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bullsfan23 Guest

Posted: Thu Sep 08, 2005 3:42 pm Post subject: Logic behind hint 


This was the puzzle below, where I was stuck:
4 _ _ _ _ _ 9 1 _
_ 8 _ 4 _ _ 7 3 _
3 _ 6 7 _ _ _ _ 4
_ _ _ _ _ 7 6 _ _
_ 5 _ _ _ _ 3 2 _
_ _ 3 5 _ _ _ _ _
9 _ _ _ _ 8 2 _ 3
8 3 2 _ _ 6 _ 7 _
_ 1 4 _ _ _ _ _ 8
Now I had a lot of possibilities, but I couldn't rule anything completely out, or in. I went to the hint finder, and it revealed a 1 in row 7, column 4.
4 _ _ _ _ _ 9 1 _
_ 8 _ 4 _ _ 7 3 _
3 _ 6 7 _ _ _ _ 4
_ _ _ _ _ 7 6 _ _
_ 5 _ _ _ _ 3 2 _
_ _ 3 5 _ _ _ _ _
9 _ _ 1 _ 8 2 _ 3
8 3 2 _ _ 6 _ 7 _
_ 1 4 _ _ _ _ _ 8
My question is qhat logic was used to reveal the 1 there in row 7, column 4? I had concluded that the 1 had to be in either column 4 or column 5 of row 7, but I can't figure out how it knew to rule out column 5, or conclude that the 1 should go in column 4.
Thanks for your help in advance. 

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chobans
Joined: 21 Aug 2005 Posts: 39

Posted: Thu Sep 08, 2005 3:58 pm Post subject: 


1 CAN go in column 5. But 1 is the ONLY number that can go in r7c4. The other 8 numbers are ruled out because they are in the same row, column or box (r7c4r9c6). 

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bullsfan23 Guest

Posted: Thu Sep 08, 2005 4:37 pm Post subject: 


thanks! 

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alanr555
Joined: 01 Aug 2005 Posts: 198 Location: Bideford Devon EX39

Posted: Thu Sep 08, 2005 8:07 pm Post subject: 


If one really wants to know the answers to "why?", it is possible to use
the Solution by Steps facility. This has a full explanation of every move
made in sequence and produces an audit trail (which can be copied to
a text editor using CtrlA and CtrlC in the usual way).
As yet these amazingly helpful annotations are not included in the hint
facility (or so I believe as I have never used the hint facility) BUT their
presence in the Stepsolver should be adequate for those wishing to
extend their own prowess by observing how solutions develop.
When I get stuck, I use the stepsolver in order to check that my solution
grid is correct. Usually, I find that I have overlooked something! However,
sometimes I find that the solver gets stuck at the same place as myself
and then I search these fora for clues as to advanced techniques.
Perhaps the hint facility should NOT have a reason as then it can prompt
the user into thinking more deeply about possible reasons! Only if this
process fails would recourse to the stepsolver then be necessary!
Alan Rayner BS23 2QT 

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Guest

Posted: Thu Sep 08, 2005 8:18 pm Post subject: 


Look at the entire row and column plus the 3 by 3 spquare which has a 6. The only number pssible is 1. 

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Guest

Posted: Wed Sep 21, 2005 1:22 am Post subject: Where is "solutions by steps?" 


Where do I find this "solutions by steps" that was mentioned as a help in understanding the logic behind what is given as the next hint? Couldn't see it anywhere in the "dailysudoku.com" site. Thanks. 

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alanr555
Joined: 01 Aug 2005 Posts: 198 Location: Bideford Devon EX39

Posted: Thu Sep 22, 2005 12:58 am Post subject: Re: Where is "solutions by steps?" 


> Where do I find this "solutions by steps" that was mentioned as a help
> in understanding the logic behind what is given as the next hint?
I have it set up as one of my "Favourites".
This shews the URL as being www.sudokusolver.co.uk/step.html
As indicated in this site, there is no real point in solvers as solvers (other
than as an exercise for programmers!!). However, the solver by steps is
a great aid to understanding. It creates a text file indicating what has been
done at each step of the solution process.
On difficulty with it is that it can take ages to start solving as it takes one
step for each initial value (ie the puzzle has a given digit in a given cell
and the solver takes a step to change the solution for that cell from the
start value of 123456789 to the single digit given. Worse than that, it
sometimes applies logic before it has set the initial values.
However, it is excellent at identifying "stop" points as (like the Hints on
this site) it does not include all the "advanced" facilities that can be
spotted by humans but which are difficult to program. A "trial and error"
facility is included for use when a stoppoint is found. I prefer to avoid
the sites that use trial and error but the Solver can be asked to prove a
UNIQUE solution. With that confirmation, the challenge is then to find
a technique to reach it WITHOUT trial and error!
Elsewhere on the site are comments about six identified techniques (of
which five are programmed and one is out as a challenge to any budding programmers).
Thus I regard it as an admirable complement to this site.
Alan Rayner BS23 2QT 

