## Next move?

Advanced methods and approaches for solving Sudoku puzzles

### Next move?

I am looking for the next logical move. Any help very much appreciated.

2** *6* 7**
*** *** *3*
*35 8*9 ***
37* *** 49*
*** *3* ***
*86 *9* 31*
*** 214 8*3
*1* *** ***
**3 95* 1*6

2,49,1489,135,6,135,7,458,14589
146789,469,14789,157,247,1257,2569,3,124589
1467,3,5,8,247,9,26,246,124
3,7,12,156,28,12568,4,9,258
1459,2459,1249,1457,3,12578,256,25678,2578
45,8,6,457,9,257,3,1,257
5679,569,79,2,1,4,8,57,3
4578,1,2478,36,78,36,259,2457,24579
478,24,3,9,5,78,1,247,6

Thank you to all who take the time to get me moving again. Is there a program that can suggest a next move to them that's stuck?
Chris
ChrisHap

Posts: 8
Joined: 06 September 2005

So far as I can see, you can't get anywhere by logic alone. You're going to have to make a guess and see where it takes you...
Last edited by zebedeezbd on Sat Sep 17, 2005 1:58 pm, edited 2 times in total.
zebedeezbd

Posts: 60
Joined: 14 September 2005

It has only one solution.
Moschopulus

Posts: 256
Joined: 16 July 2005

Try Simple Sudoku.
You can quickly copy and paste the puzzle into the program.
Then you can press the hint button.

But! I tried this with your puzzle, and the program gave
me several hints (one at a time). I followed them,
but finally reached a state where the program had no
more hints!

So I think you've got a tough one ...
Nick67

Posts: 113
Joined: 24 August 2007

Interesting comments - thank you. A programme I have solves it, but it takes longer than most puzzles!
Could I repeat my earlier question as I would like to know whether I haven't just found the right logic or a guess has to be the next move.
That is, is there a programme out there that can tell you if a guess is the only next move?
Thanks again.
Chris
ChrisHap

Posts: 8
Joined: 06 September 2005

ChrisHap wrote:That is, is there a programme out there that can tell you if a guess is the only next move?

No. One person's guess is another's swordfish, and another's xy-wing and another's forcing chains, and another's advanced colours. It's a moving line (or at the very least a very gray one).
angusj

Posts: 306
Joined: 12 June 2005

Thanks for all the interesting comments.
This puzzle came with 21 given numbers. Since I knew the solution, I put in two more to bring the equivalent given numbers up to 23. I was then able to logically fill in more squares. But eventually I came to a halt again. I then put in two more numbers to bring the equivalent given numbers up to 25. I was then able to logically complete the whole puzzle.
From this I deduce two rules.
One, the level of difficulty of a Sudoku puzzle depends on the quantity of numbers first given.
Two, each Sudoku puzzle has its own minimum quantity of numbers first given for it to be completed by logic without any guessing.
But then you people who create Sudoku puzzles know this already!!
Chris
ChrisHap

Posts: 8
Joined: 06 September 2005

One, the level of difficulty of a Sudoku puzzle depends on the quantity of numbers first given.

Unfortunately already shown to be untrue..... this one only contains 17 clues - but is solvable without resort to any fishy techniques.

Code: Select all
`.......4.53............87.2...9............5...8..7...9.7...1......4.......53..6.`

and there are some 25's and more which are completely unbreakable by any logical technique.

stuartn
stuartn

Posts: 211
Joined: 18 June 2005

Stuartn
Oh! Um!
Another rule I deduce,
a little knowledge is a dangerous thing!
ChrisHap

Posts: 8
Joined: 06 September 2005

Require 3 chains to solve this grid as given. The first chain was hard to identify.

Chain 1: (Note: This is the only chain I could spot at this stage. Can you spot another one?)
r9c6=7 => r9c1=8 => r9c1<>7
r9c6=8 => r8c5=7 => r3c5<>7 => r3c1=7 => r9c1<>7

This reduces the grid to:

Code: Select all
`{2}      {49}     {1489}   {135}    {6}      {135}    {7}      {458}    {14589}  {146789} {469}    {14789}  {157}    {247}    {1257}   {2569}   {3}      {124589} {1467}   {3}      {5}      {8}      {247}    {9}      {26}     {246}    {124}    {3}      {7}      {12}     {156}    {28}     {12568}  {4}      {9}      {258}    {1459}   {2459}   {1249}   {1457}   {3}      {12578}  {256}    {25678}  {2578}   {45}     {8}      {6}      {457}    {9}      {257}    {3}      {1}      {257}    {5679}   {569}    {79}     {2}      {1}      {4}      {8}      {57}     {3}      {4578}   {1}      {2478}   {36}     {78}     {36}     {259}    {2457}   {24579}  {48}     {24}     {3}      {9}      {5}      {78}     {1}      {247}    {6}`

This chain was identified by means of a bilocation/bivalue plot. I shall post the other chains later.
Jeff

Posts: 708
Joined: 01 August 2005

Chain 2: (Note: This is the only chain I could spot at this stage. Can you spot another one?)
r9c6=7 => r9c8<>7
r9c6=8 => r9c1=4 => r6c1=5 => r5c2<>5 => r7c2=5 => r7c8<>5 => r7c8=7 => r9c8<>7

With further basic deduction including a naked quad and 3 xy-wings, the grid reduced to:
(Note: suggest to use Angus' program as it identifies these xy-wings.)

Code: Select all
`{2}    {49}   {89}   {15}   {6}    {3}    {7}    {58}   {148}  {167}  {46}   {78}   {15}   {47}   {2}    {59}   {3}    {1489} {17}   {3}    {5}    {8}    {47}   {9}    {2}    {6}    {14}   {3}    {7}    {1}    {6}    {2}    {8}    {4}    {9}    {5}    {9}    {5}    {2}    {4}    {3}    {1}    {6}    {78}   {78}   {4}    {8}    {6}    {7}    {9}    {5}    {3}    {1}    {2}    {567}  {69}   {79}   {2}    {1}    {4}    {8}    {57}   {3}    {57}   {1}    {4}    {3}    {8}    {6}    {59}   {2}    {79}   {8}    {2}    {3}    {9}    {5}    {7}    {1}    {4}    {6}`

Chain 3: (Note: Quite a few chains can be spotted at this stage, but this one completes the grid.)
r2c5=4 => r2c2<>4
r2c5=7 => r3c5=4 => r3c1=7 => r2c1=1 => r2c2=6 => r2c2<>4

Please post the original grid with 21 numbers. I doubt that it still can be solved by double implication chains.
Jeff

Posts: 708
Joined: 01 August 2005

Jeff,
Thanks for all your work. As requested, the original puzzle.

2.. .6. 7..
... ... .3.
..5 8.9 ...
.7. ... 49.
... .3. ...
.86 ... .1.
... 2.4 8..
.1. ... ...
..3 .5. ..6

Chris
ChrisHap

Posts: 8
Joined: 06 September 2005