## need help with this puzzle

Advanced methods and approaches for solving Sudoku puzzles

### need help with this puzzle

hello. not that new to sudoku, but need help with this tough puzzle.

xx7 195 382
xx3 xxx xxx
x8x x4x xxx

2xx xxx xx3
xx6 x3x 8xx
xxx xxx xx9

xxx x6x x4x
xxx xxx 7xx
514 972 638

please let me know if it is possible without using guesswork.
vibes1234

Posts: 7
Joined: 12 September 2005

Hi vibes,

I think it is really necessary to have some guess works for this case.
No direct answer can be obtained.
Several trials have been done before the case has been solved.

To follow the rule, I just send you two numbers.
Believe me, these two numbers are the most important ones.

x47 195 382
xx3 xxx xxx
x8x x4x xxx

2xx xxx xx3
xx6 x3x 8xx
xxx xxx xx9

xxx x6x x41
xxx xxx 7xx
514 972 638

Uncle Wong.
uncle_wong_hk

Posts: 8
Joined: 12 September 2005

hello uncle wong,
could u tell me the logic used to obtain those 2 numbers ? i would really appreciate it. thanx. i sincerely believe that it may be possible to crack this sudoku without resulting in guesswork. its just that i am not an expert, therefore am not acquainted with the advanced techniques.
vibes1234

Posts: 7
Joined: 12 September 2005

Hi vibe,

Here is a workable method for your reference.

1. List out the possible numbers for each empty cell.
(46)(46)7195382
(1469)(24569)3(2678)(28)(678)(1459)(15679)(14567)
(169)8(1259)(2367)4(367)(159)(15679)(1567)
2(4579)(1589)(45678)(158)(146789)(145)(1567)3
(1479)(4579)6(2457)3(1479)8(1257)(1457)
(13478)(3457)(158)(245678)(1258)(14678)(1245)(12567)9
(3789)(2379)(289)(358)6(138)(1259)4(15)
(3689)(2369)(289)(3458)(158)(1348)7(1259)(15)
514972638

2. See if there are any empty cell that get only one possible number.
3. If the answer is yes, fill the cell with this number.
4. If the answer is no (for this case, the answer is no),
try to fill in a empty cell with a possible number (by guess, but still need to be inside the scope of the possibel numbers in the above list).
Select the empty cell that when you fill in the number,
many other empty cells will be effected.
That are the two numbers that I suggested.
5. List out the possible numbers for each empty cell again.
6. Repeat the above steps again and again.
If you get the right answer, that is fine.
But if you cannot get the right answer, that means the guess work
in step 4 is wrong. You have to redo the works starting at this point.

It is in fact not exactly a guess work.
You have to try out each possible numbers one by one.
When you reach the dead end, you have to try the next one until you solve the case.

BTW, there may be more than one answer sometimes.

I just gave this method out to another subject. Hope that it will help.
uncle_wong_hk

Posts: 8
Joined: 12 September 2005

hi uncle wong,
this is best that i could eliminate. after that i was stuck and then needed help. even i could have solved this su do ku with trial and error of course, however i was just wondering if it was possible to do it with pure logic and nothing else. however i do appreciate all the help you have given me. thanx a lot.

(46)(46)7195382
(19)(25)3(2678)(28)(678)(1459)(15679)(467)
(19)8(25)(2367)4(367)(159)(15679)(67)
2(4579)(1589)(45678)(158)(146789)(145)(1567)3
(47)(59)6(25)3(19)8(125)(47)
(3478)(3457)(158)(245678)(1258)(14678)(1245)(12567)9
(378)(2379)(289)(358)6(138)(29)4(15)
(368)(2369)(289)(3458)(158)(1348)7(29)(15)
514972638
vibes1234

Posts: 7
Joined: 12 September 2005

Hi vibes,

You have reachded the step 4.
I suggest you try to fill in the empty cells with the two numbers that I suggested and go ahead for step 5.

Sometimes, it is not so easy to deduce the number of each cell directly by a formula or else.
I wonder whether there is this formula.

See whether it work.
uncle_wong_hk

Posts: 8
Joined: 12 September 2005

I just solved this.

There is no logical way to solve this one, but you can narrow your guess down to exclusive pairs of numbers. My test cases ran through three generations of assumptions.

Further, this is not a true sudoku as I ended up with *two* solutions (there might be more)
Guest

Posts: 312
Joined: 25 November 2005

One solution...

6 4 7 1 9 5 3 8 2
9 2 3 6 8 7 5 1 4
1 8 5 2 4 3 9 7 6
2 7 8 4 6 9 1 5 3
4 9 6 5 3 1 8 2 7
3 5 1 7 2 8 4 6 9
7 3 9 8 1 6 2 4 5
8 6 2 3 5 4 7 9 1
5 1 4 9 7 2 6 3 8
Guest

Posts: 312
Joined: 25 November 2005

The puzzle is valid. There is only one solution, but not what SuperG posted. It is:

Code: Select all
` *-----------* |647|195|382| |953|826|174| |182|347|596| |---+---+---| |275|689|413| |496|231|857| |831|754|269| |---+---+---| |728|563|941| |369|418|725| |514|972|638| *-----------*`
tso

Posts: 798
Joined: 22 June 2005

Oops!

I misplaced one of the numbers in my original set up.
Guest

Posts: 312
Joined: 25 November 2005

no harm done superg. i liked ur solution for the simple reason that it just goes to show that just one number here and there can do wonders to alter the solution. anyway thanx a lot for the efforts. so tso are u also of the opinion that this puzzle cannot be solved without resolving to trial and error ???
vibes1234

Posts: 7
Joined: 12 September 2005

Well, I re-did it (correctly!).

I had to go through 3 levels of assumption, but I managed to guess correctly on 2 of them so it solved nicely.
Guest

Posts: 312
Joined: 25 November 2005