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alanr555
Joined: 01 Aug 2005 Posts: 198 Location: Bideford Devon EX39

Posted: Thu Sep 22, 2005 1:06 am Post subject: 


This is an example of the generated notes. A challenge could be to
derive the original puzzle from them! Unfortunately the limited space
for posting on this site distorts the grid layouts included  but it should
be possible to get the idea.
Notes:
==============================
Running Start Grid
Set cell [A2] to 3: Removing 3 from related row, column & block (80 to go!)
Set cell [A6] to 1: Removing 1 from related row, column & block (79 to go!)
Set cell [B3] to 6: Removing 6 from related row, column & block (78 to go!)
Set cell [B8] to 5: Removing 5 from related row, column & block (77 to go!)
Set cell [C1] to 5: Removing 5 from related row, column & block (76 to go!)
Set cell [C7] to 9: Removing 9 from related row, column & block (75 to go!)
Set cell [C8] to 8: Removing 8 from related row, column & block (74 to go!)
Set cell [C9] to 3: Removing 3 from related row, column & block (73 to go!)
Set cell [D2] to 8: Removing 8 from related row, column & block (72 to go!)
Set cell [D6] to 6: Removing 6 from related row, column & block (71 to go!)
Set cell [D7] to 3: Removing 3 from related row, column & block (70 to go!)
Set cell [D9] to 2: Removing 2 from related row, column & block (69 to go!)
Set cell [E5] to 5: Removing 5 from related row, column & block (68 to go!)
Set cell [F1] to 9: Removing 9 from related row, column & block (67 to go!)
Set cell [F3] to 3: Removing 3 from related row, column & block (66 to go!)
Set cell [F4] to 8: Removing 8 from related row, column & block (65 to go!)
Set cell [F8] to 6: Removing 6 from related row, column & block (64 to go!)
Set cell [G1] to 7: Removing 7 from related row, column & block (63 to go!)
Set cell [G2] to 1: Removing 1 from related row, column & block (62 to go!)
Set cell [G3] to 4: Removing 4 from related row, column & block (61 to go!)
Set cell [G9] to 9: Removing 9 from related row, column & block (60 to go!)
Set cell [H2] to 2: Removing 2 from related row, column & block (59 to go!)
Set cell [H7] to 8: Removing 8 from related row, column & block (58 to go!)
Set cell [I4] to 4: Removing 4 from related row, column & block (57 to go!)
Set cell [I8] to 3: Removing 3 from related row, column & block (56 to go!)
Removing 3 from [G8] just leaves [G8] as 2
Set cell [G8] to 2: Removing 2 from related row, column & block (55 to go!)
==============================
Starting Solve Method A
 1 2 3 4 5 6 7 8 9 +A  248 3 2789 25679 246789 1 2467 47 467 B  1248 479 6 2379 234789 234789 1247 5 147 C  5 47 127 267 2467 247 9 8 3 D  14 8 157 179 1479 6 3 1479 2 E  1246 467 127 12379 5 23479 147 1479 1478 F  9 457 3 8 1247 247 1457 6 1457 G  7 1 4 356 368 358 56 2 9 H  36 2 59 135679 13679 3579 8 147 14567 I  68 569 589 4 126789 25789 1567 3 1567
Grid row C only contains one 1 at column 3..
Set cell [C3] to 1: Removing 1 from related row, column & block (54 to go!)
Grid column 1 only contains one 3 at row H..
Set cell [H1] to 3: Removing 3 from related row, column & block (53 to go!)
Grid row A only contains one 5 at column 4..
Set cell [A4] to 5: Removing 5 from related row, column & block (52 to go!)
Grid row D only contains one 5 at column 3..
Set cell [D3] to 5: Removing 5 from related row, column & block (51 to go!)
Removing 5 from [H3] just leaves [H3] as 9
Set cell [H3] to 9: Removing 9 from related row, column & block (50 to go!)
Removing 5 from [I3] just leaves [I3] as 8
Set cell [I3] to 8: Removing 8 from related row, column & block (49 to go!)
Removing 8 from [I1] just leaves [I1] as 6
Set cell [I1] to 6: Removing 6 from related row, column & block (48 to go!)
