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Lulu
Joined: 21 Sep 2005
Posts: 11
Location: Manchester, England
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 Posted: Sat Oct 08, 2005 7:00 am Post subject: 8th October puzzle |
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Am I getting better at these things or was today's puzzle not really hard? Still fun to do though thanks Sam.  |
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RogerC
Joined: 08 Oct 2005
Posts: 14
Location: High Wycombe, Bucks, England
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| Posted: Sat Oct 08, 2005 7:23 pm Post subject: I agree - very hard! |
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I'm new too and thought I was doing well - even on the 'very hard' puzzles but this one has beaten me. I've looked for doubles, triples and quadruples and can find none. This probably just means I have missed something completely obvious!!
Can you help me please? I'm stuck at:
-65 742 ---
-12 9-6 ---
-97 --5 6-2
156 2-3 8--
974 851 326
283 6-4 -5-
6-8 5-9 27-
72- 468 -3-
5-- -27 -68
The hint says row 1 col 8 is a 1 but I cannot for the life of me see why.
Roger |
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Louise56
Joined: 21 Sep 2005
Posts: 94
Location: El Cajon, California USA
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| Posted: Sat Oct 08, 2005 8:36 pm Post subject: Re: I agree - very hard! |
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| RogerC wrote: | I'm new too and thought I was doing well - even on the 'very hard' puzzles but this one has beaten me. I've looked for doubles, triples and quadruples and can find none. This probably just means I have missed something completely obvious!!
Can you help me please? I'm stuck at:
-65 742 ---
-12 9-6 ---
-97 --5 6-2
156 2-3 8--
974 851 326
283 6-4 -5-
6-8 5-9 27-
72- 468 -3-
5-- -27 -68
The hint says row 1 col 8 is a 1 but I cannot for the life of me see why.
Roger |
Hi Roger,
With what you have done so far, I would look at the 3x3 box on the top right. There are some pairs there. You can see that in r2c7 and r2c9, there can only be a 5/7 pair. None of the other boxes can take a 5 or a 7. You can't have a 3 in columns 7 or 8, so the 3 must be in r1c9 (it can't be in r2c9 because of the 5/7 pair). If you look at all of row 1, there must be a 1/9 pair in r1c7 and r1c8 because you cannot have a 1 or 9 in r1c1. That means for row 1 the 8 must be in r1c1. Back to the top right box, you have a 4/8 pair in r2c8 and r3c8. See what you can do with this and write back if you get stuck again. |
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Nelsipete
Guest
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| Posted: Sat Oct 08, 2005 8:43 pm Post subject: |
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Roger, if you look at the bottom right 3x3, you will see there are the following possibilities:
-------2----------7--------1 or 4 or 9
1 or 5 or 9------3--------1 or 5 or 9
1 or 4 or 9-------6------1 or 4 or 8 or 9
The bottom righthand box is the ONLY one of the nine which has an 8 as a possibility. Therefore, it must be an 8. |
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David Bryant
Joined: 29 Jul 2005
Posts: 559
Location: Denver, Colorado
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| Posted: Sat Oct 08, 2005 8:46 pm Post subject: Why is there a "1" at r1c8? |
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I think Lulu is getting better. This one had me scratching my head for a little bit.
Just to make this clear, here's the position you have reached:
| Code: |
-65 742 ---
-12 9-6 ---
-97 --5 6-2
156 2-3 8--
974 851 326
283 6-4 -5-
6-8 5-9 27-
72- 468 -3-
5-- -27 -68 |
You can figure this out by concentrating on the top right 3x3 box (r1c7 - r3c9). The first thing you must notice is that the "1" in row 1 must appear in this top right 3x3 box -- that is, there must be a "1" at r1c7, r1c8, or r1c9. This is so because there's already a "1" in row 2 (in the top left 3x3 box), and row 1 is already filled in the top center 3x3 box.
Now look at the values {5, 7} appearing in row 1 and in column 8. The way this row and column intersect in the top right 3x3 box implies that the pair [5, 7] can ONLY go in the two cells r2c7 & r2c9. This knowledge, combined with the "3"s already appearing in columns 7 & 8, implies that r1c9 = 3. So the quadruplet {1, 4, 8, 9} must appear in the L-shaped piece of the box described as r1c7 & r1c8 & r2c8 & r3c8. Specifically those four cells, in that order, appear to have the possibilities 1/9 (r1c7), 1/8/9 (r1c8), 1/4/8 (r2c8 & r3c8).
