The New Sudoku Players' Forum

[CathyW]

I think it's no. 41 if I've counted down the list correctly!

Original puzzle is:

Code: Select all

 *-----------*
 |4.3|5..|.2.|
 |...|.16|...|
 |7..|...|...|
 |---+---+---|
 |...|.89|5..|
 |...|3..|8..|
 |2..|...|...|
 |---+---+---|
 |...|4..|.7.|
 |.9.|...|6..|
 |.1.|...|...|
 *-----------*


{4}       {68}      {3}       {5}       {79}      {78}      {179}     {2}       {16789}   
{589}     {258}     {2589}    {2789}    {1}       {6}       {3479}    {34589}   {345789} 
{7}       {2568}    {125689}  {289}     {2349}    {2348}    {1349}    {1345689} {1345689}
{136}     {3467}    {1467}    {1267}    {8}       {9}       {5}       {1346}    {123467} 
{1569}    {4567}    {145679}  {3}       {24567}   {12457}   {8}       {1469}    {124679} 
{2}       {345678}  {1456789} {167}     {4567}    {1457}    {13479}   {13469}   {134679} 
{3568}    {23568}   {2568}    {4}       {23569}   {12358}   {1239}    {7}       {123589} 
{358}     {9}       {24578}   {1278}    {2357}    {123578}  {6}       {13458}   {123458} 
{3568}    {1}       {245678}  {26789}   {235679}  {23578}   {2349}    {34589}   {234589} 



I've got to here:

Code: Select all

 
 *-----------*
 |4.3|59.|.2.|
 |...|.16|...|
 |7.1|...|9..|
 |---+---+---|
 |..6|.89|5.2|
 |...|3..|8..|
 |2..|6..|...|
 |---+---+---|
 |...|4..|.79|
 |.9.|...|6..|
 |.1.|9..|2..|
 *-----------*


{4}      {68}     {3}      {5}      {9}      {78}     {17}     {2}      {16}     
{589}    {258}    {2589}   {27}     {1}      {6}      {347}    {3458}   {34578} 
{7}      {2568}   {1}      {28}     {34}     {34}     {9}      {568}    {568}   
{13}     {47}     {6}      {17}     {8}      {9}      {5}      {34}     {2}     
{159}    {457}    {59}     {3}      {2457}   {12457}  {8}      {169}    {167}   
{2}      {34578}  {589}    {6}      {457}    {1457}   {347}    {139}    {137}   
{3568}   {2358}   {258}    {4}      {356}    {1358}   {13}     {7}      {9}     
{358}    {9}      {47}     {18}     {2357}   {123578} {6}      {13458}  {13458} 
{3568}   {1}      {47}     {9}      {3567}   {3578}   {2}      {3458}   {3458}   


Any suggestions?

[bennys]

Code: Select all

+----------------------+----------------------+----------------------+
| 4      68     3      | 5      9      78     | 17     2      1678   |
| 589    258    2589   | 278    1      6      | 347    3458   34578  |
| 7      2568   1      | 28     34     34     | 9      568    568    |
+----------------------+----------------------+----------------------+
| 13     347    6      | 17     8      9      | 5      134    2      |
| 159    457    59     | 3      2457   12457  | 8      1469   1467   |
| 2      34578  589    | 6      457    1457   | 1347   1349   1347   |
+----------------------+----------------------+----------------------+
| 3568   2358   258    | 4      356    1358   | 13     7      9      |
| 358    9      47     | 178    2357   123578 | 6      13458  13458  |
| 3568   1      47     | 9      3567   3578   | 2      3458   3458   |
+----------------------+----------------------+----------------------+

Notice that you cant have both R4C1=3 and R7C7=3 (eliminate all 3 candidates from box 7)
but R7C7=3=>R7C6=1=>R4C4=1=>R4C1=3.

so we get R7C7=1.

[TKiel]

Either value of r1c7 (1,7) forces r6c7 to be 3.

Tracy

[CathyW]

Thank you Benny and Tracy for your tips. I must be having an off day because I can't follow your arguments.

Benny - please can you explain why r4c1 and r7c7 can't both be 3 at this point (but see below), and 3 has to go somewhere in box 7 so how can you exclude all 3s?
Tracy - please can you show your chain if r1c7 = 7. I can't seem to follow one that forces r6c7 to be 3

Anyway - I did make some progress on the puzzle, though still no more actual entries.

I do hope the following are genuine and not any more of my "happy coincidences"!
xy-wing: r1c7,9; r5c9 => exclude 1 from r5c9 and 6 from r3c9.
xy-chain: [r7c7] =1= [r1c7] =7= [r1c6] =8= [r3c4] =8= [r8c4] =1= [r4c4] =7= [r4c2] =4= [r4c8] -3- [r6c7] =3= [r7c7] Loop closed and can now exclude 3 from r2c7.
xy-chain: [r2c7] =7= [r1c7] =1= [r7c7] =3= [r6c7] =4= [r2c7] Loop closed and now exclude 7 from r6c7.
Naked pair in box 6.
X-wing (3s) - exclude other 3s in row 7.
xy-chain: [r5c9] =7= [r6c9] =1= [r6c8] =9= [r5c8] =9= [r5c9] Exclude 1 from r5c8.
Locked 1s box 6, exclude 1 from r6c6.
Locked 7s box 6, exclude 7 from r2c9.
xy-chain: [r8c4] =1= [r4c4] =7= [r4c2] =4= [r4c8] =3= [r6c7] =3= [r7c7] =1= [r6c6] -1- [r8c4]. Exclude 8 from r8,9c6.

