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July 25 Very Hard

 
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CT Yankee



Joined: 17 Jul 2006
Posts: 11
Location: New England

PostPosted: Wed Jul 26, 2006 7:01 am    Post subject: July 25 Very Hard Reply with quote

This was an excellent puzzle! I had to use an X-Wing as well as an XY-Wing to solve it. I'm not certain, but I believe this may be the first puzzle from this site that definitely requires both of those techniques to solve. Or... Did anyone manage to solve it in a simpler manner? I'm pretty sure that the X-Wing (on 4s) is the best way to go, but I'm much less certain about the necessity of the XY-Wing, about which I don't remember the details except that it was in the lower left portion of the puzzle. I'm curious how other people went about solving this one.

And speaking of XY-Wings, am I the only one who thinks these are misnamed? I mean, when you come right down to it the XY-Wing really doesn't have much if anything in common with a regular X-Wing, at least not that I can see. For this reason I think the name is confusing. Personally I prefer to think of this technique as an XY-Fork, mainly because it reminds me a bit of a forking attack in Chess - in both cases you are effecting two other cells from a single cell. But I suppose it's way to late to start a debate about changing the name, as the current name seems to be universally accepted. Oh well.


Last edited by CT Yankee on Wed Jul 26, 2006 7:08 am; edited 1 time in total
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CT Yankee



Joined: 17 Jul 2006
Posts: 11
Location: New England

PostPosted: Wed Jul 26, 2006 7:04 am    Post subject: Re: July 25 Very Hard Reply with quote

Oops, duplicate post, ignore...
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ravel



Joined: 21 Apr 2006
Posts: 536

PostPosted: Wed Jul 26, 2006 7:31 am    Post subject: Reply with quote

Only the x-wing was needed (and 2 hidden pairs).

I agree, that some (most) names for solving techniques are not good. It starts with naked/hidden singles, where always the naked ones are hidden to me, up to unique rectangles, which in fact are non unique.
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fanya



Joined: 24 Jul 2006
Posts: 8

PostPosted: Wed Jul 26, 2006 1:07 pm    Post subject: 43rd cell entry Reply with quote

Ok, I'm getting pretty good with the hard puzzles, but I'm stumped with this one. I got the x-wing with the 4's. And a few hidden pairs. BUT

Why is the 43rd entry using "hint" a 7 in row 1 col 5? I don't get it.

Fanya
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Last edited by fanya on Mon Jan 31, 2011 6:39 pm; edited 2 times in total
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ravel



Joined: 21 Apr 2006
Posts: 536

PostPosted: Wed Jul 26, 2006 1:52 pm    Post subject: Reply with quote

You should be here:
Code:
. . 3 | . . 1 | . 2 6
. 2 . | 6 . 9 | 3 . 7
. 6 . | . 3 . | 4 . 1
---------------------
. 8 6 | . 9 4 | . . .
4 9 2 | . 1 . | 6 7 8
. . . | 8 6 . | . 4 .
---------------------
6 5 9 | . 2 . | . . .
2 . 8 | 1 5 6 | 7 . .
. 1 . | 9 . . | 5 6 2

In box 7 the 7 must be in row 9 (r9c1 or r9c3), therefore it cannot be in r9c5. This leaves only r5c1 for a 7 in column 5.
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Clement



Joined: 24 Apr 2006
Posts: 684
Location: Dar es Salaam Tanzania

PostPosted: Wed Jul 26, 2006 2:47 pm    Post subject: July 25 Very hard Reply with quote

I solved the puzzle by using hidden triples. In r4 there is a hidden triple {1,3,5,}c1, {1,3,5,}c8 and {5,3}c9.This leaves 2 in r4c7 and 7 in r4c4.There is another hidden triple in r8 i.e {3,4,5}c2, {4,5}c5 and {3,4}c9. This leaves 9 as the only candidate inr8c8 which leaves {5,8} as a pair in r2c8 and r3c8 thus leaving 1 in r7c8 of the pair{1,8}. This completes all the candidates in BOX9.
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ravel



Joined: 21 Apr 2006
Posts: 536

PostPosted: Wed Jul 26, 2006 4:03 pm    Post subject: Re: July 25 Very hard Reply with quote

Clement wrote:
In r4 there is a hidden triple {1,3,5,}c1, {1,3,5,}c8 and {5,3}c9.