But when you combine this information with the realization that the "1" in this 3x3 box must appear in row 1 you can split the quadruplet into the pairs {1,9} in r1c7 & r1c8, plus {4, 8} in r2c8 & r2c9. And then, since r4c8 is already a {4, 9} pair, you can place a "9" at r4c8 and at r1c7, and the infamous "1" at r1c8. dcb  |
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Louise56
Joined: 21 Sep 2005
Posts: 94
Location: El Cajon, California USA
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| Posted: Sat Oct 08, 2005 9:15 pm Post subject: |
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| This is a good puzzle for people who solve them very methodically. I am this way and I would bet that Lulu is too. David is probably very good at doing much of the solving by just looking at the puzzle and mentally figuring out where numbers go. He is likely a fast solver with most puzzles. This is a puzzle where the tortoise can beat the hare! When I solved this puzzle I first wrote down the digits 1 to 9 and next to them I wrote how many times each digit was in the puzzle. I noticed there were five 6's so I solved for them first. Then I put in the possibilities for 7's, etc. As I put in the numbers I tried to clean up as much as I could by looking for pairs and checking the rows and columns for eliminations as well as the 3x3 boxes. I'm with Lulu on this one. Maybe there is a difference between the way females and males solve these. Any thoughts out there? |
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RogerC
Joined: 08 Oct 2005
Posts: 14
Location: High Wycombe, Bucks, England
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| Posted: Sun Oct 09, 2005 6:42 am Post subject: |
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Thanks Louise and David. I missed the 5/7 pair completely although I must have looked at it 10 times! I put it down to tiredness as I had been decorating my flat all day and got very tired!!
I'm not sure about your hypothesis that females are more methodical in their approach to the puzzles, though. I tend to use the same methods each time and I even write down the number of occurences of each number! But then I have been told that I am more in touch with my feminine side than most men so maybe it is. |
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Louise56
Joined: 21 Sep 2005
Posts: 94
Location: El Cajon, California USA
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| Posted: Sun Oct 09, 2005 2:32 pm Post subject: |
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| RogerC wrote: | | I'm not sure about your hypothesis that females are more methodical in their approach to the puzzles, though. I tend to use the same methods each time and I even write down the number of occurences of each number! But then I have been told that I am more in touch with my feminine side than most men so maybe it is. |
Roger,
My husband says I'm wrong on the male/femaile hypothesis as he is very methodical as well (although he hates to ask for directions, but that's another issue). I used to teach algebra and each year there were some very intelligent students, usually boys, who had trouble because they got in the habit of skipping steps to solve equations (they could see the answers before even starting the problems). As the year went on and the equations became more complex, they had trouble solving them. Eventually these bright students learned the proper steps and did well. Anyway, that's where my hypothesis came from, a handful of eighth graders! I'm certainly in touch with my masculine side as I enjoy logic puzzles....more than shopping! |
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David Bryant
Joined: 29 Jul 2005
Posts: 559
Location: Denver, Colorado
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| Posted: Sun Oct 09, 2005 10:07 pm Post subject: |
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| Louise56 wrote: | | This is a good puzzle for people who solve them very methodically. ... David is probably very good at doing much of the solving by just looking at the puzzle and mentally figuring out where numbers go. He is likely a fast solver with most puzzles. ... |
No, I'm usually very methodical about the way I solve these puzzles. And I'm not particularly fast, although I'm getting quicker with practice. Once in a while I hit one where a lot of things appear obvious all at once, but I've learned that this may mean I've overlooked something important. And I know if I get in too much of a hurry I'll make a mistake and have to start over -- I really hate that.
I used to build a frequency table for the digits in the initial state of the grid, but now I can generally count how many times each digit appears just by looking at the puzzle. And if I don't see any obvious patterns the first time I scan the rows and columns, I generally just concentrate on the digits 1, 2, 3, ... in order like that, to make sure I'm not missing anything.
Louise, you said you used to teach algebra to eighth-graders. Do you remember the old trick of checking your arithmetic by casting out nines? One thing I have noticed about these Sudoku puzzles is that there's a sort of symmetrical relationship between the numbers that are already in the puzzle and the ones that are missing. I'm not sure I can describe this precisely, but an example might be a case where {1,3,5} are missing in a particular row, and all three of those digits already lie in a 3x3 box that's intersected by that row. Another example might be where a {3, 4} pair appears in two adjacent cells in the same row -- when I'm finally able to resolve that pair, I'll often see both the "4" and the "3" somewhere in two adjacent columns.
Anyway, what I'm driving at is that there's a sort of mirror image of the final solution embedded in the puzzle itself at every step as one goes along, and if you can spot that pattern, and visualize the way it changes each time you write in a new number, you can be certain you haven't made a mistake. dcb
Last edited by David Bryant on Tue Oct 11, 2005 1:17 pm; edited 1 time in total |
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Louise56
Joined: 21 Sep 2005
Posts: 94
Location: El Cajon, California USA
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| Posted: Tue Oct 11, 2005 12:53 am Post subject: |
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| David Bryant wrote: | | Louise, you said you used to teach algebra to eighth-graders. Do you remember the old trick of checking your arithmetic by casting out nines? One thing I have noticed about these Sudoku puzzles is that there's a sort of symmetrical relationship between the numbers that are already in the puzzle and the ones that are missing. I'm not sure I can describe this precisely, but an example might be a case where {1,3,5} are missing in a particular row, and all three of those digits already lie in a 3x3 box that's intercected by that row. Another example might be where a {3, 4} pair appears in two adjacent cells in the same row -- when I'm finally able to resolve that pair, I'll often see both the "4" and the "3" somewhere in two adjacent columns. dcb |
David,
That is interesting. There must be some kind of symmetry going on because each box, row and column add up to 45 so you can't have an area with just high or just low numbers. There's got to be some kind of reflection. I will look into it. I'll be gone for a few days and get back to you. |
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