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Why a 7 there?

 
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pat1m



Joined: 17 Jul 2006
Posts: 6

PostPosted: Tue Aug 29, 2006 6:28 pm    Post subject: Why a 7 there? Reply with quote

I inputted the following puzzle into the Draw feature, when I got stuck. According to the hint, the next move would be a 7 in r3c5. Why a 7 there and not in r1c5? Would someone be able to explain?
This is what I had:


6.....3......9 | 25.....2478.........48 | ..58 ...1 .....78
7..145...14 | 6.......348.....13489 | 589 ..34 .....2
8..145.....2 | 59.....347.......1349 | ....6 ..34 ....79
__________________________________________
9......2......8 | 4........5...............6 | ...3......7......1
1......7......5 | 3........9...............2 | ...4......8......6
4......6......3 | 8........1...............7 | ...2......9......5
__________________________________________
2......9......6 | 1.......38.............38 | 7......5.......4
3....14....14 | 7..........6..............5 |89......2 ......89
5......8 .....7 | 29......24.............49 | 1......6.......3
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AZ Matt



Joined: 03 Nov 2005
Posts: 63
Location: Hiding under my desk in Phoenix AZ USA

PostPosted: Tue Aug 29, 2006 9:02 pm    Post subject: One way... Reply with quote

I don't know if this is the fastest way to get to 7 in r3c5, pat1m, but it is the most obvious:

There is a type-1 unique rectangle in the r2c23/r8c23. r3c2 must be <5>, otherwise it could be a <1> or a <4>, and the puzzle would not be unique.

You'll get it from there...

Good luck.

Edit: Of course it occurs to me now that the draw hint would not give you the 7 for a clue if it took that route to get there. I will keep working...


Last edited by AZ Matt on Tue Aug 29, 2006 9:15 pm; edited 2 times in total
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Marty R.



Joined: 12 Feb 2006
Posts: 5180
Location: Rochester, NY, USA

PostPosted: Tue Aug 29, 2006 9:08 pm    Post subject: Re: Why a 7 there? Reply with quote

pat1m wrote:
I inputted the following puzzle into the Draw feature, when I got stuck. According to the hint, the next move would be a 7 in r3c5. Why a 7 there and not in r1c5? Would someone be able to explain?
This is what I had:


6.....3......9 | 25.....2478.........48 | ..58 ...1 .....78
7..145...14 | 6.......348.....13489 | 589 ..34 .....2
8..145.....2 | 59.....347.......1349 | ....6 ..34 ....79
__________________________________________
9......2......8 | 4........5...............6 | ...3......7......1
1......7......5 | 3........9...............2 | ...4......8......6
4......6......3 | 8........1...............7 | ...2......9......5
__________________________________________
2......9......6 | 1.......38.............38 | 7......5.......4
3....14....14 | 7..........6..............5 |89......2 ......89
5......8 .....7 | 29......24.............49 | 1......6.......3


Try this. If you look at row 1, the "4" must be in box 2, thus the "4" is eliminated from cells in rows 2 and 3 in box 2. There is now a naked pair, "38", in column 5 and those two numbers must be eliminated from all other cells in that column, leaving the "7" in r3c5.
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keith



Joined: 19 Sep 2005
Posts: 3184
Location: near Detroit, Michigan, USA

PostPosted: Tue Aug 29, 2006 9:11 pm    Post subject: Row box intersection Reply with quote

Take a look at row 1. The <4> must be in box 2. So, you can take out all the candidates <4> that are in box 2 and rows 23.

This reveals a naked pair <38> in column 5. You have now eliminated <34> from R3C5. It must be <7>.

And, by the way: Did you notice the Unique rectangle in R28C23? R2C2 must be <5>.

Keith
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ravel



Joined: 21 Apr 2006
Posts: 536

PostPosted: Tue Aug 29, 2006 9:16 pm    Post subject: Reply with quote

Alternative:
In row 1 the 4 only can be in column 4 or 6, both in box 2. Therefore you can eliminate it from r23c56 (same box). This gives you the same naked pair 38 in r27c5 in column 5 => r3c5=7.
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keith



Joined: 19 Sep 2005
Posts: 3184
Location: near Detroit, Michigan, USA

PostPosted: Tue Aug 29, 2006 9:28 pm    Post subject: Unique Loop Reply with quote

Ravel, and all,

You might enjoy this:

From the posted position, use the UR to set R2C2 = <5>.