I cannot see that. This is the puzzle before the x-wing in 4 (in r29c35):
Code:
. . 3 | . . . | . 2 6
. 2 . | 6 . 9 | 3 . 7
. 6 . | . 3 . | 4 . 1
---------------------
. 8 6 | . 9 4 | . . .
4 9 2 | . . . | 6 7 8
. . . | 8 6 . | . 4 .
---------------------
6 . 9 | . 2 . | . . .
2 . 8 | 1 . 6 | 7 . .
. 1 . | 9 . . | 5 6 2

Why cant there be a 1 in r4c7 ?
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fanya



Joined: 24 Jul 2006
Posts: 8

PostPosted: Wed Jul 26, 2006 9:21 pm    Post subject: ravel Reply with quote

Ravel wrote:
Quote:
In box 7 the 7 must be in row 9 (r9c1 or r9c3), therefore it cannot be in r9c5. This leaves only r5c1 for a 7 in column 5.


Ravel, thanks for the help. I got so exhausted trying to find new complex techniques that I forgot to use old familiar ones.

Fanya
________
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Last edited by fanya on Mon Jan 31, 2011 6:39 pm; edited 1 time in total
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fanya



Joined: 24 Jul 2006
Posts: 8

PostPosted: Wed Jul 26, 2006 9:31 pm    Post subject: Clement's comment Reply with quote

I was going to point this out before ravel's reply.

As I see it row 4 looks like this at the stage where 42 cells are filled:

Code:
#=======================#=======================#=======================#     
# 1   3 |       |       #   2   |       |       # 1 2   | 1   3 |     3 #     
#   5   |  [8]  |  (6)  #       |  [9]  |  [4]  #       |   5   |   5   #     
# 7     |       |       # 7     |       |       #       |       |       #     
#-------+-------+-------#-------+-------+-------#-------+-------+-------#     


Set {1 3 5} can't be hidden in cols 1, 8, and 9 because there's a 1 in col. 7, as ravel points out. The rule is there can't be any of the set in other cells.

Fanya
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Last edited by fanya on Fri Mar 11, 2011 11:57 am; edited 1 time in total
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Marty R.



Joined: 12 Feb 2006
Posts: 5165
Location: Rochester, NY, USA

PostPosted: Wed Jul 26, 2006 11:06 pm    Post subject: Reply with quote

Just to throw my 2 in, I used the X-Wing on "4" and an XY-Wing on "478", which was located in the upper left. Whether the latter was needed, I don't know, since I saw it and used it, following my usual practice of taking the path of least resistance to the solution.

I thought the puzzle allowed too many cells to be solved too easily and early.
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David Bryant



Joined: 29 Jul 2005
Posts: 559
Location: Denver, Colorado

PostPosted: Thu Jul 27, 2006 12:03 am    Post subject: XY-Wing not necessary Reply with quote

CT Yankee wrote:
I'm pretty sure that the X-Wing (on 4s) is the best way to go, but I'm much less certain about the necessity of the XY-Wing, about which I don't remember the details ...

I did spot an XY-Wing in this puzzle, right after using the "X-Wing" in rows 2 and 9 to set r8c5 = 5. It looked like this.

r8c2 {3, 4}
r6c2 {3, 7}
r9c3 {4, 7}
r6c3 {1, 5, 7}

The "7" at r6c3 can be eliminated. But this step is really not needed to solve the puzzle -- after finding the X-Wing and clearing the "7" from r9c5 (so that one can set r1c5 = 7) the rest is singles all the way.

Clement wrote:
In r4 there is a hidden triple {1,3,5,}c1, {1,3,5,}c8 and {5,3}c9.


I can't find this triplet, either. The complication is that I see a "7" as a possibility at r4c1 (ruling out a "naked triplet") and a "1" as a possibility at r4c7 (ruling out a "hidden triplet", also). Oh -- the {1, 3, 5} at r4c8 can be shortened to {1, 3} because the "5" in column 8 must lie in box 3. But by the time I could eliminate the "7" from r4c1, or the "1" from r4c7, there really wasn't any need for a triplet, because the X-Wing had blown the puzzle wide open anyway. dcb
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