Removing 6 from [I2] just leaves [I2] as 5
Set cell [I2] to 5: Removing 5 from related row, column & block (47 to go!)
Grid column 2 only contains one 6 at row E..
Set cell [E2] to 6: Removing 6 from related row, column & block (46 to go!)
Grid column 9 only contains one 8 at row E..
Set cell [E9] to 8: Removing 8 from related row, column & block (45 to go!)
Grid column 2 only contains one 9 at row B..
Set cell [B2] to 9: Removing 9 from related row, column & block (44 to go!)
Grid row A only contains one 9 at column 5..
Set cell [A5] to 9: Removing 9 from related row, column & block (43 to go!)
Grid row I only contains one 9 at column 6..
Set cell [I6] to 9: Removing 9 from related row, column & block (42 to go!)
Grid row I only contains one 2 at column 5..
Set cell [I5] to 2: Removing 2 from related row, column & block (41 to go!)
Grid row A only contains one 8 at column 1..
Set cell [A1] to 8: Removing 8 from related row, column & block (40 to go!)
Grid row F only contains one 2 at column 6..
Set cell [F6] to 2: Removing 2 from related row, column & block (39 to go!)
Grid row C only contains one 2 at column 4..
Set cell [C4] to 2: Removing 2 from related row, column & block (38 to go!)
Grid row C only contains one 6 at column 5..
Set cell [C5] to 6: Removing 6 from related row, column & block (37 to go!)
Ending Solve Method A
==============================
==============================
Starting Solve Method B
 1 2 3 4 5 6 7 8 9 +A  8 3 27 5 9 1 2467 47 467 B  24 9 6 37 3478 3478 1247 5 147 C  5 47 1 2 6 47 9 8 3 D  14 8 5 179 147 6 3 1479 2 E  124 6 27 1379 5 347 147 1479 8 F  9 47 3 8 147 2 1457 6 1457 G  7 1 4 36 38 358 56 2 9 H  3 2 9 167 17 57 8 147 14567 I  6 5 8 4 2 9 17 3 17
The value 4 in block [A7] must lie in row A
The value 1 in block [G7] must lie in row I
The value 7 in block [G7] must lie in row I
Removing 7 from [H8] just leaves [H8] as 4
Set cell [H8] to 4: Removing 4 from related row, column & block (36 to go!)
Removing 4 from [A8] just leaves [A8] as 7
Set cell [A8] to 7: Removing 7 from related row, column & block (35 to go!)
Removing 7 from [A3] just leaves [A3] as 2
Set cell [A3] to 2: Removing 2 from related row, column & block (34 to go!)
Removing 2 from [E3] just leaves [E3] as 7
Set cell [E3] to 7: Removing 7 from related row, column & block (33 to go!)
Removing 7 from [F2] just leaves [F2] as 4
Set cell [F2] to 4: Removing 4 from related row, column & block (32 to go!)
Removing 4 from [C2] just leaves [C2] as 7
Set cell [C2] to 7: Removing 7 from related row, column & block (31 to go!)
Removing 7 from [C6] just leaves [C6] as 4
Set cell [C6] to 4: Removing 4 from related row, column & block (30 to go!)
Removing 4 from [E6] just leaves [E6] as 3
Set cell [E6] to 3: Removing 3 from related row, column & block (29 to go!)
Removing 4 from [D1] just leaves [D1] as 1
Set cell [D1] to 1: Removing 1 from related row, column & block (28 to go!)
Removing 4 from [E1] just leaves [E1] as 2
Set cell [E1] to 2: Removing 2 from related row, column & block (27 to go!)
Removing 2 from [B1] just leaves [B1] as 4
Set cell [B1] to 4: Removing 4 from related row, column & block (26 to go!)
Removing 7 from [B9] just leaves [B9] as 1
Set cell [B9] to 1: Removing 1 from related row, column & block (25 to go!)
Removing 1 from [B7] just leaves [B7] as 2
Set cell [B7] to 2: Removing 2 from related row, column & block (24 to go!)
Removing 1 from [I9] just leaves [I9] as 7
Set cell [I9] to 7: Removing 7 from related row, column & block (23 to go!)
Removing 7 from [I7] just leaves [I7] as 1
Set cell [I7] to 1: Removing 1 from related row, column & block (22 to go!)
Removing 1 from [E7] just leaves [E7] as 4