Then you have a Type 4 unique loop: The three corners of the old UR and R23C6. This eliminates <4> from R23C6!

Keith
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AZ Matt



Joined: 03 Nov 2005
Posts: 63
Location: Hiding under my desk in Phoenix AZ USA

PostPosted: Wed Aug 30, 2006 7:17 pm    Post subject: Unique Loop? Reply with quote

I think I am missing your point, Keith. I see that the <4> must be in either r2c3 and r3c8, or r3c2 and r2c8, but in any event not in r2c56 nor r3c56. That doesn't appear to be what you are refering to.

What is a unique loop?
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ravel



Joined: 21 Apr 2006
Posts: 536

PostPosted: Wed Aug 30, 2006 9:37 pm    Post subject: Re: Unique Loop Reply with quote

keith wrote:
From the posted position, use the UR to set R2C2 = <5>.

Nice, think this solves it. Dont know which unique loop you mean.
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keith



Joined: 19 Sep 2005
Posts: 3184
Location: near Detroit, Michigan, USA

PostPosted: Wed Aug 30, 2006 10:54 pm    Post subject: Unique Loop Reply with quote

I apologize that my previous post has a sloppy explanation.

Here is the posted position:
Code:
+-------------------+-------------------+-------------------+
| 6     3     9     | 25    2478  48    | 58    1     78    |
| 7     145   14    | 6     348   13489 | 589   34    2     |
| 8     145   2     | 59    347   1349  | 6     34    79    |
+-------------------+-------------------+-------------------+
| 9     2     8     | 4     5     6     | 3     7     1     |
| 1     7     5     | 3     9     2     | 4     8     6     |
| 4     6     3     | 8     1     7     | 2     9     5     |
+-------------------+-------------------+-------------------+
| 2     9     6     | 1     38    38    | 7     5     4     |
| 3     14    14    | 7     6     5     | 89    2     89    |
| 5     8     7     | 29    24    49    | 1     6     3     |
+-------------------+-------------------+-------------------+

If you use the UR to set R2C2 = <5>, you then have another possible deadly pattern on <14>. Here it is:
Code:
+--------+--------+-------+
| . .  . | . . .  | . . . |
| . .  14| . . 14x| . . . |
| . 14 . | . . 14y| . . . |
+--------+--------+-------+
| . .  . | . . .  | . . . |
| . .  . | . . .  | . . . |
| . .  . | . . .  | . . . |
+--------+--------+-------+
| . .  . | . . .  | . . . |
| . 14 14| . . .  | . . . |
| . .  . | . . .  | . . . |
+--------+--------+-------+
Since one of R23C6 must be <1> (strong link), neither of them can be 4.

This is just an observation. In this puzzle, it is a ridiculously complicated way to make an elimination which is of little use.

In a post some time ago, Ravel pointed out the same pattern, laid out like this:
Code:
+-------+-------+-------+
| . x . | . . . | . x . |
| . x . | . x . | . . . |
| . . . | . x . | . x . |
+-------+-------+-------+

Technically, this is known as a "Unique Swordfishy Thingy".

Keith
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AZ Matt



Joined: 03 Nov 2005
Posts: 63
Location: Hiding under my desk in Phoenix AZ USA

PostPosted: Thu Aug 31, 2006 4:02 pm    Post subject: Sweet... Reply with quote

Thanks Keith. In the future, I think anytime we see a "super-advanced" solving technique in a puzzle, we should report it, whether it it is necessary to the puzzle or not. I am constantly making puzzles more difficult than they need to be simply because I get bored with the usual stuff, and I wouldn't have it any other way...
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pat1m



Joined: 17 Jul 2006
Posts: 6

PostPosted: Thu Aug 31, 2006 9:49 pm    Post subject: Why the 7 Reply with quote

Thank you all. I see the reasoning for the 7 now. I should have caught the row 1, box 2 4's thing. Thanks again. I didn't realize the rectangle 145 14 14 14 box, but now I can add that to the methods to try to solve puzzles
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