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daj95376
Joined: 23 Aug 2008
Posts: 3854
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 Posted: Mon Mar 14, 2011 5:54 pm Post subject: Puzzle 11/03/14: ~ Difficult |
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| Code: | +-----------------------+
| . . . | . 5 . | . 6 . |
| . 9 . | 7 . . | 3 8 . |
| . . 4 | . . 1 | 7 . . |
|-------+-------+-------|
| . 3 . | 5 . 2 | 6 9 . |
| 9 . . | . . 7 | . . 3 |
| . . 6 | 4 3 9 | . 7 . |
|-------+-------+-------|
| . 7 9 | 6 . . | 5 . . |
| 1 6 . | 2 . 5 | . . 7 |
| . . . | . 7 . | . 1 . |
+-----------------------+
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Play this puzzle online at the Daily Sudoku site |
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peterj
Joined: 26 Mar 2010
Posts: 974
Location: London, UK
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| Posted: Tue Mar 15, 2011 9:00 am Post subject: |
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I had some time so put my "extreme" hat on and went looking for a one-stepper... with great difficulty! Apologies for my indulgence!
| Code: | almost-er(4) b2, r8, (4)r8c8 ; r1c7<>4
(4=89)r1c64 - (9)r3c5=(9-5)r3c9=(5-8)r6c9=r7c9 - (8=49)r8c57 - (4)r8c8=er(4)[r1c6=r2c5 - r8c5=r8c7] ; r1c7<>4 |
[Edit. Fixed two typos through lack of proofreading. Thanks Danny]
Last edited by peterj on Tue Mar 15, 2011 6:25 pm; edited 1 time in total |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Tue Mar 15, 2011 6:06 pm Post subject: |
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Peter, interesting find!
First, you might check your chain for typos. Second (and rambling!), I prefer to express fin logic as an -or- condition.
| Code: | r8b2 ER(4) -or- fin( r8c8=4 ) => r1c7<>4
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Since the ER is well-defined for the elimination, all you need to show is that the fin leads to the elimination ... or that the fin is false. This chain shows that the fin leads to the elimination.
(4)r8c8 - (49=8)r8c57 - r7c9 = (8-5)r6c9 = (5-9)r3c9 = r3c5 - (9=8)r1c4 - (8=4)r1c6 - (4)r1c7
Now, I know this is a perfectly legitimate chain, and that chains allow intermediate contradictions, but it always bothers me when I notice an intermediate contradiction. Consider these assignments between r8c8 and r3c5:
r8c8=4 ( *r8c5=9 r8c7=8 ) r6c9=8 r3c9=5 *r3c5=9
When I see something like this, I would set out to show that the fin is false.
(4)r8c8 - (49=8)r8c57 - r7c9 = (8-5)r6c9 = (5-9)r3c9 = r3c5 - (9=4)r8c5 - (4)r8c8
At this point, you can conclude that the ER must be true. (Yes, my approach is really two steps instead of one.)
Regards, Danny
Note: If we convert the discontinuous loop into an SI-based AIC:
| Code: | (49=8)r8c57 - r7c9 = (8-5)r6c9 = (5-9)r3c9 = r3c5 - (9=4)r8c5 => r8c8<>4
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Then we have another example of "overlapping" endpoints (mentioned by ronk). |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Wed Mar 16, 2011 12:29 am Post subject: |
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| I had to use more conventional steps and end it with a Medusa Wrap. |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Wed Mar 16, 2011 12:55 am Post subject: |
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This puzzle needed a 7-cell XY-Chain.
| Code: | after basics
+-----------------------------------------------------------------------+
| 37 12 37 | 89 5 48 | 124 6 1249 |
| 25 9 125 | 7 24 6 | 3 8 124 |
| 6 8 4 | 3 29 1 | 7 25 259 |
|-----------------------+-----------------------+-----------------------|
| 47 3 17 | 5 8 2 | 6 9 14 |
| 9 245 258 | 1 6 7 | 248 245 3 |
| 258 125 6 | 4 3 9 | 128 7 1258 |
|-----------------------+-----------------------+-----------------------|
| 2348 7 9 | 6 1 348 | 5 234 248 |
| 1 6 38 | 2 49 5 | 489 34 7 |
| 23458 245 2358 | 89 7 348 | 2489 1 6 |
+-----------------------------------------------------------------------+
# 69 eliminations remain
c27 X-Wing <> 1 r16c9 -or-
r24 X-Wing <> 1 r16c9 extraneous
r58 X-Wing <> 8 r6c7,r9c37
c28\r59 Sashimi X-Wing <> 4 r9c7
r28\c59 Sashimi X-Wing <> 4 r7c9 extraneous
<29+8> XY-Wing r9c7/r7c9+r9c4 <> 8 r7c6 extraneous
+--------------------------------------------------------------+
| 37 12 37 | 89 5 48 | 124 6 249 |
| 25 9 125 | 7 24 6 | 3 8 124 |
| 6 8 4 | 3 29 1 | 7 25 259 |
|--------------------+--------------------+--------------------|
| 47 3 17 | 5 8 2 | 6 9 14 |
| 9 245 258 | 1 6 7 | 248 245 3 |
| 258 125 6 | 4 3 9 | 12 7 258 |
|--------------------+--------------------+--------------------|
| 2348 7 9 | 6 1 34 | 5 234 28 |
| 1 6 38 | 2 49 5 | 489 34 7 |
| 2345 245 235 | 89 7 348 | 29 1 6 |
+--------------------------------------------------------------+
# 60 eliminations remain
(4=2)r2c5 =9r3c5 =8r1c4 =9r9c4 =2r9c7 =1r6c7 =4r4c9 => r2c9<>4
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Maybe I should have listed it as "Extreme". _  _ |
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peterj
Joined: 26 Mar 2010
Posts: 974
Location: London, UK
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| Posted: Wed Mar 16, 2011 8:00 am Post subject: |
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| daj95376 wrote: | | I prefer to express fin logic as an -or- condition. |
That has been my normal method also - thinking of it more like a Kraken with two or more streams to prove the same elimination.
Not sure quite why I wrote it this way - I have done some extremes lately where players (and myself once) have used patterns within a chain and then continued the chain using the elimination from the pattern. So I have started to think of them as just "expressions" in chains.
Contradictions in chains never bother me! I am usually singlemindedly driving the chain towards the elimination I want, to notice the fallout on the way! |
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