The New Sudoku Players' Forum

[udosuk]

Can anyone solve this puzzle with singles, boxlines, subsets and one advanced move?
(Uniqueness assumption acceptable but not preferred.)

Original puzzle:

Code: Select all

 *-----------*
 |2..|.6.|...|
 |..4|3..|...|
 |.63|.4.|29.|
 |---+---+---|
 |69.|..4|...|
 |.41|.8.|73.|
 |...|1..|.42|
 |---+---+---|
 |.78|.2.|46.|
 |...|..8|5..|
 |...|.7.|..1|
 *-----------*

After singles, boxlines, subsets:

Code: Select all

 *-----------------------------------------------------------*
 | 2     158   59    | 589   6     1579  | 3     1578  4     |
 | 1789  158   4     | 3     159   2     | 168   1578  5678  |
 | 178   6     3     | 58    4     157   | 2     9     578   |
 |-------------------+-------------------+-------------------|
 | 6     9     2     | 7     3     4     | 18    158   58    |
 | 5     4     1     | 2     8     69    | 7     3     69    |
 | 38    38    7     | 1     59    569   | 69    4     2     |
 |-------------------+-------------------+-------------------|
 | 139   7     8     | 59    2     1359  | 4     6     39    |
 | 1349  123   69    | 46    19    8     | 5     27    379   |
 | 349   235   569   | 46    7     39    | 89    28    1     |
 *-----------------------------------------------------------*

[tarek]

I tried,

The best (sort of advanced move) allowed me to eliminate 4 in r9c4....but still not enough

tarek

[udosuk]

tarek, thanks for having a go!

I have studied it for quite a while and all I could found were ugly (inelegant) moves, such as:

Code: Select all

 *-----------------------------------------------------------*
 | 2     158   59    | 589   6     1579  | 3     1578  4     |
 | 1789  158   4     | 3     159   2     | 168   1578  5678  |
 | 178   6     3     | 58    4     157   | 2     9     578   |
 |-------------------+-------------------+-------------------|
 | 6     9     2     | 7     3     4     | 18    158   58    |
 | 5     4     1     | 2     8     69    | 7     3     69    |
 | 38    38    7     | 1     59    569   | 69    4     2     |
 |-------------------+-------------------+-------------------|
 | 139   7     8     | 59    2     1359  | 4     6     39    |
 | 1349  123   69    | 46    19    8     | 5     27    379   |
 | 349   235   569   | 46    7     39    | 89    28    1     |
 *-----------------------------------------------------------*

r9c8=2 => r9c7=8 => r6c7=9 => r6c5=5 => r5c6=9 => r9c6=3 => r9c2=5 => r12c2={18} => r3c1=7 => r2c1=9 => r2c5=1 => Invalid (no 1 on r3)

Therefore r9c8<>2 and singles then solve the rest.

I surely hope there can be much prettier chains...

[Steve R]

Eliminating 5 from r9c2 also solves the puzzle in singles:

r2c5 -1- r3c6 =1= r3c1 -1- {r1c2, r2c2} -5- r9c2
r2c5 -5- r6c5 -9- r6c7 =9= r9c7 =8= r9c8 =2= r9c2
r2c5 -9- r2c1 =9= r1c3 =5= r9c3 -5- r9c2

but raises the question of whether a compound nice loop is sufficiently elegant to be acceptable..

Steve

[daj95376]

My results.

Code: Select all

r1c3    =  9     [r1c3]<>5          ugly chain/net using singles only
r1c3    =  9     backdoor single

r3c4    =  5     backdoor single

r4c7    =  8     backdoor single

r5c6    =  6     [r5c6]<>9          ugly chain/net using singles only
r5c6    =  6     backdoor single

r5c9    =  9     [r5c9]<>6          ugly chain/net using singles only
r5c9    =  9     backdoor single

r6c7    =  6     [r6c7]<>9          ugly chain/net using singles only
r6c7    =  6     backdoor single

r7c4    =  9     [r7c4]<>5          ugly chain/net using singles only
r7c4    =  9     backdoor single

r8c8    =  2     [r8c8]<>7          ugly chain/net using singles only
r8c8    =  2     backdoor single

r9c7    =  9     [r9c7]<>8          ugly chain/net using singles only
r9c7    =  9     backdoor single

r9c8    =  8     [r9c8]<>2          ugly chain/net using singles only
r9c8    =  8     backdoor single


[udosuk]

Thanks for the replies, guys...

daj95376's results confirmed what I saw - no bivalue cell gives us a clear-cut "critical elimination" (i.e. one value lead to a short contradiction chain, another lead to solution through singles). I keep hoping people can find an explosive ALS or a monster fish to blow this thing apart...

Also thanks for Steve's solution, I suppose it's more elegant than the one I offered, but still too heavy a taste of T&E there...