wing, finned X-Wing, UR Type 2/4
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| Code: | +-----------------------+
| . . . | . . 3 | . 8 . |
| . 9 . | 5 . 8 | . 2 1 |
| . . 7 | . 2 . | . . 5 |
|-------+-------+-------|
| . 5 . | . . . | . . . |
| . . 2 | . 9 7 | . 1 . |
| 3 7 . | . 5 . | 2 . . |
|-------+-------+-------|
| . . . | . . 6 | . . . |
| 6 1 . | . 8 . | . 3 . |
| . 3 5 | . . . | . . 6 |
+-----------------------+
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Play this puzzle online at the Daily Sudoku site |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Sun Nov 01, 2009 9:42 am Post subject: |
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the goal of this post is to show a "crazy, over the top way" of finding some eliminations to solve this puzze in one fell swoop.
first the grid after basics...
| Code: | .------------------------.------------------------.------------------------.
| 5 2 6 | 147 147 3 | 9 8 47 |
| 4 9 3 | 5 67 8 | 67 2 1 |
| 1 8 7 | 469 2 49 | 3 46 5 |
:------------------------+------------------------+------------------------:
| 9 5 14 | 123468 1346 124 | 467 467 3478 |
| 8 6 2 | 34 9 7 | 5 1 34 |
| 3 7 14 | 68 5 14 | 2 69 89 |
:------------------------+------------------------+------------------------:
| 27 4 8 | 2379 37 6 | 1 5 279 |
| 6 1 9 | 247 8 5 | 47 3 247 |
| 27 3 5 | 12479 147 1249 | 8 479 6 |
'------------------------'------------------------'------------------------' |
second, concentrate on the cells, r58c49
notice that if the 7's are false in r8c49, then you are left with the continuous loop. also notice that this continuous loop would eliminate the 4 in r1c9, leaving a 7.
| Code: | +-------+--------+--------+
| . . . | . . . | . .-47 |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+-------+--------+--------+
| . . . | . . . | . . . |
| . . . | 34 . . | . . 34 |
| . . . | . . . | . . . |
+-------+--------+--------+
| . . . | . . . | . . . |
| . . . | 24 . . | . . 24 |
| . . . | . . . | . . . |
+-------+--------+--------+ |
(4=3)r5c4 - (3=4)r5c9 - (4=2)r8c9 - (2=4)r8c4
so what we have here is an almost continuous loop, if the 7's are false in r8c49.
so moving on, we have to show that when a 7 is either true in r8c4 or r8c9 that the 7 in r4c1 can still be eliminated. well its easy to see that a 7 in r8c4 already works...
keeping track of the progress using a graph.
(loop) - (4=7)r1c9; r1c4 <> 7
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(7)r8c4; r1c4 <> 7
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(7)r8c9 ????
two of the three are accounted for...
moving on to the last 7... if that 7 is true then...
notice the almost hidden pair {4,7}r49c8, if the 4 is false in r3c8 then the hidden pair is true. so there is a strong link on the 4 in r3c8 and the hidden pair.
also, if the hidden pair is true, then the 4 in r8c7 is false. there is a weak link between those two.
we can use that in conjuction with our 7 in r8c9...
| Code: | +-----------+--------------------+-------------------+
| 5 2 6 | 147 147 3 | 9 8 (47) |
| 4 9 3 | 5 67 8 | 67 2 1 |
| 1 8 7 | 469 2 49 | 3 6(4) 5 |
+-----------+--------------------+-------------------+
| 9 5 14 | 123468 1346 124 | 467 6(47) 3478 |
| 8 6 2 | 34 9 7 | 5 1 34 |
| 3 7 14 | 68 5 14 | 2 69 89 |
+-----------+--------------------+-------------------+
| 27 4 8 | 2379 37 6 | 1 5 29-7 |
| 6 1 9 | 247 8 5 | (47) 3 24-7 |
| 27 3 5 | 12479 147 1249 | 8 9(47) 6 |
+-----------+--------------------+-------------------+ |
(7)r8c9 - (7=4)r8c7 - hp(47)r49c8 = (4)r3c8 - (4=7)r1c9
and now the final piece is set, a 7 would be true in r1c9 if a 7 is true in r8c9. this completes the truth set graph.
(loop) - (4=7)r1c9; r1c4 <> 7
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(7)r8c4; r1c4 <> 7
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(7)r8c9 - (7=4)r8c7 - hp(47)r49c8 = (4)r3c8 - (4=7)r1c9; r1c4 <> 7
this is what it looks like when its all put together.
notice that there are other eliminations.
embedded in the logic are other implications, for example the almost hidden pair chain can stand alone to eliminate the 7's in r78c9.
and, the elimination of the 4 in r3c4...
whether the loop is true or false, a 4 either can't exist in column 4 because of the weakly linked 4's in the loop
or
a 4 will exist in r3c8 due to implications made in the almost hidden pair chain.
Last edited by storm_norm on Sun Nov 01, 2009 10:39 am; edited 2 times in total |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Sun Nov 01, 2009 10:18 am Post subject: |
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ttt,
if you are watching, how would you write the diagram on such a continuous loop implication?
my attempt would be something like.
| Code: | (4)r3c8-(4=7)r1c9
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(4)r4c8-(7)r4c8=(7)r9c8-(7)r8c9
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(4)r9c8-(4)r8c7=(7)r8c7-(7)r8c4
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loop[(4=2)r8c9-(2=4)r8c4-(4=3)r5c4-(3=4)r5c9] - (4=7)r1c9 |
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arkietech
Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA
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| Posted: Sun Nov 01, 2009 12:30 pm Post subject: |
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| storm_norm wrote: | (loop) - (4=7)r1c9; r1c4 <> 7
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(7)r8c4; r1c4 <> 7
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(7)r8c9 - (7=4)r8c7 - hp(47)r49c8 = (4)r3c8 - (4=7)r1c9; r1c4 <> 7
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Wow! Nice peice of work Norm  |
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