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December 2nd - Hard

 
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alanr555



Joined: 01 Aug 2005
Posts: 194
Location: Bideford Devon EX39

PostPosted: Fri Dec 02, 2005 12:56 am    Post subject: December 2nd - Hard Reply with quote

Code:

One never can tell with the gradings!

This one (rated Hard) was a relative doddle using Mandatory Pairs.
Quite a lot of 'Mutual Reception' cases arose and these assisted
greatly with the "Counting" of rows, columns and regions.

My solution started (as always) with a number of straightforward
allocations, then inspection by digit (1-9 in turn looking at all the
nuances of row, column and region interaction). At that point, I
usually have a look at what 'counting' can reveal. In this case
it revealed a lot and much progress was made - so much that
there was no need even to compile the 'Missing' profiles.

Solution time was less than half an hour.
Nov 29 was also rated 'Hard' - but what a difference!

Again, this one would have potential for anyone wishing to explore
the application of Mandatory Pairs as a technique.

Alan Rayner  BS23 2QT
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smith55js



Joined: 29 Nov 2005
Posts: 9
Location: Logan, UT

PostPosted: Fri Dec 02, 2005 1:01 am    Post subject: My solution... Reply with quote

1.1g8
2.2i3
3.7g5
4.7i2
5.7c1
6.7e3
7.7d8
8.2b1
9.8i7
10.9g2
4 in row 2 must be in box 1 eliminating 4's from rest of row 2
11.4f3
12.3g9
4 in column 8 must be in box 9 eliminating 4's from rest of column 9
13.3c7
5 in row 1 must be in box 3 eliminating 5's from rest of row 1
14.8d1
15.8g3
16.6a3
17.4b2
18.5a7
19.6b9
20.4d7
21.6e7
22.5e2
23.6f2
24.2e8
25.5f9
26.3e5
27.5b5
28.3b6
29.9d5
30.5d6
31.9a8
32.4c8
33.2c9
34.4h9
35.2a4
36.8f4
37.2f5
38.3i4
39.6i6
40.8h5
41.6c5
42.4g6
43.1e6
44.8a6
45.1a2
46.8c2
47.9c6
48.1c4
49.4e4
50.5g4
51.6g1
52.5h1
53.9h4
54.6h8
55.5i8

327 891 654
148 256 937
695 374 812

271 648 593
456 932 781
839 517 426

513 469 278
984 723 165
762 185 349


Again, this puzzle leads me to question the soundness of the algorithm that is calculating difficulty. This one had 3 steps that required more than just seeing that a number had only one possible location in a row/column/group. As it only had one type of 'advanced' (kind of) technique required, I would have to say this is a 'medium' puzzle. But that's just my opinion.

Does anyone have a list of techniques used in solving Sudoku's? Are there standard terms used to define them?
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David Bryant



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

PostPosted: Fri Dec 02, 2005 1:25 am    Post subject: Sudoku techniques Reply with quote

Jake Smith wrote:
Does anyone have a list of techniques used in solving Sudoku's? Are there standard terms used to define them?

You can find a good introduction to Sudoku techniques at the SadMan Software site.

Terminology is not completely standardized, but terms like "X-Wing," "XY-Wing," and "Swordfish" are widely recognized. One of the users on this site, someone_somewhere, has recently cooked up a new technique that he calls a "Constellation" -- you can read about that here and also over here. dcb
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zaks



Joined: 25 Nov 2005
Posts: 13

PostPosted: Fri Dec 02, 2005 8:53 am    Post subject: Re: My solution... Reply with quote

My version of solution actually requires no guess at all:

02 Dec (h) sdk soln

initial position (26):

3a9 9e9 1f9 4i9 2d8 3h8
9b7 5c7 3d7 1h7
7b6 6d6 4a5 1i5
7f4 2h4
1b3 9f3 2g3 7h3
8b2 3f2 7a1 1d1 8e1 9i1

we begin with evident moves:
01 1g2 02 2i7 03 7g5 04 7i8
05 7c9 06 7e7 07 7d2 08 8i3
09 9g7 10 2b9 11 3g1 12 3c3 (so much so good...)

