I cannot solve this Hard puzzle logically - help!

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I cannot solve this Hard puzzle logically - help!

Postby paulcoz » Wed Oct 18, 2006 7:56 am

Difficulty: Hard

Code: Select all
6 . . | 7 . . | 1 2 4
1 2 7 | 6 . 4 | 9 . .
. . 5 | . 2 . | 6 . 7
------+-------+------
8 6 1 | . . . | 4 . 9
2 7 9 | . 4 6 | 3 1 .
3 5 4 | . . . | 2 . 6
------+-------+------
. . . | . 1 . | 7 6 3
5 1 6 | 4 7 3 | 8 9 2
7 . . | . 6 9 | 5 4 1


This is a partly completed puzzle, but I've double-checked my numbers numerous times.

I can figure out many hard puzzles without a candidate list, the others with such a list. This one is not playing fair!:) I can complete it by trial and error, but would like to know how to do it with logic and eliminations.

When you solve it, please tell me which techniques are used.

Thanks,
Paul.
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Postby Carcul » Wed Oct 18, 2006 8:07 am

Paulcoz wrote:I can complete it by trial and error, but would like to know how to do it with logic and eliminations.


You don't need trial and error: the naked triple in column 4 is enough to complete the puzzle. Pencilmarks would make things easier, but its also quite easy to spot it without them.

Carcul
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Postby paulcoz » Wed Oct 18, 2006 8:23 am

You mean 139 in column 4?

I'll look into it, thankyou!!!

Paul.
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Postby Pat » Wed Oct 18, 2006 8:39 am

paulcoz wrote:You mean 139 in column 4?

well, yes, { 1,3,9 } would be a "hidden" trio in c4
- but having seen that,
surely you noticed the "hidden" duo { 1,9 } in that column? giving a "hidden single"
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Postby paulcoz » Wed Oct 18, 2006 9:04 am

THANKYOU (both)!!!

I couldn't see the naked triple (139) prior to Carcul's hint.

139 cannot go in either of the two bottom squares in c4, and also cannot go in r5(c4). That results in a placement (3) in a square where 1 and 9 are already ruled out - r4(c4). The puzzle can easily be completed from there.

Thanks again (I was looking at this one for ages),
Paul.
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Postby Carcul » Wed Oct 18, 2006 9:21 am

Paulcoz wrote:You mean 139 in column 4?


Actually I was referring to the naked triple 2,5,8 on cells r579c4, but the result is the same.
Could you provide us the initial grid? Thanks.

Carcul
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Postby paulcoz » Fri Oct 20, 2006 8:11 am

Hi Carcul,

Here is the original (Hard, Pappocom) puzzle:

Code: Select all
6 . . | 7 . . | . . 4
. 2 . | 6 . 4 | 9 . .
. . 5 | . 2 . | . . .
------+-------+------
8 . . | . . . | 4 . .
. 7 9 | . . . | 3 1 .
. . 4 | . . . | . . 6
------+-------+------
. . . | . 1 . | 7 . .
. . 6 | 4 . 3 | . 9 .
7 . . | . . 9 | . . 1


Regards,
Paul.
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Postby Carcul » Fri Oct 20, 2006 8:35 am

Ok Paulcoz, thanks.

Regards, Carcul
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