Set cell [E7] to 4: Removing 4 from related row, column & block (21 to go!)
Removing 4 from [A7] just leaves [A7] as 6
Set cell [A7] to 6: Removing 6 from related row, column & block (20 to go!)
Removing 6 from [A9] just leaves [A9] as 4
Set cell [A9] to 4: Removing 4 from related row, column & block (19 to go!)
Removing 6 from [G7] just leaves [G7] as 5
Set cell [G7] to 5: Removing 5 from related row, column & block (18 to go!)
Removing 5 from [G6] just leaves [G6] as 8
Set cell [G6] to 8: Removing 8 from related row, column & block (17 to go!)
Removing 8 from [G5] just leaves [G5] as 3
Set cell [G5] to 3: Removing 3 from related row, column & block (16 to go!)
Removing 3 from [G4] just leaves [G4] as 6
Set cell [G4] to 6: Removing 6 from related row, column & block (15 to go!)
Removing 8 from [B6] just leaves [B6] as 7
Set cell [B6] to 7: Removing 7 from related row, column & block (14 to go!)
Removing 7 from [B4] just leaves [B4] as 3
Set cell [B4] to 3: Removing 3 from related row, column & block (13 to go!)
Removing 7 from [B5] just leaves [B5] as 8
Set cell [B5] to 8: Removing 8 from related row, column & block (12 to go!)
Removing 7 from [H6] just leaves [H6] as 5
Set cell [H6] to 5: Removing 5 from related row, column & block (11 to go!)
Removing 4 from [D8] just leaves [D8] as 9
Set cell [D8] to 9: Removing 9 from related row, column & block (10 to go!)
Removing 9 from [D4] just leaves [D4] as 7
Set cell [D4] to 7: Removing 7 from related row, column & block (9 to go!)
Removing 7 from [D5] just leaves [D5] as 4
Set cell [D5] to 4: Removing 4 from related row, column & block (8 to go!)
Removing 7 from [H4] just leaves [H4] as 1
Set cell [H4] to 1: Removing 1 from related row, column & block (7 to go!)
Removing 1 from [H5] just leaves [H5] as 7
Set cell [H5] to 7: Removing 7 from related row, column & block (6 to go!)
Removing 7 from [H9] just leaves [H9] as 6
Set cell [H9] to 6: Removing 6 from related row, column & block (5 to go!)
Removing 7 from [F5] just leaves [F5] as 1
Set cell [F5] to 1: Removing 1 from related row, column & block (4 to go!)
Removing 1 from [F7] just leaves [F7] as 7
Set cell [F7] to 7: Removing 7 from related row, column & block (3 to go!)
Removing 7 from [F9] just leaves [F9] as 5
Set cell [F9] to 5: Removing 5 from related row, column & block (2 to go!)
Removing 1 from [E4] just leaves [E4] as 9
Set cell [E4] to 9: Removing 9 from related row, column & block (1 to go!)
Removing 9 from [E8] just leaves [E8] as 1
Set cell [E8] to 1: Removing 1 from related row, column & block (0 to go!)
Checking the grid below to see if it is valid..
 1 2 3 4 5 6 7 8 9 +A  8 3 2 5 9 1 6 7 4 B  4 9 6 3 8 7 2 5 1 C  5 7 1 2 6 4 9 8 3 D  1 8 5 7 4 6 3 9 2 E  2 6 7 9 5 3 4 1 8 F  9 4 3 8 1 2 7 6 5 G  7 1 4 6 3 8 5 2 9 H  3 2 9 1 7 5 8 4 6 I  6 5 8 4 2 9 1 3 7
A valid solution!
Difficulty score: 138
Number of guesses required: 0
Ending Solve Method B
==============================
Checking the grid to see if it is valid..
 1 2 3 4 5 6 7 8 9 +A  8 3 2 5 9 1 6 7 4 B  4 9 6 3 8 7 2 5 1 C  5 7 1 2 6 4 9 8 3 D  1 8 5 7 4 6 3 9 2 E  2 6 7 9 5 3 4 1 8 F  9 4 3 8 1 2 7 6 5 G  7 1 4 6 3 8 5 2 9 H  3 2 9 1 7 5 8 4 6 I  6 5 8 4 2 9 1 3 7
A valid solution! 

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Guest

Posted: Tue Sep 27, 2005 4:15 pm Post subject: Re: Solution by steps 


Thanks for the info. Put the web site you suggested in my favorites. Would be great if "dailysudoku.com" hint had the explanation with it, but your suggested site helps me even if it is a little unwieldly. Hard to develop my skill if I can't understand how they got the next number so an explanation is really helpful. Appreciate your help. Thanks. 

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