now remove 4 as candidate from cells e8,f8, and h6
13 -4e8 14 -4f8 15-4h6

16 4f8 (hidden single at row 7)
17 8d9 (hidden single at row 9)

due to matched pair e8,g8=>5,6 we remove 6 from cells a8,b8,c8
18 -6a8 19 -6b8 20 -6c8

which triggers the sequence of moves:

21 4b8 22 6a7 23 8g7 24 5a3 25 6b1
26 4d3 27 6e3 28 5e8 29 2e2 30 5f1
31 9a2 32 4c2 33 2c1 34 4h1 35 3e5
36 5b5 37 3b4 38 9d5 39 5d4 40 6i4
41 5i2 42 6h2 43 4g4 44 1e4 45 8a4
46 9c4 47 6c5 48 8h5 49 2f5 50 5g6
51 9h6 52 3i6 53 8f6 54 4e6 55 1c6 56 2a6
57 1a8 58 8c8 59 6f8 60 6g9 61 5h9 x!

Note that we introduce new kind of move: removing some number as candidate from some cell, hence a total number of moves is larger than
81 - number of givens (=81-26=55 in this case).

enjoy, zaks

PS or i'm missing smth or this sdk isn't "hard",
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someone_somewhere



Joined: 07 Aug 2005
Posts: 275
Location: Munich

PostPosted: Fri Dec 02, 2005 1:41 pm    Post subject: Reply with quote

Hi,

The above mentioned Sudoku puzzle could be solved by using the following techniques:
Sole Candidate in Cell= 42 times
Unique digit in Line= 7 times
in Column= 5 times
in 3x3 Block= 1 time

and in addition I had to use the:
Row on 3x3 Block interaction= 3 times

I still prefer the "old" notation of r.c. (Row and Column). And here is
my solution, that is using the above mentioned techniques:

Code:
 9 in r2c7  7 in r5c7  8 in r7c9  1 in r8c7  - Unique Horizontal
 3 in r7c3  3 in r9c7  - Unique Horizontal
 2 in r3c9  - Unique Vertical
 7 in r2c9  - Unique Vertical
 7 in r1c3  7 in r8c4  7 in r3c5  - Unique Vertical
 2 in r1c2  - Unique in 3x3 block
 4 in r3c6  - Unique Horizontal
 6 not in r3c7, it is in r1c7 or r1c8 (Row on 3x3 Block interaction)
 5 not in r1c4, it is in r2c5 or r2c6 (Row on 3x3 Block interaction)
 4 not in r8c5, it is in r7c4 or r7c5 (Row on 3x3 Block interaction)
 8 in r1c4  8 in r3c7  - Sole Candidate
 6 in r3c1  - Sole Candidate
 4 in r2c2  5 in r7c1  - Sole Candidate
 4 in r7c4  6 in r9c2  - Sole Candidate
 6 in r7c5  - Sole Candidate
 5 in r2c5  - Sole Candidate
 6 in r2c6  2 in r8c5  - Sole Candidate
 3 in r5c5  9 in r8c1  5 in r9c6  - Sole Candidate
 5 in r5c2  4 in r8c3  4 in r9c8  - Sole Candidate
 9 in r5c4  3 in r6c2  2 in r9c3  - Sole Candidate
 5 in r6c4  - Sole Candidate
 6 in r6c9  - Sole Candidate
 8 in r5c8  4 in r6c7  5 in r8c9  - Sole Candidate
 5 in r4c7  3 in r4c9  6 in r5c3  2 in r5c6  1 in r6c5  6 in r8c8  - Sole Candidate
 6 in r1c7  5 in r1c8  4 in r4c5  8 in r4c6  9 in r4c8  8 in r6c1  - Sole Candidate
 1 in r2c1  1 in r4c3  9 in r6c3  - Sole Candidate
 8 in r2c3  2 in r4c1  - Sole Candidate


see u,
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