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ravel
Joined: 21 Apr 2006
Posts: 536
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 Posted: Thu Apr 10, 2008 4:40 pm Post subject: Probably quicker with only few PM's |
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Two puzzles from the current Patterns game. Both are only hard at the beginning.
The second one is rated "too hard" by the online solver, because for some subsets needed the naked ones are too big.
| Code: | +-------+-------+-------+
| . . . | . . . | . . . |
| . . 1 | 7 . 8 | 4 . . |
| . 9 . | 5 . 2 | . 7 . |
+-------+-------+-------+
| . 7 9 | . . . | 1 6 . |
| . . . | . . . | . . . |
| . 2 3 | . . . | 8 9 . |
+-------+-------+-------+
| . 3 . | 1 . 9 | . 2 . |
| . . 8 | 3 . 4 | 7 . . |
| . . . | . . . | . . . |
+-------+-------+-------+ m_b_metcalf
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>>> play online
| Code: | +-------+-------+-------+
| . . . | . . . | . . . |
| . . 1 | 2 . 3 | 4 . . |
| . 5 . | 6 . 7 | . 8 . |
+-------+-------+-------+
| . 8 5 | . . . | 7 3 . |
| . . . | . . . | . . . |
| . 3 9 | . . . | 6 5 . |
+-------+-------+-------+
| . 7 . | 8 . 5 | . 6 . |
| . . 4 | 1 . 2 | 3 . . |
| . . . | . . . | . . . |
+-------+-------+-------+ TTHsieh
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>>> play online |
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nataraj
Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria
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| Posted: Fri Apr 11, 2008 5:55 am Post subject: |
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Thanks, ravel, for this great puzzle (I am referring to the top one, didn't get around to do the other one).
Indeed the very hard part is in the beginning. It is possible to find two xy-wings very soon and both solve at least one cell immediately to get the eliminations going.
I wrote down all the PMs for the 4-cell houses and didn't mind the extra writing (thank the creator of this site the cells are just the right size when printed out!), of course for the xy-wings only the two-candidate cells are needed.
____
Hint: both xy-wings use the same 3 candidates, again a number well known to most people, although not quite appropriate this year on account of Feb.29 |
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Victor
Joined: 29 Sep 2005
Posts: 207
Location: NI
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| Posted: Fri Apr 11, 2008 7:23 am Post subject: |
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| I preferred the 2nd one, which would have been considered an excellent puzzle in VH pre-X..-wing days. Can be done on p&p without candidate numbers - good fun! |
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ravel
Joined: 21 Apr 2006
Posts: 536
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| Posted: Fri Apr 11, 2008 7:38 am Post subject: |
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| nataraj wrote: | | ... not quite appropriate this year ... |
Yes, i should have waited till next year to post it, but i am too impatient  |
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nataraj
Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria
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| Posted: Fri Apr 11, 2008 1:50 pm Post subject: |
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| ravel wrote: | | nataraj wrote: | | ... not quite appropriate this year ... |
Yes, i should have waited till next year to post it, but i am too impatient |
And how lucky we are that you are impatient  Besides, of course, only my hint is flawed, not the puzzle. |
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nataraj
Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria
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| Posted: Fri Apr 11, 2008 2:41 pm Post subject: |
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As for the second puzzle: that naked 6-(six!)-tuple is very hard to find.
Compared to that, the naked quad later on is a piece of cake.
| Quote: | | Can be done on p&p without candidate numbers |
Not me, sir. I cannot. Nohow. |
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Victor
Joined: 29 Sep 2005
Posts: 207
Location: NI
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| Posted: Fri Apr 11, 2008 6:04 pm Post subject: |
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| Quote: | | ... that naked 6-(six!)-tuple is very hard to find. |
Ah, this is an example of why it's sometimes easier without candidate numbers! - you look for a set that can't go in given spaces, thus finding hidden ntuples. Here, you can see that 3/6/7 don't go in those 6 cells in r1, and must thus fill up the rest. (No, I'm not being wise after the the event!) The downside of this approach is of course that, if the hidden set is larger than the naked set, then it tends to be easier with candidate numbers. |
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nataraj
Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria
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| Posted: Fri Apr 11, 2008 9:38 pm Post subject: |
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| Victor wrote: | | Here, you can see that 3/6/7 don't go in those 6 cells in r1, and must thus fill up the rest. (No, I'm not being wise after the the event!) |
Victor, please bear with me for being thick. Could you explain that some more? I am quite comfortable with writing down the few places where a given number can go in the beginning. It works nicely with single numbers, and when I find that two numbers must occupy two cells in a house, I've found a hidden pair. This was the case with 3,5 in r5c45,here. So far, so good.
How is it that "you can see" that the 3/6/7 dont go in 6 cells? Obviously I am missing something here. I see that box 2 is off limits, that makes 3 cells. And r1c7 cannot contain any of 3,6,7. That leaves 5 cells for 3 numbers.
Another way to look at it:
3 can go into c139
6 can go into c1239
7 can go into c1389
How does this help us in finding the hidden triple ?
Actually,the hidden triple/naked sixt (?) only appears after finding the naked pairs 79 in col 8, 69 in col 3, and 23 in col 3. So the question is, how do you find naked pairs without writing candidate numbers?
I feel I am runnig up against a mental wall here and I hope you can help me tear it down |
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Victor
Joined: 29 Sep 2005
Posts: 207
Location: NI
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| Posted: Sat Apr 12, 2008 9:09 pm Post subject: |
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| Nataraj, I was jesting of course, but I do like to do puzzles like this without writing out all candidates. In c3 there are 2 places where 6/7/8 can't go: so we've found a (naked) pair 23 & a (hidden) triple 678. In c2 & c8 there are 2 places where 1/2/4 can't go: so we've found prs 69 in c2 & 79 in c7. (The 124 triples are the hidden ones in these columns, & so it would be easier to do this with candidate numbers: you'd instantly see the naked prs 69 & 79. I guess it is just a matter of preference that I like finding them as i've explained.) Once these prs are pencilled in, we just have to look at r1: c139 are the only cells not seen by 367. You are right: you don't see this until you've filled in the 69 & 79 prs ( tho' the 23 pr isn't used here). And now you can fix 8 in b1. Etc. |
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nataraj
Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria
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| Posted: Sun Apr 13, 2008 10:28 am Post subject: |
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| Thanks, Victor, for your explanation. Makes much sense. I'll try that approach with the next few puzzles and see how it feels. |
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