The New Sudoku Players' Forum

[vibes1234]

is it possible to continue this using only logic ? if yes, then i would appreciate it if anyone could explain the steps involved. thanx !!

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

[Jeff]

is it possible to continue this using only logic ?

If you believe that forcing chain is a logical approach, then the answer is yes. My solution to this puzzle involves two forcing chains. Having applied basic techniques, the grid reduced to:

Code: Select all

{46}     {46}     {7}      {1}      {9}      {5}      {3}      {8}      {2}     
{19}     {25}     {3}      {2678}   {28}     {678}    {1459}   {1579}   {467}   
{19}     {8}      {25}     {2367}   {4}      {367}    {159}    {1579}   {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}     
{5}      {1}      {4}      {9}      {7}      {2}      {6}      {3}      {8}

First chain:
r2c2=5 => r5c2<>5
r2c2=2 => r2c5<>2 => r6c5=2 => r5c4=5 => r5c2<>5
Therefore r5c2<>5 => r5c2=9

The grid can then be reduced to:

Code: Select all

{46}  {46}  {7}   {1}   {9}   {5}   {3}   {8}   {2}   
{19}  {5}   {3}   {678} {2}   {678} {149} {179} {467}
{19}  {8}   {2}   {367} {4}   {367} {5}   {19}  {67} 
{2}   {47}  {5}   {467} {8}   {9}   {14}  {167} {3}   
{47}  {9}   {6}   {2}   {3}   {1}   {8}   {5}   {47} 
{8}   {3}   {1}   {467} {5}   {467} {24}  {267} {9}   
{37}  {27}  {89}  {5}   {6}   {38}  {29}  {4}   {1}   
{36}  {26}  {89}  {348} {1}   {348} {7}   {29}  {5}   
{5}   {1}   {4}   {9}   {7}   {2}   {6}   {3}   {8}   

From here, the puzzle can be solved by the unique solution rule or by a second chain. Before I list my second chain, would you like to have a go first?

[Jeff]

Here is the second chain.

r5c1=4 => r5c9<>4
r5c1=7 => r4c2=4 => r7c2=7 => r7c7=2 => r6c7=4 => r5c9<>4
Therefore r5c9<>4 => r5c9=7

It's quite a long chain. Can anyone suggest a shorter one?

[Jeff]

vibes1234, are you sleeping peacefully Z Z Z Z Z

[Nick70]

First chain:

r2c5=2 => r2c2<>2 => r2c2=5 => r5c2<>5 => r5c2=9
r6c5=2 => r5c4<>2 => r5c4=5 => r5c2<>5 => r5c2=9


Second chain:

r4c2=7 => r7c2<>7 => r7c2=2 => r7c7<>2 => r6c7=2
r4c2=4 => r5c1<>4 => r5c9=4 => r6c7<>4 => r6c7=2

[Jeff]

Hi Nick, nice to know that I am not alone.

[vibes1234]

hi jeff,
thanx a lot for the suggestion. however i was not sleeping as u conveniently assumed. my net connection had gone for a toss and was trying to get it sorted. thats the reason for the delay. thanx anyway.

[vibes1234]

hey jeff,
thanx a lot for the forcing chain approach. was not aware of it before. it took some time for me to understand the approach at first, however i found it pretty convincing that it is NOT trial and error or guesswork. it is actually elimination by logic. cannot thank you enough for explaining this technique to me. cant wait to try out nicks forcing chain though. although could u tell me what is the basis for choosing a particular cell to start the chain ? i am unclear about that.
vibes

[Jeff]

.... however i found it pretty convincing that it is NOT trial and error or guesswork. it is actually elimination by logic. .......although could u tell me what is the basis for choosing a particular cell to start the chain ? i am unclear about that.

Nice to know that you are so easily convinced. Indeed, forcing chain is a logical approach. However, it remains logical as long as you don't use a trial & error method to find it. One of the processes for finding a forcing chain involves construction of a combined bilocation/bivalue plot, followed by the recognition of a nice loop. Implications can start from any cell within the loop except the final cell where inclusion or exclusion will be made. Refer Eppstein's paper here.

I know some folks identify forcing chains by entering each candidate of a starting cell into a computer solver, and then compare the output results for any single cell which is reduced to an identical single value. This single value cell is then routed back to the starting cell to obtain the forcing chain. Forcing chains that are identified in this manner, whether they are computer aided or manually performed, should be regarded as T & E in my dictionary.