Puzzle now at this point:

Code: Select all

 
{4}     {68}    {3}     {5}     {9}     {78}    {17}    {2}     {16}   
{589}   {258}   {2589}  {27}    {1}     {6}     {47}    {3458}  {3458} 
{7}     {2568}  {1}     {28}    {34}    {34}    {9}     {568}   {58}   
{13}    {47}    {6}     {17}    {8}     {9}     {5}     {34}    {2}     
{159}   {457}   {59}    {3}     {2457}  {12457} {8}     {69}    {67}   
{2}     {34578} {589}   {6}     {457}   {457}   {34}    {19}    {17}   
{568}   {2358}  {258}   {4}     {56}    {158}   {13}    {7}     {9}     
{358}   {9}     {47}    {18}    {2357}  {12357} {6}     {13458} {3458} 
{3568}  {1}     {47}    {9}     {3567}  {357}   {2}     {3458}  {3458} 


So now colouring on 3s shows that r4c1 and r7c7 can't both be 3 but I'm not sure what other eliminations that permits.

[TKiel]

CathyW,

I'm not sure that my notations are correct but here is the chain I followed:

R1c7=7=r1c6=8=r3c4=2=r2c4=7=r4c3=1=(r4c1=3)=r4c8=4

At this point we go back to the cell in parentheses:

r4c1=3=r7c2=3(because it's a single)=r7c7=1=r6c7=3

I only did this because I got the puzzle to the same spot as you and could make no further progress with my normal tactics. So I turned off the 'block invalid moves' (I use Simple Sudoku)) and started looking around for cells to were likely to lead to such a conclusion. I picked that cell (r1c7) because I could see that it would affect all of row 1, in addition to 3 and 7. I think I tried the 1 first and followed it for 5 or 6 moves, making a mental note of which cells were solved. Then I undid my moves back to where I was and inserted the 7, which did end up affecting the same cell (r6c7) in the same manner but in a much more convoluted path. I don't normally use forcing chains (except for xy-wing and colouring) to solve puzzles but it was clear to me that I wouldn't be able to solve this one in my normal manner. Turning off the 'block invalid moves' feels too much like cheating and trying one value in a cell then the other to see if it leads to a contradiction or a confirmation feels too much like guessing. (Jeff, please don't yell at me.) However, I am trying to expand my repetoire(?) so I'll chalk it up to experimentation.

Tracy

[bennys]

r4c1 and r7c7 can't both be 3 at the same time because it eliminate all 3 candidates from box 7

[TKiel]

CathyW,

This is my candidate list for the semi-solved grid in your first post

Code: Select all

 *-----------*
 |4.3|59.|.2.|
 |...|.16|...|
 |7.1|...|9..|
 |---+---+---|
 |..6|.89|5.2|
 |...|3..|8..|
 |2..|6..|...|
 |---+---+---|
 |...|4..|.79|
 |.9.|...|6..|
 |.1.|9..|2..|
 *-----------*

 
 *-----------------------------------------------------------------------------*
 | 4       68      3       | 5       9       78      | 17      2       1678    |
 | 589     258     2589    | 278     1       6       | 347     3458    34578   |
 | 7       2568    1       | 28      34      34      | 9       568     568     |
 |-------------------------+-------------------------+-------------------------|
 | 13      347     6       | 17      8       9       | 5       134     2       |
 | 159     457     59      | 3       2457    12457   | 8       1469    1467    |
 | 2       34578   589     | 6       457     1457    | 1347    1349    1347    |
 |-------------------------+-------------------------+-------------------------|
 | 3568    2358    258     | 4       356     1358    | 13      7       9       |
 | 358     9       47      | 178     2357    123578  | 6       13458   13458   |
 | 3568    1       47      | 9       3567    3578    | 2       3458    3458    |
 *-----------------------------------------------------------------------------*


Even though all of our solved cells are the same, your candidate list is different. For example, mine has r1c9=1678, yours has r1c9=16. I'm tryinig to figure out how you made some of those exclusions.

bennys--Your solution was much more elegant than mine.

Tracy

[bennys]

Thanks

[CathyW]

r4c1 and r7c7 can't both be 3 at the same time because it eliminate all 3 candidates from box 7

Don't know why I couldn't see that yesterday

Tracy - I'll check back on the exclusions I made and post again later. Can't remember at the moment and got to go to work shortly.

[CathyW]

Code: Select all

  *-----------------------------------------------------------------------------*
 | 4       68      3       | 5       9       78      | 17      2       1678    |
 | 589     258     2589    | 278     1       6       | 347     3458    34578   |
 | 7       2568    1       | 28      34      34      | 9       568     568     |
 |-------------------------+-------------------------+-------------------------|
 | 13      347     6       | 17      8       9       | 5       134     2       |
 | 159     457     59      | 3       2457    12457   | 8       1469    1467    |
 | 2       34578   589     | 6       457     1457    | 1347    1349    1347    |
 |-------------------------+-------------------------+-------------------------|
 | 3568    2358    258     | 4       356     1358    | 13      7       9       |
 | 358     9       47      | 178     2357    123578  | 6       13458   13458   |
 | 3568    1       47      | 9       3567    3578    | 2       3458    3458    |
 *-----------------------------------------------------------------------------*


Even though all of our solved cells are the same, your candidate list is different. For example, mine has r1c9=1678, yours has r1c9=16.

Looking at row 1:
[r1c7]=7=[r1c6]=8=[r1c2]-6-[r1c9]=1=[r1c7] permitting elimination of 7 and 8 in r1c9.

I had also reduced candidates as follows.
Colouring conjugate 1s enables elimination of 1s in r4c8 and r6c7.
row 4: [r4c1]-3-[r4c8]=4=[r4c2]=7=[r4c4]=1=[r4c1]. Eliminate 3 at r4c2.

Can't see now how I managed the other exclusions in box 6. Happy coincidences maybe